%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN784-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:40:01 AM UTC 2025
% Result : Unsatisfiable 0.46s 0.67s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN784-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:44:37 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.46/0.67 % SZS status Unsatisfiable
% 0.46/0.67 % SZS output start Proof
% 0.46/0.67 tff(ssPv3_type, type, (
% 0.46/0.67 ssPv3: $i > $o)).
% 0.46/0.67 tff(skf2_type, type, (
% 0.46/0.67 skf2: $i > $i)).
% 0.46/0.67 tff(elem_0_type, type, (
% 0.46/0.67 elem_0: $i)).
% 0.46/0.67 tff(ssPv1_type, type, (
% 0.46/0.67 ssPv1: $i > $o)).
% 0.46/0.67 tff(ssPv4_type, type, (
% 0.46/0.67 ssPv4: $i > $o)).
% 0.46/0.67 tff(ssPv2_type, type, (
% 0.46/0.67 ssPv2: $i > $o)).
% 0.46/0.67 tff(skf3_type, type, (
% 0.46/0.67 skf3: $i > $i)).
% 0.46/0.67 tff(ssRr_type, type, (
% 0.46/0.67 ssRr: ( $i * $i ) > $o)).
% 0.46/0.67 tff(1,assumption,(~ssPv3(skf2(elem!0))), introduced(assumption)).
% 0.46/0.67 tff(2,assumption,(~ssPv4(skf2(elem!0))), introduced(assumption)).
% 0.46/0.67 tff(3,assumption,(~ssPv4(elem!0)), introduced(assumption)).
% 0.46/0.67 tff(4,assumption,(~ssPv2(elem!0)), introduced(assumption)).
% 0.46/0.67 tff(5,assumption,(~ssPv3(elem!0)), introduced(assumption)).
% 0.46/0.67 tff(6,plain,
% 0.46/0.67 (^[U: $i] : refl(ssRr(skf3(U), U) <=> ssRr(skf3(U), U))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(7,plain,
% 0.46/0.67 (![U: $i] : ssRr(skf3(U), U) <=> ![U: $i] : ssRr(skf3(U), U)),
% 0.46/0.67 inference(quant_intro,[status(thm)],[6])).
% 0.46/0.67 tff(8,plain,
% 0.46/0.67 (![U: $i] : ssRr(skf3(U), U) <=> ![U: $i] : ssRr(skf3(U), U)),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(9,axiom,(![U: $i] : ssRr(skf3(U), U)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.46/0.67 tff(10,plain,
% 0.46/0.67 (![U: $i] : ssRr(skf3(U), U)),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.46/0.67 tff(11,plain,(
% 0.46/0.67 ![U: $i] : ssRr(skf3(U), U)),
% 0.46/0.67 inference(skolemize,[status(sab)],[10])).
% 0.46/0.67 tff(12,plain,
% 0.46/0.67 (![U: $i] : ssRr(skf3(U), U)),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.46/0.67 tff(13,plain,
% 0.46/0.67 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(elem!0), elem!0)),
% 0.46/0.67 inference(quant_inst,[status(thm)],[])).
% 0.46/0.67 tff(14,plain,
% 0.46/0.67 (ssRr(skf3(elem!0), elem!0)),
% 0.46/0.67 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.46/0.67 tff(15,plain,
% 0.46/0.67 (^[V: $i, U: $i] : refl((ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) <=> (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(16,plain,
% 0.46/0.67 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.46/0.67 inference(quant_intro,[status(thm)],[15])).
% 0.46/0.67 tff(17,plain,
% 0.46/0.67 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(18,plain,
% 0.46/0.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) <=> ((ssPv4(U) | (~ssRr(U, V))) | ssPv2(V)))), rewrite(((ssPv4(U) | (~ssRr(U, V))) | ssPv2(V)) <=> (ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) <=> (ssPv2(V) | ssPv4(U) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) <=> ((ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) | ssPv3(V)))), rewrite(((ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) | ssPv3(V)) <=> (ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) <=> (ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) | ssPv4(V)) <=> ((ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) | ssPv4(V)))), rewrite(((ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) | ssPv4(V)) <=> (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) | ssPv4(V)) <=> (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(19,plain,
% 0.46/0.67 (![V: $i, U: $i] : (((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) | ssPv4(V)) <=> ![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.46/0.67 inference(quant_intro,[status(thm)],[18])).
% 0.46/0.67 tff(20,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.46/0.67 tff(21,plain,
% 0.46/0.67 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.46/0.67 tff(22,plain,
% 0.46/0.67 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.46/0.67 tff(23,plain,(
% 0.46/0.67 ![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.46/0.67 inference(skolemize,[status(sab)],[22])).
% 0.46/0.67 tff(24,plain,
% 0.46/0.67 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.46/0.67 tff(25,plain,
% 0.46/0.67 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv2(elem!0) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(26,plain,
% 0.46/0.67 ((ssPv4(elem!0) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> (ssPv2(elem!0) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(27,plain,
% 0.46/0.67 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv2(elem!0) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))))),
% 0.46/0.67 inference(monotonicity,[status(thm)],[26])).
% 0.46/0.67 tff(28,plain,
% 0.46/0.67 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.46/0.67 inference(transitivity,[status(thm)],[27, 25])).
% 0.46/0.67 tff(29,plain,
% 0.46/0.67 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.46/0.67 inference(quant_inst,[status(thm)],[])).
% 0.46/0.67 tff(30,plain,
% 0.46/0.67 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.46/0.67 tff(31,plain,
% 0.46/0.67 (ssPv2(elem!0) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0))),
% 0.46/0.67 inference(unit_resolution,[status(thm)],[30, 24, 14])).
% 0.46/0.67 tff(32,plain,
% 0.46/0.67 (ssPv4(skf3(elem!0))),
% 0.46/0.67 inference(unit_resolution,[status(thm)],[31, 3, 4, 5])).
% 0.46/0.67 tff(33,plain,
% 0.46/0.67 (^[U: $i] : refl(ssRr(U, skf2(U)) <=> ssRr(U, skf2(U)))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(34,plain,
% 0.46/0.67 (![U: $i] : ssRr(U, skf2(U)) <=> ![U: $i] : ssRr(U, skf2(U))),
% 0.46/0.67 inference(quant_intro,[status(thm)],[33])).
% 0.46/0.67 tff(35,plain,
% 0.46/0.67 (![U: $i] : ssRr(U, skf2(U)) <=> ![U: $i] : ssRr(U, skf2(U))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(36,axiom,(![U: $i] : ssRr(U, skf2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.46/0.67 tff(37,plain,
% 0.46/0.67 (![U: $i] : ssRr(U, skf2(U))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.46/0.67 tff(38,plain,(
% 0.46/0.67 ![U: $i] : ssRr(U, skf2(U))),
% 0.46/0.67 inference(skolemize,[status(sab)],[37])).
% 0.46/0.67 tff(39,plain,
% 0.46/0.67 (![U: $i] : ssRr(U, skf2(U))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.46/0.67 tff(40,plain,
% 0.46/0.67 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(elem!0, skf2(elem!0))),
% 0.46/0.67 inference(quant_inst,[status(thm)],[])).
% 0.46/0.67 tff(41,plain,
% 0.46/0.67 (ssRr(elem!0, skf2(elem!0))),
% 0.46/0.67 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.46/0.67 tff(42,plain,
% 0.46/0.67 (^[W: $i, V: $i, U: $i] : refl((ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(43,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.46/0.67 inference(quant_intro,[status(thm)],[42])).
% 0.46/0.67 tff(44,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(45,plain,
% 0.46/0.67 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(V)) <=> ((ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv4(V)))), rewrite(((ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv4(V)) <=> (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(V)) <=> (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(46,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.46/0.67 inference(quant_intro,[status(thm)],[45])).
% 0.46/0.67 tff(47,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause19')).
% 0.46/0.67 tff(48,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.46/0.67 tff(49,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.46/0.67 tff(50,plain,(
% 0.46/0.67 ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.46/0.67 inference(skolemize,[status(sab)],[49])).
% 0.46/0.67 tff(51,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.46/0.67 tff(52,plain,
% 0.46/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(53,plain,
% 0.46/0.67 ((ssPv4(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0)))) <=> (ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(54,plain,
% 0.46/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0)))))),
% 0.46/0.67 inference(monotonicity,[status(thm)],[53])).
% 0.46/0.67 tff(55,plain,
% 0.46/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.46/0.67 inference(transitivity,[status(thm)],[54, 52])).
% 0.46/0.67 tff(56,plain,
% 0.46/0.67 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.46/0.67 inference(quant_inst,[status(thm)],[])).
% 0.46/0.67 tff(57,plain,
% 0.46/0.67 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.46/0.67 tff(58,plain,
% 0.46/0.67 (ssPv2(elem!0) | ssPv4(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0)))),
% 0.46/0.67 inference(unit_resolution,[status(thm)],[57, 51, 14, 41])).
% 0.46/0.67 tff(59,plain,
% 0.46/0.67 (~ssPv3(skf2(elem!0))),
% 0.46/0.67 inference(unit_resolution,[status(thm)],[58, 32, 4, 3])).
% 0.46/0.67 tff(60,plain,
% 0.46/0.67 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(61,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.46/0.67 inference(quant_intro,[status(thm)],[60])).
% 0.46/0.67 tff(62,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(63,plain,
% 0.46/0.67 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(W, V))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(W, V))) | ssPv3(U)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) <=> (((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(W, V))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(W, V))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) | ssPv3(V)) <=> (((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(64,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.46/0.67 inference(quant_intro,[status(thm)],[63])).
% 0.46/0.67 tff(65,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause10')).
% 0.46/0.67 tff(66,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.46/0.67 tff(67,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.46/0.67 tff(68,plain,(
% 0.46/0.67 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.46/0.67 inference(skolemize,[status(sab)],[67])).
% 0.46/0.67 tff(69,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.46/0.67 tff(70,plain,
% 0.46/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(71,plain,
% 0.46/0.67 ((ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(72,plain,
% 0.46/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))))),
% 0.46/0.67 inference(monotonicity,[status(thm)],[71])).
% 0.46/0.67 tff(73,plain,
% 0.46/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.46/0.67 inference(transitivity,[status(thm)],[72, 70])).
% 0.46/0.67 tff(74,plain,
% 0.46/0.67 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.46/0.67 inference(quant_inst,[status(thm)],[])).
% 0.46/0.67 tff(75,plain,
% 0.46/0.67 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.46/0.67 tff(76,plain,
% 0.46/0.67 (ssPv2(elem!0) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.46/0.67 inference(unit_resolution,[status(thm)],[75, 69, 41])).
% 0.46/0.67 tff(77,plain,
% 0.46/0.67 (~ssPv2(skf2(elem!0))),
% 0.46/0.67 inference(unit_resolution,[status(thm)],[76, 59, 4, 5])).
% 0.46/0.67 tff(78,plain,
% 0.46/0.67 (^[W: $i, V: $i, U: $i] : refl((ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) <=> (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(79,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.46/0.67 inference(quant_intro,[status(thm)],[78])).
% 0.46/0.67 tff(80,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.46/0.67 inference(rewrite,[status(thm)],[])).
% 0.46/0.67 tff(81,plain,
% 0.46/0.67 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(U, V)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) <=> ((ssPv4(V) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)))), rewrite(((ssPv4(V) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv3(W) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv3(W) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) <=> ((ssPv4(V) | (~ssRr(U, V)) | ssPv3(W) | (~ssRr(U, W))) | ssPv3(U)))), rewrite(((ssPv4(V) | (~ssRr(U, V)) | ssPv3(W) | (~ssRr(U, W))) | ssPv3(U)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv4(V) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) | ssPv4(U)))), rewrite(((ssPv4(V) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) | ssPv4(U)) <=> (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))))),
% 0.46/0.67 inference(bind,[status(th)],[])).
% 0.46/0.67 tff(82,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.46/0.67 inference(quant_intro,[status(thm)],[81])).
% 0.46/0.67 tff(83,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.46/0.67 tff(84,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.46/0.67 tff(85,plain,
% 0.46/0.67 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.46/0.67 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.46/0.68 tff(86,plain,(
% 0.46/0.68 ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.46/0.68 inference(skolemize,[status(sab)],[85])).
% 0.46/0.68 tff(87,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.46/0.68 tff(88,plain,
% 0.46/0.68 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(89,plain,
% 0.46/0.68 ((ssPv4(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(90,plain,
% 0.46/0.68 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0))))),
% 0.46/0.68 inference(monotonicity,[status(thm)],[89])).
% 0.46/0.68 tff(91,plain,
% 0.46/0.68 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.68 inference(transitivity,[status(thm)],[90, 88])).
% 0.46/0.68 tff(92,plain,
% 0.46/0.68 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
% 0.46/0.68 tff(93,plain,
% 0.46/0.68 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.46/0.68 tff(94,plain,
% 0.46/0.68 (ssPv4(elem!0) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[93, 87, 41])).
% 0.46/0.68 tff(95,plain,
% 0.46/0.68 (ssPv4(skf2(elem!0))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[94, 59, 5, 3])).
% 0.46/0.68 tff(96,plain,
% 0.46/0.68 (^[V: $i, U: $i] : refl((ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) <=> (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))))),
% 0.46/0.68 inference(bind,[status(th)],[])).
% 0.46/0.68 tff(97,plain,
% 0.46/0.68 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.46/0.68 inference(quant_intro,[status(thm)],[96])).
% 0.46/0.68 tff(98,plain,
% 0.46/0.68 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(99,plain,
% 0.46/0.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) | ssPv3(V)) <=> ((ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv3(V)))), rewrite(((ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv3(V)) <=> (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) | ssPv3(V)) <=> (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))))),
% 0.46/0.68 inference(bind,[status(th)],[])).
% 0.46/0.68 tff(100,plain,
% 0.46/0.68 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) | ssPv3(V)) <=> ![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.46/0.68 inference(quant_intro,[status(thm)],[99])).
% 0.46/0.68 tff(101,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.46/0.68 tff(102,plain,
% 0.46/0.68 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.46/0.68 tff(103,plain,
% 0.46/0.68 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.46/0.68 tff(104,plain,(
% 0.46/0.68 ![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.46/0.68 inference(skolemize,[status(sab)],[103])).
% 0.46/0.68 tff(105,plain,
% 0.46/0.68 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.46/0.68 tff(106,plain,
% 0.46/0.68 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(107,plain,
% 0.46/0.68 ((ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))) <=> (ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(108,plain,
% 0.46/0.68 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))))),
% 0.46/0.68 inference(monotonicity,[status(thm)],[107])).
% 0.46/0.68 tff(109,plain,
% 0.46/0.68 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.46/0.68 inference(transitivity,[status(thm)],[108, 106])).
% 0.46/0.68 tff(110,plain,
% 0.46/0.68 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
% 0.46/0.68 tff(111,plain,
% 0.46/0.68 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.46/0.68 tff(112,plain,
% 0.46/0.68 (ssPv2(elem!0) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[111, 105, 41])).
% 0.46/0.68 tff(113,plain,
% 0.46/0.68 ($false),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[112, 95, 77, 4, 59])).
% 0.46/0.68 tff(114,plain,(ssPv4(elem!0) | ssPv2(elem!0) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.68 tff(115,plain,
% 0.46/0.68 (ssPv4(elem!0)),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[114, 5, 4])).
% 0.46/0.68 tff(116,plain,
% 0.46/0.68 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(117,plain,
% 0.46/0.68 ((ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0))) <=> (ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(118,plain,
% 0.46/0.68 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0))))),
% 0.46/0.68 inference(monotonicity,[status(thm)],[117])).
% 0.46/0.68 tff(119,plain,
% 0.46/0.68 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(transitivity,[status(thm)],[118, 116])).
% 0.46/0.68 tff(120,plain,
% 0.46/0.68 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
% 0.46/0.68 tff(121,plain,
% 0.46/0.68 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.46/0.68 tff(122,plain,
% 0.46/0.68 (ssPv2(elem!0) | ssPv3(elem!0) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[121, 105, 14])).
% 0.46/0.68 tff(123,plain,
% 0.46/0.68 (ssPv2(skf3(elem!0))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[122, 115, 4, 5])).
% 0.46/0.68 tff(124,assumption,(~ssPv3(skf3(elem!0))), introduced(assumption)).
% 0.46/0.68 tff(125,plain,
% 0.46/0.68 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))))),
% 0.46/0.68 inference(bind,[status(th)],[])).
% 0.46/0.68 tff(126,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.46/0.68 inference(quant_intro,[status(thm)],[125])).
% 0.46/0.68 tff(127,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(128,plain,
% 0.46/0.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) | ssPv3(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) | ssPv3(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))))),
% 0.46/0.68 inference(bind,[status(th)],[])).
% 0.46/0.68 tff(129,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.46/0.68 inference(quant_intro,[status(thm)],[128])).
% 0.46/0.68 tff(130,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause16')).
% 0.46/0.68 tff(131,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.46/0.68 tff(132,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.46/0.68 tff(133,plain,(
% 0.46/0.68 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.46/0.68 inference(skolemize,[status(sab)],[132])).
% 0.46/0.68 tff(134,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.46/0.68 tff(135,plain,
% 0.46/0.68 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(136,plain,
% 0.46/0.68 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(skf3(elem!0)))) <=> (ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(137,plain,
% 0.46/0.68 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0))))),
% 0.46/0.68 inference(monotonicity,[status(thm)],[136])).
% 0.46/0.68 tff(138,plain,
% 0.46/0.68 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(transitivity,[status(thm)],[137, 135])).
% 0.46/0.68 tff(139,plain,
% 0.46/0.68 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(skf3(elem!0))))),
% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
% 0.46/0.68 tff(140,plain,
% 0.46/0.68 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.46/0.68 tff(141,plain,
% 0.46/0.68 (ssPv1(elem!0) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[140, 134, 14])).
% 0.46/0.68 tff(142,plain,
% 0.46/0.68 (ssPv1(elem!0)),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[141, 124, 115, 123])).
% 0.46/0.68 tff(143,plain,
% 0.46/0.68 (^[W: $i, V: $i, U: $i] : refl((ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))))),
% 0.46/0.68 inference(bind,[status(th)],[])).
% 0.46/0.68 tff(144,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.46/0.68 inference(quant_intro,[status(thm)],[143])).
% 0.46/0.68 tff(145,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(146,plain,
% 0.46/0.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) <=> (((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(U)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(U))))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(U))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(U))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(W, V)) | (~ssPv1(U)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(W, V)) | (~ssPv1(U))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(W, V)) | (~ssPv1(U))) | ssPv3(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(W, V)) | (~ssPv1(U))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) | ssPv2(V)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))))),
% 0.46/0.68 inference(bind,[status(th)],[])).
% 0.46/0.68 tff(147,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.46/0.68 inference(quant_intro,[status(thm)],[146])).
% 0.46/0.68 tff(148,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause18')).
% 0.46/0.68 tff(149,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.46/0.68 tff(150,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.46/0.68 tff(151,plain,(
% 0.46/0.68 ![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.46/0.68 inference(skolemize,[status(sab)],[150])).
% 0.46/0.68 tff(152,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.46/0.68 tff(153,plain,
% 0.46/0.68 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(154,plain,
% 0.46/0.68 ((ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0)))) <=> (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(155,plain,
% 0.46/0.68 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0))))),
% 0.46/0.68 inference(monotonicity,[status(thm)],[154])).
% 0.46/0.68 tff(156,plain,
% 0.46/0.68 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.68 inference(transitivity,[status(thm)],[155, 153])).
% 0.46/0.68 tff(157,plain,
% 0.46/0.68 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
% 0.46/0.68 tff(158,plain,
% 0.46/0.68 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.46/0.68 tff(159,plain,
% 0.46/0.68 (ssPv2(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[158, 152, 14])).
% 0.46/0.68 tff(160,plain,
% 0.46/0.68 (~ssPv1(skf3(elem!0))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[159, 124, 4, 115])).
% 0.46/0.68 tff(161,plain,
% 0.46/0.68 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))),
% 0.46/0.68 inference(bind,[status(th)],[])).
% 0.46/0.68 tff(162,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.46/0.68 inference(quant_intro,[status(thm)],[161])).
% 0.46/0.68 tff(163,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(164,plain,
% 0.46/0.68 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv4(W)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) <=> ((ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv2(X)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv2(X)) <=> (ssPv2(X) | ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) <=> (ssPv2(X) | ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) | ssPv3(V)) <=> ((ssPv2(X) | ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(V)))), rewrite(((ssPv2(X) | ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(V)) <=> (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) | ssPv3(V)) <=> (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))))),
% 0.46/0.68 inference(bind,[status(th)],[])).
% 0.46/0.68 tff(165,plain,
% 0.46/0.68 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.46/0.69 inference(quant_intro,[status(thm)],[164])).
% 0.46/0.69 tff(166,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause27')).
% 0.46/0.69 tff(167,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.46/0.69 tff(168,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.46/0.69 tff(169,plain,(
% 0.46/0.69 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.46/0.69 inference(skolemize,[status(sab)],[168])).
% 0.46/0.69 tff(170,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.46/0.69 tff(171,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(172,plain,
% 0.46/0.69 ((ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(173,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0))))),
% 0.46/0.69 inference(monotonicity,[status(thm)],[172])).
% 0.46/0.69 tff(174,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.69 inference(transitivity,[status(thm)],[173, 171])).
% 0.46/0.69 tff(175,plain,
% 0.46/0.69 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(176,plain,
% 0.46/0.69 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.46/0.69 tff(177,plain,
% 0.46/0.69 (ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[176, 170, 14, 41])).
% 0.46/0.69 tff(178,plain,
% 0.46/0.69 (ssPv2(skf2(elem!0))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[177, 160, 5, 2])).
% 0.46/0.69 tff(179,plain,
% 0.46/0.69 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))))),
% 0.46/0.69 inference(bind,[status(th)],[])).
% 0.46/0.69 tff(180,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.46/0.69 inference(quant_intro,[status(thm)],[179])).
% 0.46/0.69 tff(181,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(182,plain,
% 0.46/0.69 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) | ssPv3(U)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv3(U)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))))),
% 0.46/0.69 inference(bind,[status(th)],[])).
% 0.46/0.69 tff(183,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.46/0.69 inference(quant_intro,[status(thm)],[182])).
% 0.46/0.69 tff(184,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 0.46/0.69 tff(185,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.46/0.69 tff(186,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.46/0.69 tff(187,plain,(
% 0.46/0.69 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.46/0.69 inference(skolemize,[status(sab)],[186])).
% 0.46/0.69 tff(188,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.46/0.69 tff(189,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(190,plain,
% 0.46/0.69 (((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0))) <=> ((~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(191,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0))))),
% 0.46/0.69 inference(monotonicity,[status(thm)],[190])).
% 0.46/0.69 tff(192,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.46/0.69 inference(transitivity,[status(thm)],[191, 189])).
% 0.46/0.69 tff(193,plain,
% 0.46/0.69 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)))),
% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(194,plain,
% 0.46/0.69 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.46/0.69 tff(195,plain,
% 0.46/0.69 ((~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[194, 188, 41])).
% 0.46/0.69 tff(196,plain,
% 0.46/0.69 ($false),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[195, 178, 142, 5, 2])).
% 0.46/0.69 tff(197,plain,(ssPv3(skf3(elem!0)) | ssPv3(elem!0) | ssPv4(skf2(elem!0)) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.69 tff(198,plain,
% 0.46/0.69 (ssPv3(skf3(elem!0))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[197, 5, 2, 4])).
% 0.46/0.69 tff(199,plain,
% 0.46/0.69 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))))),
% 0.46/0.69 inference(bind,[status(th)],[])).
% 0.46/0.69 tff(200,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.46/0.69 inference(quant_intro,[status(thm)],[199])).
% 0.46/0.69 tff(201,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(202,plain,
% 0.46/0.69 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> (((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(W, V))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(V)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))))),
% 0.46/0.69 inference(bind,[status(th)],[])).
% 0.46/0.69 tff(203,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.46/0.69 inference(quant_intro,[status(thm)],[202])).
% 0.46/0.69 tff(204,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause15')).
% 0.46/0.69 tff(205,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.46/0.69 tff(206,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.46/0.69 tff(207,plain,(
% 0.46/0.69 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.46/0.69 inference(skolemize,[status(sab)],[206])).
% 0.46/0.69 tff(208,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.46/0.69 tff(209,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(210,plain,
% 0.46/0.69 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> (ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(211,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0))))),
% 0.46/0.69 inference(monotonicity,[status(thm)],[210])).
% 0.46/0.69 tff(212,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.69 inference(transitivity,[status(thm)],[211, 209])).
% 0.46/0.69 tff(213,plain,
% 0.46/0.69 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(214,plain,
% 0.46/0.69 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.46/0.69 tff(215,plain,
% 0.46/0.69 (ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[214, 208, 14])).
% 0.46/0.69 tff(216,plain,
% 0.46/0.69 (ssPv4(skf3(elem!0))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[215, 198, 5, 115])).
% 0.46/0.69 tff(217,plain,
% 0.46/0.69 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(skf3(elem!0)), skf3(elem!0))),
% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(218,plain,
% 0.46/0.69 (ssRr(skf3(skf3(elem!0)), skf3(elem!0))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[217, 12])).
% 0.46/0.69 tff(219,plain,
% 0.46/0.69 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W)))),
% 0.46/0.69 inference(bind,[status(th)],[])).
% 0.46/0.69 tff(220,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.46/0.69 inference(quant_intro,[status(thm)],[219])).
% 0.46/0.69 tff(221,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(222,plain,
% 0.46/0.69 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, W))) | (~ssPv2(V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(V, W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(V, W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))))),
% 0.46/0.69 inference(bind,[status(th)],[])).
% 0.46/0.69 tff(223,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.46/0.69 inference(quant_intro,[status(thm)],[222])).
% 0.46/0.69 tff(224,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv2(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 0.46/0.69 tff(225,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.46/0.69 tff(226,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.46/0.69 tff(227,plain,(
% 0.46/0.69 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.46/0.69 inference(skolemize,[status(sab)],[226])).
% 0.46/0.69 tff(228,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.46/0.69 tff(229,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(230,plain,
% 0.46/0.69 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0)) <=> (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(231,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.46/0.69 inference(monotonicity,[status(thm)],[230])).
% 0.46/0.69 tff(232,plain,
% 0.46/0.69 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.46/0.69 inference(transitivity,[status(thm)],[231, 229])).
% 0.46/0.69 tff(233,plain,
% 0.46/0.69 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0))),
% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(234,plain,
% 0.46/0.69 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.46/0.69 tff(235,plain,
% 0.46/0.69 (ssPv2(elem!0) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[234, 228, 14, 218])).
% 0.46/0.69 tff(236,plain,
% 0.46/0.69 (~ssPv3(skf3(skf3(elem!0)))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[235, 123, 4, 198])).
% 0.46/0.69 tff(237,plain,
% 0.46/0.69 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.46/0.69 inference(bind,[status(th)],[])).
% 0.46/0.69 tff(238,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.69 inference(quant_intro,[status(thm)],[237])).
% 0.46/0.69 tff(239,plain,
% 0.46/0.69 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(240,plain,
% 0.46/0.69 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv3(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) | ssPv3(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.46/0.70 inference(bind,[status(th)],[])).
% 0.46/0.70 tff(241,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(quant_intro,[status(thm)],[240])).
% 0.46/0.70 tff(242,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 0.46/0.70 tff(243,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.46/0.70 tff(244,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.46/0.70 tff(245,plain,(
% 0.46/0.70 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(skolemize,[status(sab)],[244])).
% 0.46/0.70 tff(246,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[245, 238])).
% 0.46/0.70 tff(247,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(248,plain,
% 0.46/0.70 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(249,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.46/0.70 inference(monotonicity,[status(thm)],[248])).
% 0.46/0.70 tff(250,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.46/0.70 inference(transitivity,[status(thm)],[249, 247])).
% 0.46/0.70 tff(251,plain,
% 0.46/0.70 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(252,plain,
% 0.46/0.70 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.46/0.70 tff(253,plain,
% 0.46/0.70 ((~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv3(skf3(skf3(elem!0)))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[252, 246, 14, 218])).
% 0.46/0.70 tff(254,plain,
% 0.46/0.70 ($false),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[253, 236, 216, 198, 115])).
% 0.46/0.70 tff(255,plain,(ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.70 tff(256,plain,
% 0.46/0.70 (ssPv3(elem!0)),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[255, 2, 4])).
% 0.46/0.70 tff(257,plain,
% 0.46/0.70 (^[W: $i, V: $i, U: $i] : refl((ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))))),
% 0.46/0.70 inference(bind,[status(th)],[])).
% 0.46/0.70 tff(258,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.46/0.70 inference(quant_intro,[status(thm)],[257])).
% 0.46/0.70 tff(259,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(260,plain,
% 0.46/0.70 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | (~ssRr(V, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | (~ssRr(V, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) | ssPv4(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) | ssPv4(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))))),
% 0.46/0.70 inference(bind,[status(th)],[])).
% 0.46/0.70 tff(261,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.46/0.70 inference(quant_intro,[status(thm)],[260])).
% 0.46/0.70 tff(262,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause9')).
% 0.46/0.70 tff(263,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.46/0.70 tff(264,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.46/0.70 tff(265,plain,(
% 0.46/0.70 ![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.46/0.70 inference(skolemize,[status(sab)],[264])).
% 0.46/0.70 tff(266,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.46/0.70 tff(267,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf3(elem!0)) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(268,plain,
% 0.46/0.70 ((ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(269,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf3(elem!0)) | ssPv4(skf2(elem!0))))),
% 0.46/0.70 inference(monotonicity,[status(thm)],[268])).
% 0.46/0.70 tff(270,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.70 inference(transitivity,[status(thm)],[269, 267])).
% 0.46/0.70 tff(271,plain,
% 0.46/0.70 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(272,plain,
% 0.46/0.70 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf3(elem!0)) | ssPv4(skf2(elem!0))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.46/0.70 tff(273,plain,
% 0.46/0.70 (ssPv4(elem!0) | (~ssPv3(elem!0)) | ssPv2(skf3(elem!0)) | ssPv4(skf2(elem!0))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[272, 266, 14, 41])).
% 0.46/0.70 tff(274,plain,
% 0.46/0.70 (ssPv2(skf3(elem!0))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[273, 3, 256, 2])).
% 0.46/0.70 tff(275,assumption,(~ssPv2(skf2(elem!0))), introduced(assumption)).
% 0.46/0.70 tff(276,plain,
% 0.46/0.70 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(277,plain,
% 0.46/0.70 ((ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(278,plain,
% 0.46/0.70 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0))))),
% 0.46/0.70 inference(monotonicity,[status(thm)],[277])).
% 0.46/0.70 tff(279,plain,
% 0.46/0.70 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.46/0.70 inference(transitivity,[status(thm)],[278, 276])).
% 0.46/0.70 tff(280,plain,
% 0.46/0.70 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(281,plain,
% 0.46/0.70 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.46/0.70 tff(282,plain,
% 0.46/0.70 (ssPv4(elem!0) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[281, 24, 41])).
% 0.46/0.70 tff(283,plain,
% 0.46/0.70 (ssPv3(skf2(elem!0))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[282, 275, 2, 3])).
% 0.46/0.70 tff(284,plain,
% 0.46/0.70 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(skf2(elem!0), skf2(skf2(elem!0)))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(285,plain,
% 0.46/0.70 (ssRr(skf2(elem!0), skf2(skf2(elem!0)))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[284, 39])).
% 0.46/0.70 tff(286,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(287,plain,
% 0.46/0.70 ((ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> (ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(288,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.46/0.70 inference(monotonicity,[status(thm)],[287])).
% 0.46/0.70 tff(289,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.46/0.70 inference(transitivity,[status(thm)],[288, 286])).
% 0.46/0.70 tff(290,plain,
% 0.46/0.70 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(291,plain,
% 0.46/0.70 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.46/0.70 tff(292,plain,
% 0.46/0.70 (ssPv2(elem!0) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(skf2(skf2(elem!0)))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[291, 266, 41, 285])).
% 0.46/0.70 tff(293,plain,
% 0.46/0.70 (ssPv4(skf2(skf2(elem!0)))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[292, 283, 4, 2])).
% 0.46/0.70 tff(294,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(295,plain,
% 0.46/0.70 ((ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(296,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.46/0.70 inference(monotonicity,[status(thm)],[295])).
% 0.46/0.70 tff(297,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.46/0.70 inference(transitivity,[status(thm)],[296, 294])).
% 0.46/0.70 tff(298,plain,
% 0.46/0.70 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(299,plain,
% 0.46/0.70 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.46/0.70 tff(300,plain,
% 0.46/0.70 ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[299, 208, 285])).
% 0.46/0.70 tff(301,plain,
% 0.46/0.70 (ssPv3(skf2(skf2(elem!0)))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[300, 293, 2, 283])).
% 0.46/0.70 tff(302,plain,
% 0.46/0.70 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.46/0.70 inference(bind,[status(th)],[])).
% 0.46/0.70 tff(303,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(quant_intro,[status(thm)],[302])).
% 0.46/0.70 tff(304,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(305,plain,
% 0.46/0.70 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv3(X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv3(X))) <=> ((~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> ((~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) <=> (((~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv4(U)))), rewrite((((~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) | ssPv2(V)) <=> ((ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)))), rewrite(((ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) | ssPv2(V)) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.46/0.70 inference(bind,[status(th)],[])).
% 0.46/0.70 tff(306,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(quant_intro,[status(thm)],[305])).
% 0.46/0.70 tff(307,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.46/0.70 tff(308,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.46/0.70 tff(309,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[308, 304])).
% 0.46/0.70 tff(310,plain,(
% 0.46/0.70 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(skolemize,[status(sab)],[309])).
% 0.46/0.70 tff(311,plain,
% 0.46/0.70 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[310, 303])).
% 0.46/0.70 tff(312,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(313,plain,
% 0.46/0.70 ((ssPv4(elem!0) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))) <=> (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(314,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(elem!0) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))))),
% 0.46/0.70 inference(monotonicity,[status(thm)],[313])).
% 0.46/0.70 tff(315,plain,
% 0.46/0.70 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(elem!0) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.70 inference(transitivity,[status(thm)],[314, 312])).
% 0.46/0.70 tff(316,plain,
% 0.46/0.70 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(elem!0) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(317,plain,
% 0.46/0.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.46/0.71 tff(318,plain,
% 0.46/0.71 (ssPv4(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[317, 311, 41, 285])).
% 0.46/0.71 tff(319,plain,
% 0.46/0.71 ($false),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[318, 301, 293, 3, 275])).
% 0.46/0.71 tff(320,plain,(ssPv2(skf2(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0)) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.71 tff(321,plain,
% 0.46/0.71 (ssPv2(skf2(elem!0))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[320, 3, 2, 4])).
% 0.46/0.71 tff(322,plain,
% 0.46/0.71 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) <=> (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))),
% 0.46/0.71 inference(bind,[status(th)],[])).
% 0.46/0.71 tff(323,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.46/0.71 inference(quant_intro,[status(thm)],[322])).
% 0.46/0.71 tff(324,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(325,plain,
% 0.46/0.71 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> (((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssRr(V, X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | ssPv4(X)))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) | ssPv4(V)) <=> ((ssPv4(X) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | ssPv4(V)))), rewrite(((ssPv4(X) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | ssPv4(V)) <=> (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) | ssPv4(V)) <=> (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))))),
% 0.46/0.71 inference(bind,[status(th)],[])).
% 0.46/0.71 tff(326,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.46/0.71 inference(quant_intro,[status(thm)],[325])).
% 0.46/0.71 tff(327,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.46/0.71 tff(328,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.46/0.71 tff(329,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.46/0.71 tff(330,plain,(
% 0.46/0.71 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.46/0.71 inference(skolemize,[status(sab)],[329])).
% 0.46/0.71 tff(331,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[330, 323])).
% 0.46/0.71 tff(332,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(333,plain,
% 0.46/0.71 ((ssPv4(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0)))) <=> (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(334,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0))))),
% 0.46/0.71 inference(monotonicity,[status(thm)],[333])).
% 0.46/0.71 tff(335,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.46/0.71 inference(transitivity,[status(thm)],[334, 332])).
% 0.46/0.71 tff(336,plain,
% 0.46/0.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(337,plain,
% 0.46/0.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.46/0.71 tff(338,plain,
% 0.46/0.71 (ssPv4(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[337, 331, 14, 41])).
% 0.46/0.71 tff(339,plain,
% 0.46/0.71 (~ssPv3(skf3(elem!0))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[338, 321, 3, 2])).
% 0.46/0.71 tff(340,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(341,plain,
% 0.46/0.71 ((ssPv2(elem!0) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> (ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(342,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(elem!0) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0)))))),
% 0.46/0.71 inference(monotonicity,[status(thm)],[341])).
% 0.46/0.71 tff(343,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(elem!0) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.46/0.71 inference(transitivity,[status(thm)],[342, 340])).
% 0.46/0.71 tff(344,plain,
% 0.46/0.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(elem!0) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(345,plain,
% 0.46/0.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv2(elem!0) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.46/0.71 tff(346,plain,
% 0.46/0.71 (ssPv2(elem!0) | ssPv4(elem!0) | ssPv3(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0)))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[345, 170, 14, 218])).
% 0.46/0.71 tff(347,plain,
% 0.46/0.71 (ssPv1(skf3(skf3(elem!0)))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[346, 339, 4, 3])).
% 0.46/0.71 tff(348,plain,
% 0.46/0.71 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) <=> (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))))),
% 0.46/0.71 inference(bind,[status(th)],[])).
% 0.46/0.71 tff(349,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.46/0.71 inference(quant_intro,[status(thm)],[348])).
% 0.46/0.71 tff(350,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(351,plain,
% 0.46/0.71 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) <=> (((~ssPv1(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv1(V))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv1(V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X)) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) | ssPv2(X)))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))))),
% 0.46/0.71 inference(bind,[status(th)],[])).
% 0.46/0.71 tff(352,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.46/0.71 inference(quant_intro,[status(thm)],[351])).
% 0.46/0.71 tff(353,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.46/0.71 tff(354,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.46/0.71 tff(355,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[354, 350])).
% 0.46/0.71 tff(356,plain,(
% 0.46/0.71 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.46/0.71 inference(skolemize,[status(sab)],[355])).
% 0.46/0.71 tff(357,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[356, 349])).
% 0.46/0.71 tff(358,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ssPv2(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(359,plain,
% 0.46/0.71 ((ssPv2(elem!0) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0))) <=> (ssPv2(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(360,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))))),
% 0.46/0.71 inference(monotonicity,[status(thm)],[359])).
% 0.46/0.71 tff(361,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ssPv2(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.46/0.71 inference(transitivity,[status(thm)],[360, 358])).
% 0.46/0.71 tff(362,plain,
% 0.46/0.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(363,plain,
% 0.46/0.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ssPv2(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.46/0.71 tff(364,plain,
% 0.46/0.71 (ssPv2(elem!0) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[363, 357, 14, 218])).
% 0.46/0.71 tff(365,plain,
% 0.46/0.71 (~ssPv1(skf3(elem!0))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[364, 347, 4, 256])).
% 0.46/0.71 tff(366,plain,
% 0.46/0.71 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W))))),
% 0.46/0.71 inference(bind,[status(th)],[])).
% 0.46/0.71 tff(367,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.46/0.71 inference(quant_intro,[status(thm)],[366])).
% 0.46/0.71 tff(368,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(369,plain,
% 0.46/0.71 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssPv4(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> (((~ssPv4(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(W))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssRr(X, V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssRr(X, V))) <=> ((~ssPv4(U)) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) <=> ((~ssPv4(U)) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) <=> (((~ssPv4(U)) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv1(X)))), rewrite((((~ssPv4(U)) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv1(X)) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) | ssPv2(V)) <=> (((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv2(V)))), rewrite((((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv2(V)) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) | ssPv2(V)) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))))),
% 0.46/0.71 inference(bind,[status(th)],[])).
% 0.46/0.71 tff(370,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.46/0.71 inference(quant_intro,[status(thm)],[369])).
% 0.46/0.71 tff(371,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 0.46/0.71 tff(372,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.46/0.71 tff(373,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[372, 368])).
% 0.46/0.71 tff(374,plain,(
% 0.46/0.71 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.46/0.71 inference(skolemize,[status(sab)],[373])).
% 0.46/0.71 tff(375,plain,
% 0.46/0.71 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[374, 367])).
% 0.46/0.71 tff(376,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(377,plain,
% 0.46/0.71 (((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0)))) <=> (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(378,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0))))),
% 0.46/0.71 inference(monotonicity,[status(thm)],[377])).
% 0.46/0.71 tff(379,plain,
% 0.46/0.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)))),
% 0.46/0.72 inference(transitivity,[status(thm)],[378, 376])).
% 0.46/0.72 tff(380,plain,
% 0.46/0.72 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))))),
% 0.46/0.72 inference(quant_inst,[status(thm)],[])).
% 0.46/0.72 tff(381,plain,
% 0.46/0.72 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0))),
% 0.46/0.72 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.46/0.72 tff(382,plain,
% 0.46/0.72 (ssPv2(elem!0) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0))),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[381, 375, 14])).
% 0.46/0.72 tff(383,plain,
% 0.46/0.72 (~ssPv4(skf3(elem!0))),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[382, 365, 4, 274])).
% 0.46/0.72 tff(384,plain,
% 0.46/0.72 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))))),
% 0.46/0.72 inference(bind,[status(th)],[])).
% 0.46/0.72 tff(385,plain,
% 0.46/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.46/0.72 inference(quant_intro,[status(thm)],[384])).
% 0.46/0.72 tff(386,plain,
% 0.46/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(387,plain,
% 0.46/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(388,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[387])).
% 0.56/0.72 tff(389,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 0.56/0.72 tff(390,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.56/0.72 tff(391,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[390, 386])).
% 0.56/0.72 tff(392,plain,(
% 0.56/0.72 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.56/0.72 inference(skolemize,[status(sab)],[391])).
% 0.56/0.72 tff(393,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[392, 385])).
% 0.56/0.72 tff(394,plain,
% 0.56/0.72 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(395,plain,
% 0.56/0.72 ((ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0))))) <=> (ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(396,plain,
% 0.56/0.72 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[395])).
% 0.56/0.72 tff(397,plain,
% 0.56/0.72 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(transitivity,[status(thm)],[396, 394])).
% 0.56/0.72 tff(398,plain,
% 0.56/0.72 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(399,plain,
% 0.56/0.72 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.56/0.72 tff(400,plain,
% 0.56/0.72 (ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[399, 393, 218])).
% 0.56/0.72 tff(401,plain,
% 0.56/0.72 (ssPv4(skf3(skf3(elem!0)))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[400, 383, 274, 347])).
% 0.56/0.72 tff(402,plain,
% 0.56/0.72 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(403,plain,
% 0.56/0.72 (ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[402, 12])).
% 0.56/0.72 tff(404,plain,
% 0.56/0.72 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W)))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(405,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[404])).
% 0.56/0.72 tff(406,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(407,plain,
% 0.56/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(408,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[407])).
% 0.56/0.72 tff(409,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause23')).
% 0.56/0.72 tff(410,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.56/0.72 tff(411,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[410, 406])).
% 0.56/0.72 tff(412,plain,(
% 0.56/0.72 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.56/0.72 inference(skolemize,[status(sab)],[411])).
% 0.56/0.72 tff(413,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[412, 405])).
% 0.56/0.72 tff(414,plain,
% 0.56/0.72 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(415,plain,
% 0.56/0.72 (((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0))) <=> (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(416,plain,
% 0.56/0.72 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0)))))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[415])).
% 0.56/0.72 tff(417,plain,
% 0.56/0.72 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))))),
% 0.56/0.72 inference(transitivity,[status(thm)],[416, 414])).
% 0.56/0.72 tff(418,plain,
% 0.56/0.72 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(419,plain,
% 0.56/0.72 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.56/0.72 tff(420,plain,
% 0.56/0.72 (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[419, 413, 218, 403])).
% 0.56/0.72 tff(421,plain,
% 0.56/0.72 (~ssPv4(skf3(skf3(skf3(elem!0))))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[420, 401, 347, 365])).
% 0.56/0.72 tff(422,plain,
% 0.56/0.72 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V))) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(423,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[422])).
% 0.56/0.72 tff(424,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(425,plain,
% 0.56/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(W, V))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(W, V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) | ssPv2(W)) <=> ((ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))) | ssPv2(W)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(426,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[425])).
% 0.56/0.72 tff(427,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) | ssPv2(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause12')).
% 0.56/0.72 tff(428,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.56/0.72 tff(429,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[428, 424])).
% 0.56/0.72 tff(430,plain,(
% 0.56/0.72 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.56/0.72 inference(skolemize,[status(sab)],[429])).
% 0.56/0.72 tff(431,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[430, 423])).
% 0.56/0.72 tff(432,plain,
% 0.56/0.72 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(433,plain,
% 0.56/0.72 ((ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0))))) <=> ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(434,plain,
% 0.56/0.72 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0))))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[433])).
% 0.56/0.72 tff(435,plain,
% 0.56/0.72 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(transitivity,[status(thm)],[434, 432])).
% 0.56/0.72 tff(436,plain,
% 0.56/0.72 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(437,plain,
% 0.56/0.72 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0))))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.56/0.72 tff(438,plain,
% 0.56/0.72 ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0))))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[437, 431, 403])).
% 0.56/0.72 tff(439,plain,
% 0.56/0.72 (ssPv2(skf3(skf3(skf3(elem!0))))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[438, 401, 347, 421])).
% 0.56/0.72 tff(440,plain,
% 0.56/0.72 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(441,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[440])).
% 0.56/0.72 tff(442,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(443,plain,
% 0.56/0.72 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(U))) <=> ((~ssPv2(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | (~ssPv4(V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | (~ssPv4(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv4(W)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv4(W)) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(X)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(X)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(444,plain,
% 0.56/0.72 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[443])).
% 0.56/0.72 tff(445,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.56/0.73 tff(446,plain,
% 0.56/0.73 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.56/0.73 tff(447,plain,
% 0.56/0.73 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[446, 442])).
% 0.56/0.73 tff(448,plain,(
% 0.56/0.73 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.56/0.73 inference(skolemize,[status(sab)],[447])).
% 0.56/0.73 tff(449,plain,
% 0.56/0.73 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[448, 441])).
% 0.56/0.73 tff(450,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0))))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(451,plain,
% 0.56/0.73 ((ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))) <=> (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0))))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(452,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0)))))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[451])).
% 0.56/0.73 tff(453,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0))))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[452, 450])).
% 0.56/0.73 tff(454,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(455,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.56/0.73 tff(456,plain,
% 0.56/0.73 (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[455, 449, 218, 403])).
% 0.56/0.73 tff(457,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[456, 439, 401, 339, 383])).
% 0.56/0.73 tff(458,plain,(ssPv4(elem!0) | ssPv2(elem!0) | ssPv4(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(459,plain,
% 0.56/0.73 (ssPv4(elem!0)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[458, 2, 4])).
% 0.56/0.73 tff(460,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(461,plain,
% 0.56/0.73 ((ssPv4(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(462,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[461])).
% 0.56/0.73 tff(463,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[462, 460])).
% 0.56/0.73 tff(464,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(465,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.56/0.73 tff(466,plain,
% 0.56/0.73 (ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[465, 51, 41, 285])).
% 0.56/0.73 tff(467,plain,
% 0.56/0.73 (~ssPv3(skf2(skf2(elem!0)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[466, 275, 2, 459])).
% 0.56/0.73 tff(468,assumption,(~ssPv3(skf2(skf2(elem!0)))), introduced(assumption)).
% 0.56/0.73 tff(469,assumption,(ssPv3(skf2(elem!0))), introduced(assumption)).
% 0.56/0.73 tff(470,plain,
% 0.56/0.73 (ssPv4(skf2(skf2(elem!0)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[292, 469, 4, 2])).
% 0.56/0.73 tff(471,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[300, 470, 469, 2, 468])).
% 0.56/0.73 tff(472,plain,((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(473,plain,
% 0.56/0.73 (~ssPv3(skf2(elem!0))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[472, 467, 2, 4])).
% 0.56/0.73 tff(474,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(475,plain,
% 0.56/0.73 ((ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(476,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[475])).
% 0.56/0.73 tff(477,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[476, 474])).
% 0.56/0.73 tff(478,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(479,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.56/0.73 tff(480,plain,
% 0.56/0.73 (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[479, 69, 285])).
% 0.56/0.73 tff(481,plain,
% 0.56/0.73 (~ssPv2(skf2(skf2(elem!0)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[480, 473, 275, 467])).
% 0.56/0.73 tff(482,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(483,plain,
% 0.56/0.73 ((ssPv4(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> (ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(484,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[483])).
% 0.56/0.73 tff(485,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[484, 482])).
% 0.56/0.73 tff(486,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(487,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.56/0.73 tff(488,plain,
% 0.56/0.73 (ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[487, 87, 285])).
% 0.56/0.73 tff(489,plain,
% 0.56/0.73 (ssPv4(skf2(skf2(elem!0)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[488, 473, 2, 467])).
% 0.56/0.73 tff(490,plain,
% 0.56/0.73 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(491,plain,
% 0.56/0.73 ((ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(skf2(elem!0))))) <=> (ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(492,plain,
% 0.56/0.73 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[491])).
% 0.56/0.73 tff(493,plain,
% 0.56/0.73 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[492, 490])).
% 0.56/0.73 tff(494,plain,
% 0.56/0.73 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(495,plain,
% 0.56/0.73 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.56/0.73 tff(496,plain,
% 0.56/0.73 (ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[495, 105, 285])).
% 0.56/0.73 tff(497,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[496, 489, 481, 275, 467])).
% 0.56/0.73 tff(498,plain,(ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(499,plain,
% 0.56/0.73 (ssPv2(skf2(elem!0))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[498, 2, 4])).
% 0.56/0.73 tff(500,assumption,(~ssPv2(skf3(elem!0))), introduced(assumption)).
% 0.56/0.73 tff(501,assumption,(ssPv3(elem!0)), introduced(assumption)).
% 0.56/0.73 tff(502,assumption,(ssPv4(elem!0)), introduced(assumption)).
% 0.56/0.73 tff(503,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(504,plain,
% 0.56/0.73 ((ssPv4(skf3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0))) <=> ((~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(505,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[504])).
% 0.56/0.73 tff(506,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[505, 503])).
% 0.56/0.73 tff(507,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(508,plain,
% 0.56/0.73 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.56/0.73 tff(509,plain,
% 0.56/0.73 ((~ssPv3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[508, 311, 14, 218])).
% 0.56/0.73 tff(510,plain,
% 0.56/0.73 (ssPv4(skf3(skf3(elem!0)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[509, 500, 501, 502])).
% 0.56/0.73 tff(511,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(512,plain,
% 0.56/0.73 ((ssPv4(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0))) <=> ((~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(513,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[512])).
% 0.56/0.73 tff(514,plain,
% 0.56/0.73 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[513, 511])).
% 0.56/0.74 tff(515,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(516,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.56/0.74 tff(517,plain,
% 0.56/0.74 ((~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[516, 51, 14, 218])).
% 0.56/0.74 tff(518,plain,
% 0.56/0.74 (ssPv4(skf3(elem!0))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[517, 510, 501, 500])).
% 0.56/0.74 tff(519,plain,
% 0.56/0.74 (^[V: $i, U: $i] : refl((ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(520,plain,
% 0.56/0.74 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) <=> ![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[519])).
% 0.56/0.74 tff(521,plain,
% 0.56/0.74 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) <=> ![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(522,plain,
% 0.56/0.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(523,plain,
% 0.56/0.74 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> ![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[522])).
% 0.56/0.74 tff(524,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.56/0.74 tff(525,plain,
% 0.56/0.74 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.56/0.74 tff(526,plain,
% 0.56/0.74 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[525, 521])).
% 0.56/0.74 tff(527,plain,(
% 0.56/0.74 ![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[526])).
% 0.56/0.74 tff(528,plain,
% 0.56/0.74 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[527, 520])).
% 0.56/0.74 tff(529,plain,
% 0.56/0.74 (((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(530,plain,
% 0.56/0.74 ((ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0))) <=> (ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(531,plain,
% 0.56/0.74 (((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[530])).
% 0.56/0.74 tff(532,plain,
% 0.56/0.74 (((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[531, 529])).
% 0.56/0.74 tff(533,plain,
% 0.56/0.74 ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(534,plain,
% 0.56/0.74 ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.56/0.74 tff(535,plain,
% 0.56/0.74 (ssPv2(elem!0) | (~ssPv1(elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[534, 528, 14])).
% 0.56/0.74 tff(536,plain,
% 0.56/0.74 (~ssPv1(elem!0)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[535, 500, 4, 502])).
% 0.56/0.74 tff(537,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(538,plain,
% 0.56/0.74 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0)) <=> (ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(539,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[538])).
% 0.56/0.74 tff(540,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[539, 537])).
% 0.56/0.74 tff(541,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(542,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.56/0.74 tff(543,plain,
% 0.56/0.74 (ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[542, 413, 14, 218])).
% 0.56/0.74 tff(544,plain,
% 0.56/0.74 (~ssPv1(skf3(elem!0))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[543, 518, 536, 510])).
% 0.56/0.74 tff(545,plain,
% 0.56/0.74 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W)))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(546,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[545])).
% 0.56/0.74 tff(547,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(548,plain,
% 0.56/0.74 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W))) | ssPv1(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(U) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv1(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(U) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv1(U)) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(U) | (~ssRr(V, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(U) | (~ssRr(V, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv1(U)) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv1(U)) | ssPv2(W)) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W)) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W)) | ssPv1(V)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv1(U)) | ssPv2(W)) | ssPv1(V)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(549,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv1(U)) | ssPv2(W)) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[548])).
% 0.56/0.74 tff(550,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv1(U)) | ssPv2(W)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause11')).
% 0.56/0.74 tff(551,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.56/0.74 tff(552,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[551, 547])).
% 0.56/0.74 tff(553,plain,(
% 0.56/0.74 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))),
% 0.56/0.74 inference(skolemize,[status(sab)],[552])).
% 0.56/0.74 tff(554,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[553, 546])).
% 0.56/0.74 tff(555,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(556,plain,
% 0.56/0.74 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0)) <=> (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(557,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0)))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[556])).
% 0.56/0.74 tff(558,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[557, 555])).
% 0.56/0.74 tff(559,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(560,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv1(V) | ssPv1(U) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.56/0.74 tff(561,plain,
% 0.56/0.74 (ssPv2(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[560, 554, 14, 218])).
% 0.56/0.74 tff(562,plain,
% 0.56/0.74 (ssPv1(skf3(skf3(elem!0)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[561, 544, 4, 518])).
% 0.56/0.74 tff(563,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(564,plain,
% 0.56/0.74 ((ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))) <=> (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(565,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[564])).
% 0.56/0.74 tff(566,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[565, 563])).
% 0.56/0.74 tff(567,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(568,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.56/0.74 tff(569,plain,
% 0.56/0.74 (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[568, 152, 218])).
% 0.56/0.74 tff(570,plain,
% 0.56/0.74 (ssPv3(skf3(skf3(elem!0)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[569, 562, 500, 518])).
% 0.56/0.74 tff(571,plain,
% 0.56/0.74 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(572,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[571])).
% 0.56/0.74 tff(573,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(574,plain,
% 0.56/0.74 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(575,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[574])).
% 0.56/0.74 tff(576,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause25')).
% 0.56/0.74 tff(577,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.56/0.74 tff(578,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[577, 573])).
% 0.56/0.74 tff(579,plain,(
% 0.56/0.74 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[578])).
% 0.56/0.74 tff(580,plain,
% 0.56/0.74 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[579, 572])).
% 0.56/0.74 tff(581,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(582,plain,
% 0.56/0.74 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0))) <=> ((~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(583,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[582])).
% 0.56/0.74 tff(584,plain,
% 0.56/0.74 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[583, 581])).
% 0.56/0.74 tff(585,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(586,plain,
% 0.56/0.74 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.56/0.74 tff(587,plain,
% 0.56/0.74 ((~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[586, 580, 14, 218])).
% 0.56/0.74 tff(588,plain,
% 0.56/0.74 (~ssPv3(skf3(elem!0))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[587, 544, 501, 510])).
% 0.56/0.74 tff(589,plain,
% 0.56/0.74 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(590,plain,
% 0.56/0.74 ((ssPv3(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0)))) <=> (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(591,plain,
% 0.56/0.75 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[590])).
% 0.56/0.75 tff(592,plain,
% 0.56/0.75 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[591, 589])).
% 0.56/0.75 tff(593,plain,
% 0.56/0.75 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(594,plain,
% 0.56/0.75 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.56/0.75 tff(595,plain,
% 0.56/0.75 (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[594, 105, 218])).
% 0.56/0.75 tff(596,plain,
% 0.56/0.75 (ssPv2(skf3(skf3(elem!0)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[595, 588, 500, 518])).
% 0.56/0.75 tff(597,plain,
% 0.56/0.75 (~ssPv4(skf3(skf3(skf3(elem!0))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[420, 562, 510, 544])).
% 0.56/0.75 tff(598,plain,
% 0.56/0.75 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(599,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[598])).
% 0.56/0.75 tff(600,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(601,plain,
% 0.56/0.75 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv2(W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(602,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[601])).
% 0.56/0.75 tff(603,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause24')).
% 0.56/0.75 tff(604,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.56/0.75 tff(605,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[604, 600])).
% 0.56/0.75 tff(606,plain,(
% 0.56/0.75 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.56/0.75 inference(skolemize,[status(sab)],[605])).
% 0.56/0.75 tff(607,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[606, 599])).
% 0.56/0.75 tff(608,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | ssPv4(skf3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(609,plain,
% 0.56/0.75 ((ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0))))) <=> ((~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(610,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | ssPv4(skf3(skf3(skf3(elem!0))))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[609])).
% 0.56/0.75 tff(611,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[610, 608])).
% 0.56/0.75 tff(612,plain,
% 0.56/0.75 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(613,plain,
% 0.56/0.75 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | ssPv4(skf3(skf3(skf3(elem!0))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.56/0.75 tff(614,plain,
% 0.56/0.75 ((~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | ssPv4(skf3(skf3(skf3(elem!0))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[613, 607, 403])).
% 0.56/0.75 tff(615,plain,
% 0.56/0.75 (~ssPv3(skf3(skf3(skf3(elem!0))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[614, 597, 570, 596])).
% 0.56/0.75 tff(616,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv4(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(617,plain,
% 0.56/0.75 (((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0)))) <=> ((~ssPv4(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(618,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0))))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[617])).
% 0.56/0.75 tff(619,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv4(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[618, 616])).
% 0.56/0.75 tff(620,plain,
% 0.56/0.75 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(621,plain,
% 0.56/0.75 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv4(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.56/0.75 tff(622,plain,
% 0.56/0.75 ((~ssPv4(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[621, 246, 218, 403])).
% 0.56/0.75 tff(623,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[622, 615, 570, 510, 518])).
% 0.56/0.75 tff(624,plain,(ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv3(elem!0)) | (~ssPv4(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(625,plain,
% 0.56/0.75 (ssPv2(skf3(elem!0))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[624, 256, 4, 459])).
% 0.56/0.75 tff(626,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(627,plain,
% 0.56/0.75 ((ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(628,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[627])).
% 0.56/0.75 tff(629,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.56/0.75 inference(transitivity,[status(thm)],[628, 626])).
% 0.56/0.75 tff(630,plain,
% 0.56/0.75 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(631,plain,
% 0.56/0.75 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.56/0.75 tff(632,plain,
% 0.56/0.75 (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[631, 449, 14, 41])).
% 0.56/0.75 tff(633,plain,
% 0.56/0.75 (ssPv3(skf2(elem!0))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[632, 625, 2, 459])).
% 0.56/0.75 tff(634,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(635,plain,
% 0.56/0.75 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))) <=> ((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(636,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[635])).
% 0.56/0.75 tff(637,plain,
% 0.56/0.75 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[636, 634])).
% 0.56/0.75 tff(638,plain,
% 0.56/0.75 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(639,plain,
% 0.56/0.75 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.56/0.75 tff(640,plain,
% 0.56/0.75 ((~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[639, 228, 41, 285])).
% 0.56/0.75 tff(641,plain,
% 0.56/0.75 (ssPv2(skf2(skf2(elem!0)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[640, 633, 256, 499])).
% 0.56/0.75 tff(642,plain,
% 0.56/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(643,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[642])).
% 0.56/0.75 tff(644,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(645,plain,
% 0.56/0.75 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(646,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[645])).
% 0.56/0.75 tff(647,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause26')).
% 0.56/0.75 tff(648,plain,
% 0.56/0.75 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.56/0.76 tff(649,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[648, 644])).
% 0.56/0.76 tff(650,plain,(
% 0.56/0.76 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.56/0.76 inference(skolemize,[status(sab)],[649])).
% 0.56/0.76 tff(651,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[650, 643])).
% 0.56/0.76 tff(652,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(653,plain,
% 0.56/0.76 (((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(654,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0)))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[653])).
% 0.56/0.76 tff(655,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.56/0.76 inference(transitivity,[status(thm)],[654, 652])).
% 0.56/0.76 tff(656,plain,
% 0.56/0.76 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(657,plain,
% 0.56/0.76 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.56/0.76 tff(658,plain,
% 0.56/0.76 ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0)))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[657, 651, 14, 41])).
% 0.56/0.76 tff(659,plain,
% 0.56/0.76 (ssPv1(elem!0)),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[658, 633, 256, 625])).
% 0.56/0.76 tff(660,plain,
% 0.56/0.76 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))),
% 0.56/0.76 inference(bind,[status(th)],[])).
% 0.56/0.76 tff(661,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.56/0.76 inference(quant_intro,[status(thm)],[660])).
% 0.56/0.76 tff(662,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(663,plain,
% 0.56/0.76 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> (((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv3(V))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv3(V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))))),
% 0.56/0.76 inference(bind,[status(th)],[])).
% 0.56/0.76 tff(664,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.56/0.76 inference(quant_intro,[status(thm)],[663])).
% 0.56/0.76 tff(665,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.56/0.76 tff(666,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.56/0.76 tff(667,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[666, 662])).
% 0.56/0.76 tff(668,plain,(
% 0.56/0.76 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.56/0.76 inference(skolemize,[status(sab)],[667])).
% 0.56/0.76 tff(669,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[668, 661])).
% 0.56/0.76 tff(670,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(671,plain,
% 0.56/0.76 (((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(672,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[671])).
% 0.56/0.76 tff(673,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.56/0.76 inference(transitivity,[status(thm)],[672, 670])).
% 0.56/0.76 tff(674,plain,
% 0.56/0.76 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(675,plain,
% 0.56/0.76 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.56/0.76 tff(676,plain,
% 0.56/0.76 ((~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0))))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[675, 669, 41, 285])).
% 0.56/0.76 tff(677,plain,
% 0.56/0.76 (~ssPv1(skf2(skf2(elem!0)))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[676, 633, 256, 659])).
% 0.56/0.76 tff(678,plain,
% 0.56/0.76 (ssPv3(skf2(skf2(elem!0)))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[472, 633, 2, 4])).
% 0.56/0.76 tff(679,plain,
% 0.56/0.76 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V))))),
% 0.56/0.76 inference(bind,[status(th)],[])).
% 0.56/0.76 tff(680,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.56/0.76 inference(quant_intro,[status(thm)],[679])).
% 0.56/0.76 tff(681,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(682,plain,
% 0.56/0.76 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(U))) <=> ((~ssPv2(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv1(X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv1(V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))))),
% 0.56/0.76 inference(bind,[status(th)],[])).
% 0.56/0.76 tff(683,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.56/0.76 inference(quant_intro,[status(thm)],[682])).
% 0.56/0.76 tff(684,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.56/0.76 tff(685,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.56/0.76 tff(686,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[685, 681])).
% 0.56/0.76 tff(687,plain,(
% 0.56/0.76 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.56/0.76 inference(skolemize,[status(sab)],[686])).
% 0.56/0.76 tff(688,plain,
% 0.56/0.76 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[687, 680])).
% 0.56/0.76 tff(689,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(690,plain,
% 0.56/0.76 (((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(691,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[690])).
% 0.56/0.76 tff(692,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.56/0.76 inference(transitivity,[status(thm)],[691, 689])).
% 0.56/0.76 tff(693,plain,
% 0.56/0.76 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(694,plain,
% 0.56/0.76 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[693, 692])).
% 0.56/0.76 tff(695,plain,
% 0.56/0.76 ((~ssPv1(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[694, 688, 14, 41])).
% 0.56/0.76 tff(696,plain,
% 0.56/0.76 (~ssPv1(skf2(elem!0))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[695, 659, 499, 625])).
% 0.56/0.76 tff(697,plain,
% 0.56/0.76 (^[V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))))),
% 0.56/0.76 inference(bind,[status(th)],[])).
% 0.56/0.76 tff(698,plain,
% 0.56/0.76 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.56/0.76 inference(quant_intro,[status(thm)],[697])).
% 0.56/0.76 tff(699,plain,
% 0.56/0.76 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(700,plain,
% 0.56/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv2(V))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv2(V))) | ssPv1(U)) <=> ((~ssRr(U, V)) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) <=> ((~ssRr(U, V)) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) | ssPv1(V)) <=> (((~ssRr(U, V)) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))))),
% 0.56/0.76 inference(bind,[status(th)],[])).
% 0.56/0.76 tff(701,plain,
% 0.56/0.76 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) | ssPv1(V)) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.56/0.76 inference(quant_intro,[status(thm)],[700])).
% 0.56/0.76 tff(702,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.56/0.76 tff(703,plain,
% 0.56/0.76 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[702, 701])).
% 0.56/0.76 tff(704,plain,
% 0.56/0.76 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[703, 699])).
% 0.56/0.76 tff(705,plain,(
% 0.56/0.76 ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.56/0.76 inference(skolemize,[status(sab)],[704])).
% 0.56/0.76 tff(706,plain,
% 0.56/0.76 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[705, 698])).
% 0.56/0.76 tff(707,plain,
% 0.56/0.76 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | (ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(708,plain,
% 0.56/0.76 (((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))) <=> (ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(709,plain,
% 0.56/0.76 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | (ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0)))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[708])).
% 0.56/0.76 tff(710,plain,
% 0.56/0.76 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.56/0.76 inference(transitivity,[status(thm)],[709, 707])).
% 0.56/0.76 tff(711,plain,
% 0.56/0.76 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(712,plain,
% 0.56/0.76 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.56/0.76 tff(713,plain,
% 0.56/0.76 (ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0)))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[712, 706, 285])).
% 0.56/0.76 tff(714,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[713, 696, 678, 677, 641])).
% 0.56/0.76 tff(715,plain,(ssPv4(skf2(elem!0)) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.76 tff(716,plain,
% 0.56/0.76 (ssPv4(skf2(elem!0))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[715, 4])).
% 0.56/0.76 tff(717,plain,
% 0.56/0.76 (ssPv3(elem!0)),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[114, 3, 4])).
% 0.56/0.76 tff(718,plain,
% 0.56/0.76 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(719,plain,
% 0.56/0.76 ((ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(720,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[719])).
% 0.56/0.77 tff(721,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(transitivity,[status(thm)],[720, 718])).
% 0.56/0.77 tff(722,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.56/0.77 inference(quant_inst,[status(thm)],[])).
% 0.56/0.77 tff(723,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.56/0.77 tff(724,plain,
% 0.56/0.77 (ssPv4(elem!0) | (~ssPv3(elem!0)) | ssPv3(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[723, 208, 41])).
% 0.56/0.77 tff(725,plain,
% 0.56/0.77 (ssPv3(skf2(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[724, 717, 716, 3])).
% 0.56/0.77 tff(726,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(727,plain,
% 0.56/0.77 ((ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> (ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(728,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0)))))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[727])).
% 0.56/0.77 tff(729,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(transitivity,[status(thm)],[728, 726])).
% 0.56/0.77 tff(730,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(quant_inst,[status(thm)],[])).
% 0.56/0.77 tff(731,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[730, 729])).
% 0.56/0.77 tff(732,plain,
% 0.56/0.77 (ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0)))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[731, 311, 14, 41])).
% 0.56/0.77 tff(733,plain,
% 0.56/0.77 (ssPv4(skf3(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[732, 725, 4, 716])).
% 0.56/0.77 tff(734,plain,
% 0.56/0.77 ($false),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[58, 733, 725, 4, 3])).
% 0.56/0.77 tff(735,plain,(ssPv4(elem!0) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.77 tff(736,plain,
% 0.56/0.77 (ssPv4(elem!0)),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[735, 4])).
% 0.56/0.77 tff(737,assumption,(ssPv2(skf3(elem!0))), introduced(assumption)).
% 0.56/0.77 tff(738,plain,
% 0.56/0.77 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.56/0.77 inference(bind,[status(th)],[])).
% 0.56/0.77 tff(739,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.56/0.77 inference(quant_intro,[status(thm)],[738])).
% 0.56/0.77 tff(740,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(741,plain,
% 0.56/0.77 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(U))) <=> ((~ssPv2(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv3(X)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) | ssPv2(V)) <=> ((ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)))), rewrite(((ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) | ssPv2(V)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.56/0.77 inference(bind,[status(th)],[])).
% 0.56/0.77 tff(742,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.56/0.77 inference(quant_intro,[status(thm)],[741])).
% 0.56/0.77 tff(743,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.56/0.77 tff(744,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.56/0.77 tff(745,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[744, 740])).
% 0.56/0.77 tff(746,plain,(
% 0.56/0.77 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.56/0.77 inference(skolemize,[status(sab)],[745])).
% 0.56/0.77 tff(747,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[746, 739])).
% 0.56/0.77 tff(748,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(749,plain,
% 0.56/0.77 ((ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(750,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf2(elem!0)))))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[749])).
% 0.56/0.77 tff(751,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(transitivity,[status(thm)],[750, 748])).
% 0.56/0.77 tff(752,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.56/0.77 inference(quant_inst,[status(thm)],[])).
% 0.56/0.77 tff(753,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf2(elem!0)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.56/0.77 tff(754,plain,
% 0.56/0.77 (ssPv2(elem!0) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf2(elem!0)))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[753, 747, 14, 41])).
% 0.56/0.77 tff(755,plain,
% 0.56/0.77 (ssPv3(skf2(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[754, 737, 4, 716])).
% 0.56/0.77 tff(756,plain,
% 0.56/0.77 (ssPv4(skf3(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[732, 755, 4, 716])).
% 0.56/0.77 tff(757,plain,
% 0.56/0.77 (ssPv1(skf3(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[382, 756, 4, 737])).
% 0.56/0.77 tff(758,plain,
% 0.56/0.77 (ssPv3(skf3(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[159, 757, 4, 736])).
% 0.56/0.77 tff(759,plain,
% 0.56/0.77 (~ssPv3(skf3(skf3(elem!0)))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[235, 758, 4, 737])).
% 0.56/0.77 tff(760,plain,
% 0.56/0.77 ($false),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[253, 759, 758, 756, 736])).
% 0.56/0.77 tff(761,plain,((~ssPv2(skf3(elem!0))) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.77 tff(762,plain,
% 0.56/0.77 (~ssPv2(skf3(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[761, 4])).
% 0.56/0.77 tff(763,plain,
% 0.56/0.77 (ssPv3(elem!0)),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[122, 762, 4, 736])).
% 0.56/0.77 tff(764,plain,
% 0.56/0.77 ($false),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[624, 763, 762, 4, 736])).
% 0.56/0.77 tff(765,plain,(ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.77 tff(766,plain,
% 0.56/0.77 (ssPv3(skf2(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[94, 5, 3, 2])).
% 0.56/0.77 tff(767,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(768,plain,
% 0.56/0.77 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(769,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv3(skf3(elem!0))))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[768])).
% 0.56/0.77 tff(770,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.56/0.77 inference(transitivity,[status(thm)],[769, 767])).
% 0.56/0.77 tff(771,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.56/0.77 inference(quant_inst,[status(thm)],[])).
% 0.56/0.77 tff(772,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[771, 770])).
% 0.56/0.77 tff(773,plain,
% 0.56/0.77 ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv2(skf3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[772, 69, 14])).
% 0.56/0.77 tff(774,plain,
% 0.56/0.77 (ssPv3(skf3(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[773, 500, 765, 5])).
% 0.56/0.77 tff(775,plain,
% 0.56/0.77 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) <=> ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))))),
% 0.56/0.77 inference(bind,[status(th)],[])).
% 0.56/0.77 tff(776,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.56/0.77 inference(quant_intro,[status(thm)],[775])).
% 0.56/0.77 tff(777,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(778,plain,
% 0.56/0.77 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> (((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv3(X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv3(X))) <=> ((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> ((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) <=> (((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)))), rewrite((((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) <=> ((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) | ssPv3(V)) <=> (((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(V)))), rewrite((((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(V)) <=> ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) | ssPv3(V)) <=> ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))))),
% 0.56/0.77 inference(bind,[status(th)],[])).
% 0.56/0.77 tff(779,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.56/0.77 inference(quant_intro,[status(thm)],[778])).
% 0.56/0.77 tff(780,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.56/0.77 tff(781,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[780, 779])).
% 0.56/0.77 tff(782,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[781, 777])).
% 0.56/0.77 tff(783,plain,(
% 0.56/0.77 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.56/0.77 inference(skolemize,[status(sab)],[782])).
% 0.56/0.77 tff(784,plain,
% 0.56/0.77 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[783, 776])).
% 0.56/0.77 tff(785,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(786,plain,
% 0.56/0.77 (((~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0))) <=> (ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(787,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0)))))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[786])).
% 0.56/0.77 tff(788,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.56/0.77 inference(transitivity,[status(thm)],[787, 785])).
% 0.56/0.77 tff(789,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.56/0.77 inference(quant_inst,[status(thm)],[])).
% 0.56/0.77 tff(790,plain,
% 0.56/0.77 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0)))),
% 0.56/0.77 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.56/0.77 tff(791,plain,
% 0.56/0.77 (ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0)))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[790, 784, 14, 41])).
% 0.56/0.77 tff(792,plain,
% 0.56/0.77 (ssPv4(skf3(elem!0))),
% 0.56/0.77 inference(unit_resolution,[status(thm)],[791, 774, 5, 766])).
% 0.56/0.77 tff(793,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(794,plain,
% 0.56/0.77 ((ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> (ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.56/0.77 inference(rewrite,[status(thm)],[])).
% 0.56/0.77 tff(795,plain,
% 0.56/0.77 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))))),
% 0.56/0.77 inference(monotonicity,[status(thm)],[794])).
% 0.56/0.77 tff(796,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.56/0.78 inference(transitivity,[status(thm)],[795, 793])).
% 0.56/0.78 tff(797,plain,
% 0.56/0.78 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.56/0.78 inference(quant_inst,[status(thm)],[])).
% 0.56/0.78 tff(798,plain,
% 0.56/0.78 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.56/0.78 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.56/0.78 tff(799,plain,
% 0.56/0.78 (ssPv4(elem!0) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[798, 449, 14, 218])).
% 0.56/0.78 tff(800,plain,
% 0.56/0.78 (~ssPv2(skf3(skf3(elem!0)))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[799, 792, 3, 5])).
% 0.56/0.78 tff(801,plain,
% 0.56/0.78 (~ssPv2(skf2(elem!0))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[338, 774, 3, 2])).
% 0.56/0.78 tff(802,plain,
% 0.56/0.78 (ssPv1(skf3(elem!0))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[177, 801, 5, 2])).
% 0.56/0.78 tff(803,plain,
% 0.56/0.78 (((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(804,plain,
% 0.56/0.78 ((ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0)))) <=> (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(805,plain,
% 0.56/0.78 (((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))))),
% 0.56/0.78 inference(monotonicity,[status(thm)],[804])).
% 0.56/0.78 tff(806,plain,
% 0.56/0.78 (((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.56/0.78 inference(transitivity,[status(thm)],[805, 803])).
% 0.56/0.78 tff(807,plain,
% 0.56/0.78 ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))))),
% 0.56/0.78 inference(quant_inst,[status(thm)],[])).
% 0.56/0.78 tff(808,plain,
% 0.56/0.78 ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.56/0.78 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.56/0.78 tff(809,plain,
% 0.56/0.78 (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[808, 528, 218])).
% 0.56/0.78 tff(810,plain,
% 0.56/0.78 ($false),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[809, 802, 800, 500, 792])).
% 0.56/0.78 tff(811,plain,(ssPv2(skf3(elem!0)) | ssPv3(elem!0) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.78 tff(812,plain,
% 0.56/0.78 (ssPv2(skf3(elem!0))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[811, 5, 2, 3])).
% 0.56/0.78 tff(813,plain,
% 0.56/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U))))),
% 0.56/0.78 inference(bind,[status(th)],[])).
% 0.56/0.78 tff(814,plain,
% 0.56/0.78 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.56/0.78 inference(quant_intro,[status(thm)],[813])).
% 0.56/0.78 tff(815,plain,
% 0.56/0.78 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(816,plain,
% 0.56/0.78 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))))),
% 0.56/0.78 inference(bind,[status(th)],[])).
% 0.56/0.78 tff(817,plain,
% 0.56/0.78 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.56/0.78 inference(quant_intro,[status(thm)],[816])).
% 0.56/0.78 tff(818,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv4(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause21')).
% 0.56/0.78 tff(819,plain,
% 0.56/0.78 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.56/0.78 inference(modus_ponens,[status(thm)],[818, 817])).
% 0.56/0.78 tff(820,plain,
% 0.56/0.78 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.56/0.78 inference(modus_ponens,[status(thm)],[819, 815])).
% 0.56/0.78 tff(821,plain,(
% 0.56/0.78 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.56/0.78 inference(skolemize,[status(sab)],[820])).
% 0.56/0.78 tff(822,plain,
% 0.56/0.78 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.56/0.78 inference(modus_ponens,[status(thm)],[821, 814])).
% 0.56/0.78 tff(823,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(824,plain,
% 0.56/0.78 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(elem!0)))) <=> ((~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(825,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0)))))),
% 0.56/0.78 inference(monotonicity,[status(thm)],[824])).
% 0.56/0.78 tff(826,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.56/0.78 inference(transitivity,[status(thm)],[825, 823])).
% 0.56/0.78 tff(827,plain,
% 0.56/0.78 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(elem!0))))),
% 0.56/0.78 inference(quant_inst,[status(thm)],[])).
% 0.56/0.78 tff(828,plain,
% 0.56/0.78 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0)))),
% 0.56/0.78 inference(modus_ponens,[status(thm)],[827, 826])).
% 0.56/0.78 tff(829,plain,
% 0.56/0.78 ((~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0)))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[828, 822, 14])).
% 0.56/0.78 tff(830,plain,
% 0.56/0.78 (~ssPv4(skf3(elem!0))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[829, 812, 765, 3])).
% 0.56/0.78 tff(831,plain,
% 0.56/0.78 (~ssPv3(skf3(elem!0))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[791, 830, 5, 766])).
% 0.56/0.78 tff(832,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(833,plain,
% 0.56/0.78 ((ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0))) <=> (ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(834,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0))))),
% 0.56/0.78 inference(monotonicity,[status(thm)],[833])).
% 0.56/0.78 tff(835,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))),
% 0.56/0.78 inference(transitivity,[status(thm)],[834, 832])).
% 0.56/0.78 tff(836,plain,
% 0.56/0.78 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.56/0.78 inference(quant_inst,[status(thm)],[])).
% 0.56/0.78 tff(837,plain,
% 0.56/0.78 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0))),
% 0.56/0.78 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.56/0.78 tff(838,plain,
% 0.56/0.78 (ssPv4(elem!0) | ssPv3(elem!0) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[837, 87, 14])).
% 0.56/0.78 tff(839,plain,
% 0.56/0.78 ($false),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[838, 831, 830, 3, 5])).
% 0.56/0.78 tff(840,plain,(ssPv3(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.78 tff(841,plain,
% 0.56/0.78 (ssPv3(elem!0)),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[840, 2, 3])).
% 0.56/0.78 tff(842,plain,
% 0.56/0.78 (ssPv2(skf3(elem!0))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[273, 841, 3, 2])).
% 0.56/0.78 tff(843,plain,
% 0.56/0.78 (~ssPv4(skf3(elem!0))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[829, 842, 765, 3])).
% 0.56/0.78 tff(844,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(845,plain,
% 0.56/0.78 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0))) <=> ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(846,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))))),
% 0.56/0.78 inference(monotonicity,[status(thm)],[845])).
% 0.56/0.78 tff(847,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.56/0.78 inference(transitivity,[status(thm)],[846, 844])).
% 0.56/0.78 tff(848,plain,
% 0.56/0.78 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))),
% 0.56/0.78 inference(quant_inst,[status(thm)],[])).
% 0.56/0.78 tff(849,plain,
% 0.56/0.78 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))),
% 0.56/0.78 inference(modus_ponens,[status(thm)],[848, 847])).
% 0.56/0.78 tff(850,plain,
% 0.56/0.78 ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0)))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[849, 607, 14])).
% 0.56/0.78 tff(851,plain,
% 0.56/0.78 (~ssPv3(skf3(elem!0))),
% 0.56/0.78 inference(unit_resolution,[status(thm)],[850, 843, 765, 841])).
% 0.56/0.78 tff(852,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssPv2(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssPv2(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(853,plain,
% 0.56/0.78 ((ssPv4(elem!0) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0))) <=> ((~ssPv2(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.56/0.78 inference(rewrite,[status(thm)],[])).
% 0.56/0.78 tff(854,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssPv2(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.56/0.78 inference(monotonicity,[status(thm)],[853])).
% 0.56/0.78 tff(855,plain,
% 0.56/0.78 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssPv2(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.63/0.78 inference(transitivity,[status(thm)],[854, 852])).
% 0.63/0.78 tff(856,plain,
% 0.63/0.78 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))),
% 0.63/0.78 inference(quant_inst,[status(thm)],[])).
% 0.63/0.78 tff(857,plain,
% 0.63/0.78 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssPv2(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.63/0.78 tff(858,plain,
% 0.63/0.78 ((~ssPv2(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[857, 331, 14, 218])).
% 0.63/0.78 tff(859,plain,
% 0.63/0.78 (~ssPv3(skf3(skf3(elem!0)))),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[858, 843, 765, 3])).
% 0.63/0.78 tff(860,plain,
% 0.63/0.78 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(861,plain,
% 0.63/0.78 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))) <=> ((~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(862,plain,
% 0.63/0.78 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[861])).
% 0.63/0.78 tff(863,plain,
% 0.63/0.78 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.78 inference(transitivity,[status(thm)],[862, 860])).
% 0.63/0.78 tff(864,plain,
% 0.63/0.78 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.63/0.78 inference(quant_inst,[status(thm)],[])).
% 0.63/0.78 tff(865,plain,
% 0.63/0.78 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.63/0.79 tff(866,plain,
% 0.63/0.79 ((~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[865, 69, 218])).
% 0.63/0.79 tff(867,plain,
% 0.63/0.79 (ssPv2(skf3(skf3(elem!0)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[866, 859, 842, 851])).
% 0.63/0.79 tff(868,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(869,plain,
% 0.63/0.79 ((ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))) <=> (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(870,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[869])).
% 0.63/0.79 tff(871,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.79 inference(transitivity,[status(thm)],[870, 868])).
% 0.63/0.79 tff(872,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(873,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.63/0.79 tff(874,plain,
% 0.63/0.79 (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[873, 87, 218])).
% 0.63/0.79 tff(875,plain,
% 0.63/0.79 (ssPv4(skf3(skf3(elem!0)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[874, 859, 851, 843])).
% 0.63/0.79 tff(876,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(877,plain,
% 0.63/0.79 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0))))) <=> (ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(878,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[877])).
% 0.63/0.79 tff(879,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.63/0.79 inference(transitivity,[status(thm)],[878, 876])).
% 0.63/0.79 tff(880,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(881,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.63/0.79 tff(882,plain,
% 0.63/0.79 (ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[881, 822, 218])).
% 0.63/0.79 tff(883,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[882, 875, 867, 842, 843])).
% 0.63/0.79 tff(884,plain,(ssPv4(skf2(elem!0)) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(885,plain,
% 0.63/0.79 (ssPv4(skf2(elem!0))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[884, 3])).
% 0.63/0.79 tff(886,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(887,plain,
% 0.63/0.79 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0))) <=> ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(888,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[887])).
% 0.63/0.79 tff(889,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.79 inference(transitivity,[status(thm)],[888, 886])).
% 0.63/0.79 tff(890,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(891,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.63/0.79 tff(892,plain,
% 0.63/0.79 ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[891, 134, 41])).
% 0.63/0.79 tff(893,plain,
% 0.63/0.79 (ssPv1(skf2(elem!0))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[892, 5, 765, 885])).
% 0.63/0.79 tff(894,assumption,(ssPv1(elem!0)), introduced(assumption)).
% 0.63/0.79 tff(895,assumption,(ssPv1(skf2(elem!0))), introduced(assumption)).
% 0.63/0.79 tff(896,assumption,(ssPv4(skf2(skf2(elem!0)))), introduced(assumption)).
% 0.63/0.79 tff(897,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(898,plain,
% 0.63/0.79 ((ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(899,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[898])).
% 0.63/0.79 tff(900,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.79 inference(transitivity,[status(thm)],[899, 897])).
% 0.63/0.79 tff(901,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(902,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.63/0.79 tff(903,plain,
% 0.63/0.79 (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[902, 152, 285])).
% 0.63/0.79 tff(904,plain,
% 0.63/0.79 (ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[903, 896, 1, 895])).
% 0.63/0.79 tff(905,plain,
% 0.63/0.79 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(906,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[905])).
% 0.63/0.79 tff(907,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(908,plain,
% 0.63/0.79 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv2(X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv2(X))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(909,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[908])).
% 0.63/0.79 tff(910,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.63/0.79 tff(911,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.63/0.79 tff(912,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[911, 907])).
% 0.63/0.79 tff(913,plain,(
% 0.63/0.79 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.63/0.79 inference(skolemize,[status(sab)],[912])).
% 0.63/0.79 tff(914,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[913, 906])).
% 0.63/0.79 tff(915,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(916,plain,
% 0.63/0.79 ((ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0)))) <=> (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(917,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[916])).
% 0.63/0.79 tff(918,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.79 inference(transitivity,[status(thm)],[917, 915])).
% 0.63/0.79 tff(919,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(920,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.63/0.79 tff(921,plain,
% 0.63/0.79 (ssPv4(elem!0) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[920, 914, 41, 285])).
% 0.63/0.79 tff(922,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[921, 904, 896, 3, 895])).
% 0.63/0.79 tff(923,plain,((~ssPv4(skf2(skf2(elem!0)))) | ssPv4(elem!0) | (~ssPv1(skf2(elem!0))) | ssPv3(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(924,plain,
% 0.63/0.79 (~ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[923, 1, 895, 3])).
% 0.63/0.79 tff(925,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(926,plain,
% 0.63/0.79 ((ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(927,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[926])).
% 0.63/0.79 tff(928,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[927, 925])).
% 0.63/0.80 tff(929,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(930,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.63/0.80 tff(931,plain,
% 0.63/0.80 ((~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[930, 449, 41, 285])).
% 0.63/0.80 tff(932,plain,
% 0.63/0.80 (ssPv3(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[931, 924, 765, 885])).
% 0.63/0.80 tff(933,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(934,plain,
% 0.63/0.80 (((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv1(skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(935,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0))))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[934])).
% 0.63/0.80 tff(936,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[935, 933])).
% 0.63/0.80 tff(937,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv1(skf2(elem!0))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(938,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.63/0.80 tff(939,plain,
% 0.63/0.80 (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[938, 188, 285])).
% 0.63/0.80 tff(940,plain,
% 0.63/0.80 (~ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[939, 924, 1, 895])).
% 0.63/0.80 tff(941,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(942,plain,
% 0.63/0.80 ((ssPv2(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(943,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[942])).
% 0.63/0.80 tff(944,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[943, 941])).
% 0.63/0.80 tff(945,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(946,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.63/0.80 tff(947,plain,
% 0.63/0.80 ((~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[946, 357, 41, 285])).
% 0.63/0.80 tff(948,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[947, 940, 932, 895, 894])).
% 0.63/0.80 tff(949,plain,(ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(950,plain,
% 0.63/0.80 (ssPv3(skf2(elem!0))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[949, 894, 893, 3])).
% 0.63/0.80 tff(951,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(952,plain,
% 0.63/0.80 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))) <=> (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(953,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[952])).
% 0.63/0.80 tff(954,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[953, 951])).
% 0.63/0.80 tff(955,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(956,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[955, 954])).
% 0.63/0.80 tff(957,plain,
% 0.63/0.80 (ssPv3(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[956, 246, 41, 285])).
% 0.63/0.80 tff(958,plain,
% 0.63/0.80 (~ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[957, 950, 885, 5])).
% 0.63/0.80 tff(959,plain,
% 0.63/0.80 (ssPv3(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[931, 958, 765, 885])).
% 0.63/0.80 tff(960,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ((~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(961,plain,
% 0.63/0.80 ((ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(962,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ((~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[961])).
% 0.63/0.80 tff(963,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[962, 960])).
% 0.63/0.80 tff(964,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(965,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[964, 963])).
% 0.63/0.80 tff(966,plain,
% 0.63/0.80 ((~ssPv1(elem!0)) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[965, 152, 41])).
% 0.63/0.80 tff(967,plain,
% 0.63/0.80 (ssPv2(skf2(elem!0))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[966, 894, 5, 885])).
% 0.63/0.80 tff(968,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(969,plain,
% 0.63/0.80 (((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))) <=> ((~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(970,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0))))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[969])).
% 0.63/0.80 tff(971,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[970, 968])).
% 0.63/0.80 tff(972,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(973,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[972, 971])).
% 0.63/0.80 tff(974,plain,
% 0.63/0.80 ((~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[973, 822, 285])).
% 0.63/0.80 tff(975,plain,
% 0.63/0.80 (~ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[974, 958, 885, 967])).
% 0.63/0.80 tff(976,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[947, 975, 959, 893, 894])).
% 0.63/0.80 tff(977,plain,((~ssPv1(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(978,plain,
% 0.63/0.80 (~ssPv1(elem!0)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[977, 5, 3])).
% 0.63/0.80 tff(979,assumption,(~ssPv1(elem!0)), introduced(assumption)).
% 0.63/0.80 tff(980,plain,
% 0.63/0.80 (~ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[939, 1, 924, 895])).
% 0.63/0.80 tff(981,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(982,plain,
% 0.63/0.80 ((ssPv2(skf2(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(983,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[982])).
% 0.63/0.80 tff(984,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[983, 981])).
% 0.63/0.80 tff(985,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(986,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.63/0.80 tff(987,plain,
% 0.63/0.80 (ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[986, 170, 41, 285])).
% 0.63/0.80 tff(988,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[987, 980, 1, 979, 924])).
% 0.63/0.80 tff(989,plain,(ssPv3(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv1(skf2(elem!0))) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(990,plain,
% 0.63/0.80 (ssPv3(skf2(elem!0))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[989, 978, 893, 3])).
% 0.63/0.80 tff(991,plain,
% 0.63/0.80 (~ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[957, 990, 885, 5])).
% 0.63/0.80 tff(992,plain,
% 0.63/0.80 (ssPv3(skf2(skf2(elem!0)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[931, 991, 765, 885])).
% 0.63/0.80 tff(993,assumption,(~ssPv3(skf2(skf2(skf2(elem!0))))), introduced(assumption)).
% 0.63/0.80 tff(994,assumption,(~ssPv4(skf2(skf2(elem!0)))), introduced(assumption)).
% 0.63/0.80 tff(995,assumption,(ssPv3(skf2(skf2(elem!0)))), introduced(assumption)).
% 0.63/0.80 tff(996,plain,
% 0.63/0.80 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(997,plain,
% 0.63/0.80 (ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[996, 39])).
% 0.63/0.80 tff(998,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ((~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(999,plain,
% 0.63/0.81 ((ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0)))))) <=> ((~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1000,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ((~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0)))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[999])).
% 0.63/0.81 tff(1001,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1000, 998])).
% 0.63/0.81 tff(1002,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1003,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv4(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 0.63/0.81 tff(1004,plain,
% 0.63/0.81 ((~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1003, 208, 997])).
% 0.63/0.81 tff(1005,plain,
% 0.63/0.81 (~ssPv4(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1004, 993, 994, 995])).
% 0.63/0.81 tff(1006,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))) | ssPv4(skf2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))) | ssPv4(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1007,plain,
% 0.63/0.81 ((ssPv4(skf2(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0)))))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))) | ssPv4(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1008,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))) | ssPv4(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1007])).
% 0.63/0.81 tff(1009,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))) | ssPv4(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1008, 1006])).
% 0.63/0.81 tff(1010,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1011,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))) | ssPv4(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.63/0.81 tff(1012,plain,
% 0.63/0.81 ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(skf2(elem!0))))) | ssPv4(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1011, 331, 285, 997])).
% 0.63/0.81 tff(1013,plain,
% 0.63/0.81 (~ssPv2(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1012, 1005, 469, 994])).
% 0.63/0.81 tff(1014,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1015,plain,
% 0.63/0.81 ((ssPv4(skf2(skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0)))))) <=> (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1016,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1015])).
% 0.63/0.81 tff(1017,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1016, 1014])).
% 0.63/0.81 tff(1018,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1019,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.63/0.81 tff(1020,plain,
% 0.63/0.81 (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1019, 24, 997])).
% 0.63/0.81 tff(1021,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1020, 1013, 1005, 994, 993])).
% 0.63/0.81 tff(1022,plain,(ssPv3(skf2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(1023,plain,
% 0.63/0.81 (ssPv3(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1022, 991, 990, 992])).
% 0.63/0.81 tff(1024,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1025,plain,
% 0.63/0.81 ((ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0)))))) <=> ((~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1026,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0)))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1025])).
% 0.63/0.81 tff(1027,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1026, 1024])).
% 0.63/0.81 tff(1028,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1029,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 0.63/0.81 tff(1030,plain,
% 0.63/0.81 ((~ssPv3(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssPv2(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1029, 607, 997])).
% 0.63/0.81 tff(1031,plain,
% 0.63/0.81 (~ssPv2(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1030, 1023, 991, 992])).
% 0.63/0.81 tff(1032,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1033,plain,
% 0.63/0.81 ((ssPv4(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(skf2(elem!0)))))) <=> ((~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1034,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0)))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1033])).
% 0.63/0.81 tff(1035,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1034, 1032])).
% 0.63/0.81 tff(1036,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1037,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 0.63/0.81 tff(1038,plain,
% 0.63/0.81 ((~ssPv4(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1037, 51, 285, 997])).
% 0.63/0.81 tff(1039,plain,
% 0.63/0.81 (ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1038, 1023, 885, 991])).
% 0.63/0.81 tff(1040,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1041,plain,
% 0.63/0.81 (((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0))))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1042,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1041])).
% 0.63/0.81 tff(1043,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1042, 1040])).
% 0.63/0.81 tff(1044,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0)))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1045,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv2(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.63/0.81 tff(1046,plain,
% 0.63/0.81 ((~ssPv3(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(skf2(elem!0))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1045, 228, 285, 997])).
% 0.63/0.81 tff(1047,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1046, 1039, 1031, 990, 992])).
% 0.63/0.81 tff(1048,plain,(ssPv3(elem!0) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(1049,plain,
% 0.63/0.81 (ssPv3(elem!0)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1048, 3])).
% 0.63/0.81 tff(1050,plain,
% 0.63/0.81 (ssPv3(skf2(elem!0))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[724, 1049, 885, 3])).
% 0.63/0.81 tff(1051,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1052,plain,
% 0.63/0.81 ((ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0)))) <=> (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1053,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1052])).
% 0.63/0.81 tff(1054,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1053, 1051])).
% 0.63/0.82 tff(1055,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1056,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 0.63/0.82 tff(1057,plain,
% 0.63/0.82 (ssPv4(elem!0) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1056, 607, 41])).
% 0.63/0.82 tff(1058,plain,
% 0.63/0.82 (~ssPv2(skf2(elem!0))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1057, 1050, 1049, 3])).
% 0.63/0.82 tff(1059,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1060,plain,
% 0.63/0.82 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0))) <=> ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1061,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0)))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1060])).
% 0.63/0.82 tff(1062,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1061, 1059])).
% 0.63/0.82 tff(1063,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1064,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 0.63/0.82 tff(1065,plain,
% 0.63/0.82 ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1064, 228, 14, 41])).
% 0.63/0.82 tff(1066,plain,
% 0.63/0.82 (~ssPv3(skf3(elem!0))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1065, 1058, 765, 1049])).
% 0.63/0.82 tff(1067,plain,
% 0.63/0.82 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) <=> (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(1068,plain,
% 0.63/0.82 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[1067])).
% 0.63/0.82 tff(1069,plain,
% 0.63/0.82 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1070,plain,
% 0.63/0.82 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv4(X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv4(X))) <=> ((~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) <=> ((~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) <=> (((~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(U)))), rewrite((((~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) <=> ((ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(W)))), rewrite(((ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(W)) <=> (ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) <=> (ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) | ssPv4(V)) <=> ((ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) | ssPv4(V)))), rewrite(((ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) | ssPv4(V)) <=> (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) | ssPv4(V)) <=> (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(1071,plain,
% 0.63/0.82 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[1070])).
% 0.63/0.82 tff(1072,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 0.63/0.82 tff(1073,plain,
% 0.63/0.82 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.63/0.82 tff(1074,plain,
% 0.63/0.82 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1073, 1069])).
% 0.63/0.82 tff(1075,plain,(
% 0.63/0.82 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.63/0.82 inference(skolemize,[status(sab)],[1074])).
% 0.63/0.82 tff(1076,plain,
% 0.63/0.82 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1075, 1068])).
% 0.63/0.82 tff(1077,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1078,plain,
% 0.63/0.82 ((ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1079,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0)))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1078])).
% 0.63/0.82 tff(1080,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1079, 1077])).
% 0.63/0.82 tff(1081,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1082,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 0.63/0.82 tff(1083,plain,
% 0.63/0.82 (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1082, 1076, 14, 41])).
% 0.63/0.82 tff(1084,plain,
% 0.63/0.82 (ssPv4(skf3(elem!0))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1083, 1066, 885, 3])).
% 0.63/0.82 tff(1085,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1086,plain,
% 0.63/0.82 (((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv1(skf3(elem!0)))) <=> ((~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1087,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0)))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1086])).
% 0.63/0.82 tff(1088,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1087, 1085])).
% 0.63/0.82 tff(1089,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv1(skf3(elem!0))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1090,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 0.63/0.82 tff(1091,plain,
% 0.63/0.82 ((~ssPv2(elem!0)) | ssPv4(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1090, 188, 14])).
% 0.63/0.82 tff(1092,plain,
% 0.63/0.82 (~ssPv1(skf3(elem!0))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1091, 1066, 765, 3])).
% 0.63/0.82 tff(1093,plain,
% 0.63/0.82 (~ssPv2(skf3(elem!0))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[829, 1084, 765, 3])).
% 0.63/0.82 tff(1094,plain,
% 0.63/0.82 (ssPv2(skf3(skf3(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[595, 1093, 1066, 1084])).
% 0.63/0.82 tff(1095,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1096,plain,
% 0.63/0.82 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0))))) <=> ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1097,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1096])).
% 0.63/0.82 tff(1098,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1097, 1095])).
% 0.63/0.82 tff(1099,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1100,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.63/0.82 tff(1101,plain,
% 0.63/0.82 ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1100, 134, 218])).
% 0.63/0.82 tff(1102,plain,
% 0.63/0.82 (ssPv3(skf3(skf3(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1101, 1094, 1084, 1092])).
% 0.63/0.82 tff(1103,plain,
% 0.63/0.82 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(skf3(elem!0), skf2(skf3(elem!0)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1104,plain,
% 0.63/0.82 (ssRr(skf3(elem!0), skf2(skf3(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1103, 39])).
% 0.63/0.82 tff(1105,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1106,plain,
% 0.63/0.82 ((ssPv3(skf2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0))) <=> (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1107,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1106])).
% 0.63/0.82 tff(1108,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1107, 1105])).
% 0.63/0.82 tff(1109,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1110,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 0.63/0.82 tff(1111,plain,
% 0.63/0.82 (ssPv4(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf2(skf3(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1110, 449, 14, 218, 1104])).
% 0.63/0.82 tff(1112,plain,
% 0.63/0.82 (ssPv3(skf2(skf3(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1111, 1094, 3, 1084])).
% 0.63/0.82 tff(1113,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1114,plain,
% 0.63/0.82 (((~ssPv3(skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))) <=> (ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1115,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1114])).
% 0.63/0.82 tff(1116,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1115, 1113])).
% 0.63/0.82 tff(1117,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1118,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 0.63/0.82 tff(1119,plain,
% 0.63/0.82 (ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1118, 784, 218, 1104])).
% 0.63/0.82 tff(1120,plain,
% 0.63/0.82 (ssPv4(skf3(skf3(elem!0)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1119, 1112, 1066, 1102])).
% 0.63/0.82 tff(1121,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1122,plain,
% 0.63/0.82 (((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0))) <=> (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1123,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0)))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1122])).
% 0.63/0.82 tff(1124,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1123, 1121])).
% 0.63/0.82 tff(1125,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1126,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1125, 1124])).
% 0.63/0.82 tff(1127,plain,
% 0.63/0.82 (ssPv2(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1126, 228, 218, 403])).
% 0.63/0.82 tff(1128,plain,
% 0.63/0.82 (~ssPv3(skf3(skf3(skf3(elem!0))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1127, 1102, 1093, 1094])).
% 0.63/0.82 tff(1129,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[622, 1128, 1102, 1120, 1084])).
% 0.63/0.82 tff(1130,plain,(ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(1131,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1132,plain,
% 0.63/0.82 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv2(elem!0))) <=> ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1133,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1132])).
% 0.63/0.83 tff(1134,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1133, 1131])).
% 0.63/0.83 tff(1135,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv2(elem!0)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1136,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.63/0.83 tff(1137,plain,
% 0.63/0.83 ((~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1136, 822, 41])).
% 0.63/0.83 tff(1138,plain,
% 0.63/0.83 ((~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1137, 765, 1130])).
% 0.63/0.83 tff(1139,plain,
% 0.63/0.83 (~ssPv2(skf2(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1138, 2])).
% 0.63/0.83 tff(1140,plain,
% 0.63/0.83 (ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[466, 1130])).
% 0.63/0.83 tff(1141,plain,
% 0.63/0.83 (~ssPv3(skf2(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1140, 2, 1139])).
% 0.63/0.83 tff(1142,plain,
% 0.63/0.83 (ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[488, 1141, 1, 2])).
% 0.63/0.83 tff(1143,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1144,plain,
% 0.63/0.83 ((ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))) <=> ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1145,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1144])).
% 0.63/0.83 tff(1146,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1145, 1143])).
% 0.63/0.83 tff(1147,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1148,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 0.63/0.83 tff(1149,plain,
% 0.63/0.83 ((~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1148, 747, 41, 285])).
% 0.63/0.83 tff(1150,plain,
% 0.63/0.83 (ssPv2(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1149, 765])).
% 0.63/0.83 tff(1151,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1150, 1142, 1141, 1139])).
% 0.63/0.83 tff(1152,plain,(ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(1153,plain,
% 0.63/0.83 (ssPv4(skf2(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1152, 1])).
% 0.63/0.83 tff(1154,assumption,(ssPv4(skf2(elem!0))), introduced(assumption)).
% 0.63/0.83 tff(1155,assumption,(~ssPv1(skf2(elem!0))), introduced(assumption)).
% 0.63/0.83 tff(1156,plain,
% 0.63/0.83 (ssPv3(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[892, 765])).
% 0.63/0.83 tff(1157,plain,
% 0.63/0.83 (ssPv3(elem!0)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1156, 1155, 1154])).
% 0.63/0.83 tff(1158,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1159,plain,
% 0.63/0.83 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> ((~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1160,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1159])).
% 0.63/0.83 tff(1161,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1160, 1158])).
% 0.63/0.83 tff(1162,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1163,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.63/0.83 tff(1164,plain,
% 0.63/0.83 ((~ssPv3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1163, 246, 14, 41])).
% 0.63/0.83 tff(1165,plain,
% 0.63/0.83 ((~ssPv3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1164, 1130])).
% 0.63/0.83 tff(1166,plain,
% 0.63/0.83 (ssPv3(skf3(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1165, 1157, 1154])).
% 0.63/0.83 tff(1167,plain,
% 0.63/0.83 (^[V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1168,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1167])).
% 0.63/0.83 tff(1169,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1170,plain,
% 0.63/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(U))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(U))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(U)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(U))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) | ssPv1(U)) <=> (((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(U))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(U))) | ssPv1(U)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) | ssPv1(U)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1171,plain,
% 0.63/0.83 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) | ssPv1(U)) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1170])).
% 0.63/0.83 tff(1172,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) | ssPv1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.63/0.83 tff(1173,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 0.63/0.83 tff(1174,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1173, 1169])).
% 0.63/0.83 tff(1175,plain,(
% 0.63/0.83 ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[1174])).
% 0.63/0.83 tff(1176,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1175, 1168])).
% 0.63/0.83 tff(1177,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1178,plain,
% 0.63/0.83 (((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)) | (~ssPv3(elem!0))) <=> ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1179,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)) | (~ssPv3(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1178])).
% 0.63/0.83 tff(1180,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)) | (~ssPv3(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1179, 1177])).
% 0.63/0.83 tff(1181,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)) | (~ssPv3(elem!0)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1182,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 0.63/0.83 tff(1183,plain,
% 0.63/0.83 ((~ssPv3(elem!0)) | ssPv1(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1182, 1176, 41])).
% 0.63/0.83 tff(1184,plain,
% 0.63/0.83 ((~ssPv3(elem!0)) | ssPv1(elem!0) | ssPv1(skf2(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1183, 1130])).
% 0.63/0.83 tff(1185,plain,
% 0.63/0.83 (ssPv1(elem!0)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1184, 1157, 1155])).
% 0.63/0.83 tff(1186,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1187,plain,
% 0.63/0.83 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0))) <=> ((~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1188,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1187])).
% 0.63/0.83 tff(1189,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1188, 1186])).
% 0.63/0.83 tff(1190,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1191,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 0.63/0.83 tff(1192,plain,
% 0.63/0.83 ((~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1191, 413, 14, 41])).
% 0.63/0.83 tff(1193,plain,
% 0.63/0.83 ((~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1192, 1130])).
% 0.63/0.83 tff(1194,plain,
% 0.63/0.83 (~ssPv4(skf3(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1193, 1185, 1155])).
% 0.63/0.83 tff(1195,plain,
% 0.63/0.83 ((~ssPv3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[850, 765])).
% 0.63/0.83 tff(1196,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1195, 1194, 1166, 1157])).
% 0.63/0.83 tff(1197,plain,(ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(1198,plain,
% 0.63/0.83 (ssPv1(skf2(elem!0))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1197, 1153])).
% 0.63/0.83 tff(1199,plain,
% 0.63/0.83 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1200,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1199])).
% 0.63/0.83 tff(1201,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1202,plain,
% 0.63/0.83 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssPv4(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> (((~ssPv4(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(W))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssRr(V, X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv3(X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv3(X))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | (~ssPv1(V))) <=> (((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv1(V))))), rewrite((((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv1(V))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | (~ssPv1(V))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1203,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1202])).
% 0.63/0.83 tff(1204,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | (~ssPv1(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.63/0.83 tff(1205,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.63/0.83 tff(1206,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1205, 1201])).
% 0.63/0.83 tff(1207,plain,(
% 0.63/0.83 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[1206])).
% 0.63/0.83 tff(1208,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1207, 1200])).
% 0.63/0.83 tff(1209,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1210,plain,
% 0.63/0.83 (((~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0)))) <=> ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1211,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1210])).
% 0.63/0.83 tff(1212,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1211, 1209])).
% 0.63/0.83 tff(1213,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0))))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1214,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 0.63/0.83 tff(1215,plain,
% 0.63/0.83 ((~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1214, 1208, 41, 285])).
% 0.63/0.83 tff(1216,plain,
% 0.63/0.83 ((~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1215, 765, 1130])).
% 0.63/0.83 tff(1217,plain,
% 0.63/0.83 (~ssPv3(skf2(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1216, 1198])).
% 0.63/0.83 tff(1218,plain,
% 0.63/0.83 ((~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[931, 765])).
% 0.63/0.83 tff(1219,plain,
% 0.63/0.83 (ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1218, 1217, 1153])).
% 0.63/0.83 tff(1220,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1221,plain,
% 0.63/0.83 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1222,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0)))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1221])).
% 0.63/0.83 tff(1223,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1222, 1220])).
% 0.63/0.83 tff(1224,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1225,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.63/0.83 tff(1226,plain,
% 0.63/0.83 ((~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv1(skf2(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1225, 413, 41, 285])).
% 0.63/0.83 tff(1227,plain,
% 0.63/0.83 ((~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1226, 1130])).
% 0.63/0.83 tff(1228,plain,
% 0.63/0.83 (ssPv1(skf2(skf2(elem!0)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1227, 1198, 1153])).
% 0.63/0.83 tff(1229,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1230,plain,
% 0.63/0.84 (((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0)))) <=> ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1231,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1230])).
% 0.63/0.84 tff(1232,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1231, 1229])).
% 0.63/0.84 tff(1233,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1234,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 0.63/0.84 tff(1235,plain,
% 0.63/0.84 ((~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1234, 688, 41, 285])).
% 0.63/0.84 tff(1236,plain,
% 0.63/0.84 ((~ssPv1(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1235, 765])).
% 0.63/0.84 tff(1237,plain,
% 0.63/0.84 (~ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1236, 1228, 1198])).
% 0.63/0.84 tff(1238,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[903, 1237, 1219, 1, 1198])).
% 0.63/0.84 tff(1239,plain,(ssPv3(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(1240,plain,
% 0.63/0.84 (~ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[300, 2, 1141, 1239])).
% 0.63/0.84 tff(1241,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1242,plain,
% 0.63/0.84 ((ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> (ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1243,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1242])).
% 0.63/0.84 tff(1244,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1243, 1241])).
% 0.63/0.84 tff(1245,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1246,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.63/0.84 tff(1247,plain,
% 0.63/0.84 (ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1246, 24, 285])).
% 0.63/0.84 tff(1248,plain,
% 0.63/0.84 (ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1247, 2, 1141, 1240])).
% 0.63/0.84 tff(1249,plain,
% 0.63/0.84 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(skf2(elem!0)), skf2(elem!0))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1250,plain,
% 0.63/0.84 (ssRr(skf3(skf2(elem!0)), skf2(elem!0))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1249, 12])).
% 0.63/0.84 tff(1251,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1252,plain,
% 0.63/0.84 ((ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))) <=> (ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1253,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1252])).
% 0.63/0.84 tff(1254,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0)))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1253, 1251])).
% 0.63/0.84 tff(1255,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1256,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv3(skf3(skf2(elem!0))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 0.63/0.84 tff(1257,plain,
% 0.63/0.84 (ssPv4(skf2(elem!0)) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv3(skf3(skf2(elem!0))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1256, 331, 1250, 285])).
% 0.63/0.84 tff(1258,plain,
% 0.63/0.84 (~ssPv3(skf3(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1257, 1248, 2, 1240])).
% 0.63/0.84 tff(1259,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1260,plain,
% 0.63/0.84 (((~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0))) <=> ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1261,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0)))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1260])).
% 0.63/0.84 tff(1262,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1261, 1259])).
% 0.63/0.84 tff(1263,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1264,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 0.63/0.84 tff(1265,plain,
% 0.63/0.84 ((~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf3(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1264, 375, 41, 1250])).
% 0.63/0.84 tff(1266,plain,
% 0.63/0.84 (ssPv2(skf2(elem!0)) | ssPv1(skf3(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1265, 765, 1130])).
% 0.63/0.84 tff(1267,plain,
% 0.63/0.84 (ssPv1(skf3(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1266, 1139])).
% 0.63/0.84 tff(1268,plain,
% 0.63/0.84 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1269,plain,
% 0.63/0.84 (ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1268, 12])).
% 0.63/0.84 tff(1270,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssPv1(skf3(skf3(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssPv1(skf3(skf3(skf2(elem!0))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1271,plain,
% 0.63/0.84 ((ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf3(skf2(elem!0))))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssPv1(skf3(skf3(skf2(elem!0))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1272,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf3(skf2(elem!0))))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssPv1(skf3(skf3(skf2(elem!0)))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1271])).
% 0.63/0.84 tff(1273,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf3(skf2(elem!0))))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssPv1(skf3(skf3(skf2(elem!0))))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1272, 1270])).
% 0.63/0.84 tff(1274,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf3(skf2(elem!0))))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1275,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | (~ssPv1(skf3(skf3(skf2(elem!0)))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 0.63/0.84 tff(1276,plain,
% 0.63/0.84 ((~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(skf2(elem!0)))) | (~ssPv1(skf3(skf3(skf2(elem!0)))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1275, 357, 1250, 1269])).
% 0.63/0.84 tff(1277,plain,
% 0.63/0.84 (~ssPv1(skf3(skf3(skf2(elem!0))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1276, 1267, 1239, 1139])).
% 0.63/0.84 tff(1278,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv1(skf3(skf3(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv1(skf3(skf3(skf2(elem!0)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1279,plain,
% 0.63/0.84 ((ssPv2(skf2(elem!0)) | ssPv1(skf3(skf3(skf2(elem!0)))) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0)))) <=> (ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv1(skf3(skf3(skf2(elem!0)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1280,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf3(skf3(skf2(elem!0)))) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv1(skf3(skf3(skf2(elem!0))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1279])).
% 0.63/0.84 tff(1281,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf3(skf3(skf2(elem!0)))) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv1(skf3(skf3(skf2(elem!0)))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1280, 1278])).
% 0.63/0.84 tff(1282,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf3(skf3(skf2(elem!0)))) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1283,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf3(skf2(elem!0))) | (~ssRr(skf3(skf2(elem!0)), skf2(elem!0))) | (~ssRr(skf3(skf3(skf2(elem!0))), skf3(skf2(elem!0)))) | ssPv1(skf3(skf3(skf2(elem!0))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 0.63/0.84 tff(1284,plain,
% 0.63/0.84 (ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf3(skf2(elem!0))) | ssPv1(skf3(skf3(skf2(elem!0))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1283, 170, 1250, 1269])).
% 0.63/0.84 tff(1285,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1284, 1277, 1258, 2, 1139])).
% 0.63/0.84 tff(1286,plain,(ssPv4(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(1287,plain,
% 0.63/0.84 (ssPv1(skf2(elem!0))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1197, 1286])).
% 0.63/0.84 tff(1288,plain,
% 0.63/0.84 (~ssPv3(skf2(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1216, 1287])).
% 0.63/0.84 tff(1289,plain,
% 0.63/0.84 (ssPv4(skf2(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1218, 1288, 1286])).
% 0.63/0.84 tff(1290,plain,
% 0.63/0.84 (ssPv3(elem!0)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[957, 1289, 1286, 1239])).
% 0.63/0.84 tff(1291,plain,
% 0.63/0.84 (ssPv1(skf2(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1227, 1287, 1286])).
% 0.63/0.84 tff(1292,plain,
% 0.63/0.84 (~ssPv2(skf2(skf2(elem!0)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1236, 1291, 1287])).
% 0.63/0.84 tff(1293,plain,
% 0.63/0.84 (ssPv2(skf2(elem!0))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1150, 1289, 1288])).
% 0.63/0.84 tff(1294,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[640, 1293, 1292, 1290, 1239])).
% 0.63/0.84 % SZS output end Proof
% 0.63/0.85 % E exiting
%------------------------------------------------------------------------------