%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN796-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:40:02 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.45s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN796-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:47:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.45 % SZS status Unsatisfiable
% 0.18/0.45 % SZS output start Proof
% 0.18/0.45 tff(ssPv2_type, type, (
% 0.18/0.45 ssPv2: $i > $o)).
% 0.18/0.45 tff(elem_0_type, type, (
% 0.18/0.45 elem_0: $i)).
% 0.18/0.45 tff(ssPv1_type, type, (
% 0.18/0.45 ssPv1: $i > $o)).
% 0.18/0.45 tff(skf2_type, type, (
% 0.18/0.45 skf2: $i > $i)).
% 0.18/0.45 tff(ssPv4_type, type, (
% 0.18/0.45 ssPv4: $i > $o)).
% 0.18/0.45 tff(skf3_type, type, (
% 0.18/0.45 skf3: $i > $i)).
% 0.18/0.45 tff(ssPv3_type, type, (
% 0.18/0.45 ssPv3: $i > $o)).
% 0.18/0.45 tff(ssRr_type, type, (
% 0.18/0.45 ssRr: ( $i * $i ) > $o)).
% 0.18/0.45 tff(1,assumption,(~ssPv2(elem!0)), introduced(assumption)).
% 0.18/0.45 tff(2,assumption,(~ssPv1(skf3(elem!0))), introduced(assumption)).
% 0.18/0.45 tff(3,assumption,(~ssPv1(elem!0)), introduced(assumption)).
% 0.18/0.45 tff(4,assumption,(~ssPv3(skf3(elem!0))), introduced(assumption)).
% 0.18/0.45 tff(5,assumption,(~ssPv2(skf2(elem!0))), introduced(assumption)).
% 0.18/0.45 tff(6,assumption,(~ssPv4(skf3(elem!0))), introduced(assumption)).
% 0.18/0.45 tff(7,plain,
% 0.18/0.45 (^[U: $i] : refl(ssRr(skf3(U), U) <=> ssRr(skf3(U), U))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(8,plain,
% 0.18/0.45 (![U: $i] : ssRr(skf3(U), U) <=> ![U: $i] : ssRr(skf3(U), U)),
% 0.18/0.45 inference(quant_intro,[status(thm)],[7])).
% 0.18/0.45 tff(9,plain,
% 0.18/0.45 (![U: $i] : ssRr(skf3(U), U) <=> ![U: $i] : ssRr(skf3(U), U)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(10,axiom,(![U: $i] : ssRr(skf3(U), U)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.18/0.45 tff(11,plain,
% 0.18/0.45 (![U: $i] : ssRr(skf3(U), U)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.18/0.45 tff(12,plain,(
% 0.18/0.45 ![U: $i] : ssRr(skf3(U), U)),
% 0.18/0.45 inference(skolemize,[status(sab)],[11])).
% 0.18/0.45 tff(13,plain,
% 0.18/0.45 (![U: $i] : ssRr(skf3(U), U)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.18/0.45 tff(14,plain,
% 0.18/0.45 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(elem!0), elem!0)),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(15,plain,
% 0.18/0.45 (ssRr(skf3(elem!0), elem!0)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.18/0.45 tff(16,plain,
% 0.18/0.45 (^[V: $i, U: $i] : refl((ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) <=> (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(17,plain,
% 0.18/0.45 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.45 tff(18,plain,
% 0.18/0.45 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(19,plain,
% 0.18/0.45 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) <=> ((ssPv3(V) | (~ssRr(U, V))) | ssPv1(U)))), rewrite(((ssPv3(V) | (~ssRr(U, V))) | ssPv1(U)) <=> (ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) <=> (ssPv1(U) | ssPv3(V) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) <=> ((ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) | ssPv3(U)))), rewrite(((ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) | ssPv3(U)) <=> (ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) <=> (ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) | ssPv4(U)))), rewrite(((ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) | ssPv4(U)) <=> (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) | ssPv4(U)) <=> (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(20,plain,
% 0.18/0.45 (![V: $i, U: $i] : (((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) | ssPv4(U)) <=> ![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.45 tff(21,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.18/0.45 tff(22,plain,
% 0.18/0.45 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.45 tff(23,plain,
% 0.18/0.45 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.45 tff(24,plain,(
% 0.18/0.45 ![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.18/0.45 inference(skolemize,[status(sab)],[23])).
% 0.18/0.45 tff(25,plain,
% 0.18/0.45 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.18/0.45 tff(26,plain,
% 0.18/0.45 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(27,plain,
% 0.18/0.45 ((ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(28,plain,
% 0.18/0.45 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[27])).
% 0.18/0.45 tff(29,plain,
% 0.18/0.45 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[28, 26])).
% 0.18/0.45 tff(30,plain,
% 0.18/0.45 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(31,plain,
% 0.18/0.45 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.45 tff(32,plain,
% 0.18/0.45 (ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[31, 25, 15])).
% 0.18/0.45 tff(33,plain,
% 0.18/0.45 (ssPv3(elem!0)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[32, 6, 2, 4])).
% 0.18/0.45 tff(34,plain,
% 0.18/0.45 (^[U: $i] : refl(ssRr(U, skf2(U)) <=> ssRr(U, skf2(U)))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(35,plain,
% 0.18/0.45 (![U: $i] : ssRr(U, skf2(U)) <=> ![U: $i] : ssRr(U, skf2(U))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.45 tff(36,plain,
% 0.18/0.45 (![U: $i] : ssRr(U, skf2(U)) <=> ![U: $i] : ssRr(U, skf2(U))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(37,axiom,(![U: $i] : ssRr(U, skf2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.18/0.45 tff(38,plain,
% 0.18/0.45 (![U: $i] : ssRr(U, skf2(U))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.45 tff(39,plain,(
% 0.18/0.45 ![U: $i] : ssRr(U, skf2(U))),
% 0.18/0.45 inference(skolemize,[status(sab)],[38])).
% 0.18/0.45 tff(40,plain,
% 0.18/0.45 (![U: $i] : ssRr(U, skf2(U))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.18/0.45 tff(41,plain,
% 0.18/0.45 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(elem!0, skf2(elem!0))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(42,plain,
% 0.18/0.45 (ssRr(elem!0, skf2(elem!0))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.18/0.45 tff(43,plain,
% 0.18/0.45 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(44,plain,
% 0.18/0.45 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.45 tff(45,plain,
% 0.18/0.45 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(46,plain,
% 0.18/0.45 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) <=> ((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv2(W)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> ((ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv1(V)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv1(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(47,plain,
% 0.18/0.45 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[46])).
% 0.18/0.45 tff(48,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 0.18/0.45 tff(49,plain,
% 0.18/0.45 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.18/0.45 tff(50,plain,
% 0.18/0.45 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.18/0.45 tff(51,plain,(
% 0.18/0.45 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.45 inference(skolemize,[status(sab)],[50])).
% 0.18/0.45 tff(52,plain,
% 0.18/0.45 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.18/0.45 tff(53,plain,
% 0.18/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(54,plain,
% 0.18/0.45 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(55,plain,
% 0.18/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[54])).
% 0.18/0.45 tff(56,plain,
% 0.18/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[55, 53])).
% 0.18/0.45 tff(57,plain,
% 0.18/0.45 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(58,plain,
% 0.18/0.45 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.18/0.45 tff(59,plain,
% 0.18/0.45 (ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[58, 52, 15, 42])).
% 0.18/0.45 tff(60,plain,
% 0.18/0.45 (~ssPv3(elem!0)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[59, 6, 3, 5])).
% 0.18/0.45 tff(61,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[32, 60, 6, 2, 4])).
% 0.18/0.45 tff(62,plain,(ssPv4(skf3(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(63,plain,
% 0.18/0.45 (ssPv4(skf3(elem!0))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[62, 3, 4, 2, 5])).
% 0.18/0.45 tff(64,plain,
% 0.18/0.45 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(skf3(elem!0)), skf3(elem!0))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(65,plain,
% 0.18/0.45 (ssRr(skf3(skf3(elem!0)), skf3(elem!0))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[64, 13])).
% 0.18/0.45 tff(66,plain,
% 0.18/0.45 (^[V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(67,plain,
% 0.18/0.45 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[66])).
% 0.18/0.45 tff(68,plain,
% 0.18/0.45 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(69,plain,
% 0.18/0.45 (^[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)) | ssPv1(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) | ssPv3(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(70,plain,
% 0.18/0.46 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) | ssPv3(V)) <=> ![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[69])).
% 0.18/0.46 tff(71,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.18/0.46 tff(72,plain,
% 0.18/0.46 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.46 tff(73,plain,
% 0.18/0.46 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.18/0.46 tff(74,plain,(
% 0.18/0.46 ![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[73])).
% 0.18/0.46 tff(75,plain,
% 0.18/0.46 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.18/0.46 tff(76,plain,
% 0.18/0.46 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(77,plain,
% 0.18/0.46 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0)))) <=> (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(78,plain,
% 0.18/0.46 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[77])).
% 0.18/0.46 tff(79,plain,
% 0.18/0.46 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[78, 76])).
% 0.18/0.46 tff(80,plain,
% 0.18/0.46 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(81,plain,
% 0.18/0.46 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.46 tff(82,plain,
% 0.18/0.46 (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[81, 75, 65])).
% 0.18/0.46 tff(83,plain,
% 0.18/0.46 (ssPv2(skf3(skf3(elem!0)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[82, 63, 4, 2])).
% 0.18/0.46 tff(84,plain,
% 0.18/0.46 (^[V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(85,plain,
% 0.18/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.46 tff(86,plain,
% 0.18/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(87,plain,
% 0.18/0.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) <=> (((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) | ssPv3(U)) <=> (((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(88,plain,
% 0.18/0.46 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) | ssPv3(U)) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[87])).
% 0.18/0.46 tff(89,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.18/0.46 tff(90,plain,
% 0.18/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.46 tff(91,plain,
% 0.18/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.18/0.46 tff(92,plain,(
% 0.18/0.46 ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[91])).
% 0.18/0.46 tff(93,plain,
% 0.18/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.18/0.46 tff(94,plain,
% 0.18/0.46 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(95,plain,
% 0.18/0.46 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(96,plain,
% 0.18/0.46 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[95])).
% 0.18/0.46 tff(97,plain,
% 0.18/0.46 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[96, 94])).
% 0.18/0.46 tff(98,plain,
% 0.18/0.46 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(99,plain,
% 0.18/0.46 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.46 tff(100,plain,
% 0.18/0.46 (ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[99, 93, 15])).
% 0.18/0.46 tff(101,plain,
% 0.18/0.46 (ssPv2(skf3(elem!0))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[100, 63, 3, 4])).
% 0.18/0.46 tff(102,plain,
% 0.18/0.46 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(103,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[102])).
% 0.18/0.46 tff(104,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(105,plain,
% 0.18/0.46 (^[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))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) <=> (((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) | ssPv3(V)) <=> (((~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(106,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.46 tff(107,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 0.18/0.46 tff(108,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.46 tff(109,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.18/0.46 tff(110,plain,(
% 0.18/0.46 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[109])).
% 0.18/0.46 tff(111,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.18/0.46 tff(112,plain,
% 0.18/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(113,plain,
% 0.18/0.46 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(114,plain,
% 0.18/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[113])).
% 0.18/0.46 tff(115,plain,
% 0.18/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[114, 112])).
% 0.18/0.46 tff(116,plain,
% 0.18/0.46 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(117,plain,
% 0.18/0.46 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.18/0.46 tff(118,plain,
% 0.18/0.46 ((~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[117, 111, 15, 42])).
% 0.18/0.46 tff(119,plain,
% 0.18/0.46 (ssPv3(elem!0)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[118, 101, 3, 5])).
% 0.18/0.46 tff(120,plain,
% 0.18/0.46 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(121,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[120])).
% 0.18/0.46 tff(122,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(123,plain,
% 0.18/0.46 (^[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))) | (~ssPv3(W))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv2(V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv2(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) | ssPv1(X)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv1(X)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(124,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) | ssPv1(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[123])).
% 0.18/0.46 tff(125,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) | ssPv1(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.18/0.46 tff(126,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.18/0.46 tff(127,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.18/0.46 tff(128,plain,(
% 0.18/0.46 ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[127])).
% 0.18/0.46 tff(129,plain,
% 0.18/0.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.18/0.46 tff(130,plain,
% 0.18/0.46 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(131,plain,
% 0.18/0.46 ((ssPv1(elem!0) | (~ssPv2(skf3(skf3(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)) | (~ssPv3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(132,plain,
% 0.18/0.46 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(elem!0) | (~ssPv2(skf3(skf3(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)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[131])).
% 0.18/0.46 tff(133,plain,
% 0.18/0.46 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(elem!0) | (~ssPv2(skf3(skf3(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)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[132, 130])).
% 0.18/0.47 tff(134,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(elem!0) | (~ssPv2(skf3(skf3(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)) | (~ssPv3(elem!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(135,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.18/0.47 tff(136,plain,
% 0.18/0.47 ((~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[135, 129, 15, 65])).
% 0.18/0.47 tff(137,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[136, 119, 101, 3, 83])).
% 0.18/0.47 tff(138,plain,(ssPv1(elem!0) | ssPv2(skf2(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(139,plain,
% 0.18/0.47 (ssPv1(elem!0)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[138, 2, 4, 5])).
% 0.18/0.47 tff(140,plain,
% 0.18/0.47 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) <=> (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(141,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[140])).
% 0.18/0.47 tff(142,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(143,plain,
% 0.18/0.47 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) | ssPv4(U)))), rewrite(((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) | ssPv4(U)) <=> (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) | ssPv4(U)) <=> (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(144,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[143])).
% 0.18/0.47 tff(145,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause11')).
% 0.18/0.47 tff(146,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.18/0.47 tff(147,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.18/0.47 tff(148,plain,(
% 0.18/0.47 ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[147])).
% 0.18/0.47 tff(149,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.18/0.47 tff(150,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(151,plain,
% 0.18/0.47 ((ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(152,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[151])).
% 0.18/0.47 tff(153,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0))),
% 0.18/0.47 inference(transitivity,[status(thm)],[152, 150])).
% 0.18/0.47 tff(154,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(155,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.18/0.47 tff(156,plain,
% 0.18/0.47 ((~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[155, 149, 15])).
% 0.18/0.47 tff(157,plain,
% 0.18/0.47 (ssPv2(elem!0)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[156, 6, 4, 139])).
% 0.18/0.47 tff(158,plain,
% 0.18/0.47 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(159,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[158])).
% 0.18/0.47 tff(160,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(161,plain,
% 0.18/0.47 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv3(V))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) <=> ((ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv2(W)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(162,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[161])).
% 0.18/0.47 tff(163,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause18')).
% 0.18/0.47 tff(164,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.18/0.47 tff(165,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.18/0.47 tff(166,plain,(
% 0.18/0.47 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[165])).
% 0.18/0.47 tff(167,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.18/0.47 tff(168,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(169,plain,
% 0.18/0.47 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(170,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv2(elem!0))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[169])).
% 0.18/0.47 tff(171,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[170, 168])).
% 0.18/0.47 tff(172,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(173,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv2(elem!0))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.18/0.47 tff(174,plain,
% 0.18/0.47 (ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv2(elem!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[173, 167, 15, 42])).
% 0.18/0.47 tff(175,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[174, 157, 6, 5, 33])).
% 0.18/0.47 tff(176,plain,(ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(177,plain,
% 0.18/0.47 (ssPv4(skf3(elem!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[176, 2, 5, 4])).
% 0.18/0.47 tff(178,plain,
% 0.18/0.47 (ssPv2(skf3(skf3(elem!0)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[82, 177, 4, 2])).
% 0.18/0.47 tff(179,plain,
% 0.18/0.47 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(skf3(elem!0), skf2(skf3(elem!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(180,plain,
% 0.18/0.47 (ssRr(skf3(elem!0), skf2(skf3(elem!0)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[179, 40])).
% 0.18/0.47 tff(181,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf2(skf3(elem!0))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(182,plain,
% 0.18/0.47 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0))))) <=> (ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf2(skf3(elem!0))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(183,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf2(skf3(elem!0)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[182])).
% 0.18/0.47 tff(184,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf2(skf3(elem!0))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[183, 181])).
% 0.18/0.47 tff(185,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(186,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf2(skf3(elem!0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.18/0.47 tff(187,plain,
% 0.18/0.47 (ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv2(skf2(skf3(elem!0)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[186, 111, 65, 180])).
% 0.18/0.47 tff(188,plain,
% 0.18/0.47 (ssPv2(skf2(skf3(elem!0)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[187, 178, 4, 2])).
% 0.18/0.47 tff(189,plain,
% 0.18/0.47 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(190,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[189])).
% 0.18/0.47 tff(191,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(192,plain,
% 0.18/0.47 (^[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(W))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) | ssPv3(U)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(193,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[192])).
% 0.18/0.47 tff(194,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause26')).
% 0.18/0.47 tff(195,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.18/0.47 tff(196,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.18/0.47 tff(197,plain,(
% 0.18/0.47 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[196])).
% 0.18/0.47 tff(198,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.18/0.47 tff(199,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(200,plain,
% 0.18/0.47 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf3(elem!0)) | (~ssPv2(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(201,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf3(elem!0)) | (~ssPv2(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[200])).
% 0.18/0.47 tff(202,plain,
% 0.18/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf3(elem!0)) | (~ssPv2(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0)))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[201, 199])).
% 0.18/0.47 tff(203,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv2(skf3(elem!0)) | (~ssPv2(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(204,plain,
% 0.18/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.18/0.47 tff(205,plain,
% 0.18/0.47 (ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(skf2(skf3(elem!0))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[204, 198, 15, 180])).
% 0.18/0.47 tff(206,plain,
% 0.18/0.47 (ssPv2(skf3(elem!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[205, 188, 4, 139])).
% 0.18/0.47 tff(207,plain,
% 0.18/0.47 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W)) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(208,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[207])).
% 0.18/0.47 tff(209,plain,
% 0.18/0.47 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(210,plain,
% 0.18/0.47 (^[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(W, V))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) <=> (((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv2(V))))), rewrite((((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv2(V))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) | ssPv3(W)) <=> (((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(W)))), rewrite((((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(W)) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) | ssPv3(W)) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(211,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[210])).
% 0.18/0.48 tff(212,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) | ssPv3(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.18/0.48 tff(213,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.18/0.48 tff(214,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.18/0.48 tff(215,plain,(
% 0.18/0.48 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.48 inference(skolemize,[status(sab)],[214])).
% 0.18/0.48 tff(216,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.18/0.48 tff(217,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(218,plain,
% 0.18/0.48 (((~ssPv2(skf3(skf3(elem!0)))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(219,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(skf3(skf3(elem!0)))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(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] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[218])).
% 0.18/0.48 tff(220,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(skf3(skf3(elem!0)))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(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] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[219, 217])).
% 0.18/0.48 tff(221,plain,
% 0.18/0.48 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(skf3(skf3(elem!0)))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(222,plain,
% 0.18/0.48 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.18/0.48 tff(223,plain,
% 0.18/0.48 ((~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[222, 216, 15, 65])).
% 0.18/0.48 tff(224,plain,
% 0.18/0.48 (ssPv3(skf3(skf3(elem!0)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[223, 206, 139, 178])).
% 0.18/0.48 tff(225,plain,
% 0.18/0.48 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(226,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[225])).
% 0.18/0.48 tff(227,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(228,plain,
% 0.18/0.48 (^[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)) | (~ssPv1(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(U))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(U))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(229,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[228])).
% 0.18/0.48 tff(230,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) | ssPv1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.18/0.48 tff(231,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.18/0.48 tff(232,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.18/0.48 tff(233,plain,(
% 0.18/0.48 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[232])).
% 0.18/0.48 tff(234,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.18/0.48 tff(235,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(236,plain,
% 0.18/0.48 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))) <=> (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(237,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv1(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)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[236])).
% 0.18/0.48 tff(238,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv1(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)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[237, 235])).
% 0.18/0.48 tff(239,plain,
% 0.18/0.48 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(240,plain,
% 0.18/0.48 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.18/0.48 tff(241,plain,
% 0.18/0.48 (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[240, 234, 65])).
% 0.18/0.48 tff(242,plain,
% 0.18/0.48 (~ssPv1(skf3(skf3(elem!0)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[241, 206, 2, 224])).
% 0.18/0.48 tff(243,plain,
% 0.18/0.48 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(244,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[243])).
% 0.18/0.48 tff(245,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(246,plain,
% 0.18/0.48 (^[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))) | (~ssPv2(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv2(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv1(V)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv1(V)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv1(V)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv1(V)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(247,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[246])).
% 0.18/0.48 tff(248,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause27')).
% 0.18/0.48 tff(249,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.18/0.48 tff(250,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.18/0.48 tff(251,plain,(
% 0.18/0.48 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[250])).
% 0.18/0.48 tff(252,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.18/0.48 tff(253,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(254,plain,
% 0.18/0.48 ((ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(255,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[254])).
% 0.18/0.48 tff(256,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[255, 253])).
% 0.18/0.48 tff(257,plain,
% 0.18/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(258,plain,
% 0.18/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.18/0.48 tff(259,plain,
% 0.18/0.48 (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv1(skf3(skf3(elem!0)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[258, 252, 15, 65])).
% 0.18/0.48 tff(260,plain,
% 0.18/0.48 (~ssPv4(elem!0)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[259, 206, 2, 242])).
% 0.18/0.48 tff(261,plain,
% 0.18/0.48 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(262,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[261])).
% 0.18/0.48 tff(263,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(264,plain,
% 0.18/0.48 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv4(W)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) | ssPv1(V)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) | ssPv1(V)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) | ssPv1(V)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) | ssPv1(V)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(265,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[264])).
% 0.18/0.48 tff(266,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 0.18/0.48 tff(267,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.18/0.48 tff(268,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.18/0.48 tff(269,plain,(
% 0.18/0.48 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.18/0.48 inference(skolemize,[status(sab)],[268])).
% 0.18/0.48 tff(270,plain,
% 0.18/0.48 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[269, 262])).
% 0.18/0.48 tff(271,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(272,plain,
% 0.18/0.48 ((ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0)) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(273,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[272])).
% 0.18/0.48 tff(274,plain,
% 0.18/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[273, 271])).
% 0.18/0.48 tff(275,plain,
% 0.18/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(276,plain,
% 0.18/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.18/0.48 tff(277,plain,
% 0.18/0.48 (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | ssPv1(skf3(skf3(elem!0)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[276, 270, 15, 65])).
% 0.18/0.48 tff(278,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[277, 260, 206, 2, 242])).
% 0.18/0.48 tff(279,plain,(ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(280,plain,
% 0.18/0.48 (ssPv1(skf3(elem!0))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[279, 5, 4])).
% 0.18/0.48 tff(281,plain,
% 0.18/0.48 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(282,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[281])).
% 0.18/0.49 tff(283,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(284,plain,
% 0.18/0.49 (^[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)) | (~ssRr(U, W)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(285,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[284])).
% 0.18/0.49 tff(286,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 0.18/0.49 tff(287,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.18/0.49 tff(288,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[287, 283])).
% 0.18/0.49 tff(289,plain,(
% 0.18/0.49 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[288])).
% 0.18/0.49 tff(290,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[289, 282])).
% 0.18/0.49 tff(291,plain,
% 0.18/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(292,plain,
% 0.18/0.49 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(293,plain,
% 0.18/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[292])).
% 0.18/0.49 tff(294,plain,
% 0.18/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[293, 291])).
% 0.18/0.49 tff(295,plain,
% 0.18/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(296,plain,
% 0.18/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.18/0.49 tff(297,plain,
% 0.18/0.49 (ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[296, 290, 15])).
% 0.18/0.49 tff(298,plain,
% 0.18/0.49 (~ssPv3(elem!0)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[297, 3, 280, 4])).
% 0.18/0.49 tff(299,plain,
% 0.18/0.49 (~ssPv2(skf3(elem!0))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[118, 298, 3, 5])).
% 0.18/0.49 tff(300,plain,
% 0.18/0.49 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(301,plain,
% 0.18/0.49 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(302,plain,
% 0.18/0.49 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[301])).
% 0.18/0.49 tff(303,plain,
% 0.18/0.49 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[302, 300])).
% 0.18/0.49 tff(304,plain,
% 0.18/0.49 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(305,plain,
% 0.18/0.49 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.18/0.49 tff(306,plain,
% 0.18/0.49 (ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[305, 75, 15])).
% 0.18/0.49 tff(307,plain,
% 0.18/0.49 (~ssPv4(elem!0)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[306, 299, 3, 298])).
% 0.18/0.49 tff(308,plain,
% 0.18/0.49 (^[V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(309,plain,
% 0.18/0.49 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[308])).
% 0.18/0.49 tff(310,plain,
% 0.18/0.49 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(311,plain,
% 0.18/0.49 (^[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))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) | ssPv4(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv2(V))) | ssPv4(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv2(V))) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(312,plain,
% 0.18/0.49 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) | ssPv4(V)) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[311])).
% 0.18/0.49 tff(313,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.18/0.49 tff(314,plain,
% 0.18/0.49 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.18/0.49 tff(315,plain,
% 0.18/0.49 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[314, 310])).
% 0.18/0.49 tff(316,plain,(
% 0.18/0.49 ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[315])).
% 0.18/0.49 tff(317,plain,
% 0.18/0.49 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[316, 309])).
% 0.18/0.49 tff(318,plain,
% 0.18/0.49 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(319,plain,
% 0.18/0.49 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(320,plain,
% 0.18/0.49 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.18/0.49 tff(321,plain,
% 0.18/0.49 (ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[320, 317, 15])).
% 0.18/0.49 tff(322,plain,
% 0.18/0.49 (~ssPv2(elem!0)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[321, 299, 307, 3])).
% 0.18/0.49 tff(323,plain,
% 0.18/0.49 (~ssPv4(skf3(elem!0))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[100, 299, 3, 4])).
% 0.18/0.49 tff(324,plain,
% 0.18/0.49 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W))) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(325,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[324])).
% 0.18/0.49 tff(326,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(327,plain,
% 0.18/0.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) <=> ((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W))) | ssPv2(W)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W))) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> ((ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W))) | ssPv1(V)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W))) | ssPv1(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) | ssPv2(V)) <=> ((ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W))) | ssPv2(V)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W))) | ssPv2(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) | ssPv2(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(328,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[327])).
% 0.18/0.49 tff(329,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.18/0.49 tff(330,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.18/0.49 tff(331,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[330, 326])).
% 0.18/0.49 tff(332,plain,(
% 0.18/0.49 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[331])).
% 0.18/0.49 tff(333,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[332, 325])).
% 0.18/0.49 tff(334,plain,
% 0.18/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(335,plain,
% 0.18/0.49 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(336,plain,
% 0.18/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[335])).
% 0.18/0.49 tff(337,plain,
% 0.18/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.18/0.49 inference(transitivity,[status(thm)],[336, 334])).
% 0.18/0.49 tff(338,plain,
% 0.18/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(339,plain,
% 0.18/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.18/0.49 tff(340,plain,
% 0.18/0.49 (ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[339, 333, 15, 42])).
% 0.18/0.49 tff(341,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[340, 323, 322, 5, 3])).
% 0.18/0.49 tff(342,plain,(ssPv1(elem!0) | ssPv2(skf2(elem!0)) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(343,plain,
% 0.18/0.49 (ssPv1(elem!0)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[342, 5, 4])).
% 0.18/0.49 tff(344,plain,
% 0.18/0.49 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(345,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[344])).
% 0.18/0.49 tff(346,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(347,plain,
% 0.18/0.49 (^[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))) | (~ssPv1(W))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X)) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | ssPv2(X)))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(348,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[347])).
% 0.18/0.49 tff(349,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.18/0.49 tff(350,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.18/0.49 tff(351,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[350, 346])).
% 0.18/0.49 tff(352,plain,(
% 0.18/0.49 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[351])).
% 0.18/0.49 tff(353,plain,
% 0.18/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[352, 345])).
% 0.18/0.49 tff(354,plain,
% 0.18/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(skf2(elem!0)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(355,plain,
% 0.18/0.49 ((ssPv2(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(skf2(elem!0)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(356,plain,
% 0.18/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (ssPv2(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(skf2(elem!0))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[355])).
% 0.18/0.49 tff(357,plain,
% 0.18/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (ssPv2(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(skf2(elem!0)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[356, 354])).
% 0.18/0.49 tff(358,plain,
% 0.18/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (ssPv2(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(359,plain,
% 0.18/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(skf2(elem!0))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.18/0.50 tff(360,plain,
% 0.18/0.50 ((~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(skf2(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[359, 353, 15, 42])).
% 0.18/0.50 tff(361,plain,
% 0.18/0.50 (~ssPv4(skf3(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[360, 343, 280, 5])).
% 0.18/0.50 tff(362,plain,
% 0.18/0.50 (ssPv2(elem!0)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[156, 361, 4, 343])).
% 0.18/0.50 tff(363,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(364,plain,
% 0.18/0.50 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(365,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[364])).
% 0.18/0.50 tff(366,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[365, 363])).
% 0.18/0.50 tff(367,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(368,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.18/0.50 tff(369,plain,
% 0.18/0.50 (ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[368, 198, 15])).
% 0.18/0.50 tff(370,plain,
% 0.18/0.50 (ssPv2(skf3(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[369, 362, 4, 343])).
% 0.18/0.50 tff(371,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(372,plain,
% 0.18/0.50 (((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(373,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[372])).
% 0.18/0.50 tff(374,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[373, 371])).
% 0.18/0.50 tff(375,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(376,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.18/0.50 tff(377,plain,
% 0.18/0.50 ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[376, 216, 15, 42])).
% 0.18/0.50 tff(378,plain,
% 0.18/0.50 (~ssPv1(skf2(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[377, 370, 4, 362])).
% 0.18/0.50 tff(379,plain,
% 0.18/0.50 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) <=> (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(380,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[379])).
% 0.18/0.50 tff(381,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(382,plain,
% 0.18/0.50 (^[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))) | (~ssRr(V, X))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | (~ssPv1(V))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | (~ssPv1(V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(W)))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(W)) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) | ssPv1(X)) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) | ssPv1(X)))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(383,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) | ssPv1(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[382])).
% 0.18/0.50 tff(384,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) | ssPv1(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.18/0.50 tff(385,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.18/0.50 tff(386,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[385, 381])).
% 0.18/0.50 tff(387,plain,(
% 0.18/0.50 ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.18/0.50 inference(skolemize,[status(sab)],[386])).
% 0.18/0.50 tff(388,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[387, 380])).
% 0.18/0.50 tff(389,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(390,plain,
% 0.18/0.50 ((ssPv1(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(391,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[390])).
% 0.18/0.50 tff(392,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[391, 389])).
% 0.18/0.50 tff(393,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(394,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.18/0.50 tff(395,plain,
% 0.18/0.50 (ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[394, 388, 15, 42])).
% 0.18/0.50 tff(396,plain,
% 0.18/0.50 (ssPv3(skf2(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[395, 378, 280, 343])).
% 0.18/0.50 tff(397,plain,
% 0.18/0.50 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(398,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[397])).
% 0.18/0.50 tff(399,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(400,plain,
% 0.18/0.50 (^[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)) | (~ssRr(U, W)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(401,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[400])).
% 0.18/0.50 tff(402,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) | ssPv1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.18/0.50 tff(403,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.18/0.50 tff(404,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[403, 399])).
% 0.18/0.50 tff(405,plain,(
% 0.18/0.50 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.18/0.50 inference(skolemize,[status(sab)],[404])).
% 0.18/0.50 tff(406,plain,
% 0.18/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[405, 398])).
% 0.18/0.50 tff(407,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(408,plain,
% 0.18/0.50 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(409,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[408])).
% 0.18/0.50 tff(410,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[409, 407])).
% 0.18/0.50 tff(411,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(elem!0))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(412,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.18/0.50 tff(413,plain,
% 0.18/0.50 (ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[412, 406, 42])).
% 0.18/0.50 tff(414,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[413, 396, 378, 343, 362])).
% 0.18/0.50 tff(415,plain,(ssPv2(skf2(elem!0)) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(416,plain,
% 0.18/0.50 (ssPv2(skf2(elem!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[415, 4])).
% 0.18/0.50 tff(417,assumption,(ssPv2(skf2(elem!0))), introduced(assumption)).
% 0.18/0.50 tff(418,assumption,(~ssPv1(skf2(elem!0))), introduced(assumption)).
% 0.18/0.50 tff(419,plain,
% 0.18/0.50 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(skf2(elem!0), skf2(skf2(elem!0)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(420,plain,
% 0.18/0.50 (ssRr(skf2(elem!0), skf2(skf2(elem!0)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[419, 40])).
% 0.18/0.50 tff(421,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(422,plain,
% 0.18/0.50 ((ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(423,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[422])).
% 0.18/0.50 tff(424,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[423, 421])).
% 0.18/0.50 tff(425,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(426,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.18/0.50 tff(427,plain,
% 0.18/0.50 (ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[426, 252, 42, 420])).
% 0.18/0.50 tff(428,plain,
% 0.18/0.50 (~ssPv4(skf2(skf2(elem!0)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[427, 418, 417, 3])).
% 0.18/0.50 tff(429,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(430,plain,
% 0.18/0.50 ((ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(431,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[430])).
% 0.18/0.50 tff(432,plain,
% 0.18/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[431, 429])).
% 0.18/0.50 tff(433,plain,
% 0.18/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(434,plain,
% 0.18/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.18/0.51 tff(435,plain,
% 0.18/0.51 (ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[434, 270, 42, 420])).
% 0.18/0.51 tff(436,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[435, 428, 418, 417, 3])).
% 0.18/0.51 tff(437,plain,(ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(438,plain,
% 0.18/0.51 (ssPv1(skf2(elem!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[437, 3, 416])).
% 0.18/0.51 tff(439,plain,
% 0.18/0.51 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(440,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[439])).
% 0.18/0.51 tff(441,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(442,plain,
% 0.18/0.51 (^[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))) | (~ssPv1(X))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) <=> (((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(U)))), rewrite((((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) <=> ((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv1(W)))), rewrite(((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv1(W)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) | ssPv1(V)) <=> ((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) | ssPv1(V)))), rewrite(((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) | ssPv1(V)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) | ssPv1(V)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(443,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[442])).
% 0.18/0.51 tff(444,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.18/0.51 tff(445,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.18/0.51 tff(446,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[445, 441])).
% 0.18/0.51 tff(447,plain,(
% 0.18/0.51 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.18/0.51 inference(skolemize,[status(sab)],[446])).
% 0.18/0.51 tff(448,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[447, 440])).
% 0.18/0.51 tff(449,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(450,plain,
% 0.18/0.51 ((ssPv3(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(451,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (ssPv3(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[450])).
% 0.18/0.51 tff(452,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (ssPv3(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[451, 449])).
% 0.18/0.51 tff(453,plain,
% 0.18/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (ssPv3(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(454,plain,
% 0.18/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.18/0.51 tff(455,plain,
% 0.18/0.51 (ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[454, 448, 15, 42])).
% 0.18/0.51 tff(456,plain,
% 0.18/0.51 (~ssPv1(skf2(elem!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[455, 3, 2, 4])).
% 0.18/0.51 tff(457,plain,
% 0.18/0.51 (~ssPv4(skf2(skf2(elem!0)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[427, 456, 416, 3])).
% 0.18/0.51 tff(458,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[435, 457, 456, 416, 3])).
% 0.18/0.51 tff(459,plain,(ssPv1(elem!0) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(460,plain,
% 0.18/0.51 (ssPv1(elem!0)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[459, 2, 4])).
% 0.18/0.51 tff(461,assumption,(ssPv1(elem!0)), introduced(assumption)).
% 0.18/0.51 tff(462,assumption,(ssPv3(elem!0)), introduced(assumption)).
% 0.18/0.51 tff(463,plain,
% 0.18/0.51 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(464,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[463])).
% 0.18/0.51 tff(465,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(466,plain,
% 0.18/0.51 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(467,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[466])).
% 0.18/0.51 tff(468,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.18/0.51 tff(469,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.18/0.51 tff(470,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[469, 465])).
% 0.18/0.51 tff(471,plain,(
% 0.18/0.51 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.18/0.51 inference(skolemize,[status(sab)],[470])).
% 0.18/0.51 tff(472,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[471, 464])).
% 0.18/0.51 tff(473,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(474,plain,
% 0.18/0.51 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(475,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[474])).
% 0.18/0.51 tff(476,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[475, 473])).
% 0.18/0.51 tff(477,plain,
% 0.18/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf2(elem!0))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(478,plain,
% 0.18/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.18/0.51 tff(479,plain,
% 0.18/0.51 ((~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[478, 472, 15, 42])).
% 0.18/0.51 tff(480,plain,
% 0.18/0.51 (~ssPv1(skf2(elem!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[479, 462, 461, 4])).
% 0.18/0.51 tff(481,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(482,plain,
% 0.18/0.51 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(483,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0)))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[482])).
% 0.18/0.51 tff(484,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[483, 481])).
% 0.18/0.51 tff(485,plain,
% 0.18/0.51 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(486,plain,
% 0.18/0.51 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.18/0.51 tff(487,plain,
% 0.18/0.51 (ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[486, 234, 42])).
% 0.18/0.51 tff(488,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[487, 480, 462, 461, 416])).
% 0.18/0.51 tff(489,plain,((~ssPv3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(490,plain,
% 0.18/0.51 (~ssPv3(elem!0)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[489, 460, 4])).
% 0.18/0.51 tff(491,plain,
% 0.18/0.51 (ssPv4(skf3(elem!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[32, 490, 2, 4])).
% 0.18/0.51 tff(492,plain,
% 0.18/0.51 (ssPv2(skf3(skf3(elem!0)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[82, 491, 4, 2])).
% 0.18/0.51 tff(493,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(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)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(494,plain,
% 0.18/0.51 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0))))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(495,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[494])).
% 0.18/0.51 tff(496,plain,
% 0.18/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[495, 493])).
% 0.18/0.51 tff(497,plain,
% 0.18/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(498,plain,
% 0.18/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.18/0.51 tff(499,plain,
% 0.18/0.51 (ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[498, 111, 15, 65])).
% 0.18/0.51 tff(500,plain,
% 0.18/0.51 (ssPv2(elem!0)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[499, 492, 4, 2])).
% 0.18/0.51 tff(501,plain,
% 0.18/0.51 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W)))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(502,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[501])).
% 0.18/0.51 tff(503,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(504,plain,
% 0.18/0.51 (^[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(W, V))) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V))) | ssPv3(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) | ssPv4(V)) <=> ((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)) | ssPv4(V)))), rewrite(((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)) | ssPv4(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) | ssPv4(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(505,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[504])).
% 0.18/0.51 tff(506,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause10')).
% 0.18/0.51 tff(507,plain,
% 0.18/0.51 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.18/0.52 tff(508,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[507, 503])).
% 0.18/0.52 tff(509,plain,(
% 0.18/0.52 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.52 inference(skolemize,[status(sab)],[508])).
% 0.18/0.52 tff(510,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[509, 502])).
% 0.18/0.52 tff(511,plain,
% 0.18/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(512,plain,
% 0.18/0.52 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(513,plain,
% 0.18/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0)))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[512])).
% 0.18/0.52 tff(514,plain,
% 0.18/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0))),
% 0.18/0.52 inference(transitivity,[status(thm)],[513, 511])).
% 0.18/0.52 tff(515,plain,
% 0.18/0.52 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(516,plain,
% 0.18/0.52 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.18/0.52 tff(517,plain,
% 0.18/0.52 (ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[516, 510, 15])).
% 0.18/0.52 tff(518,plain,
% 0.18/0.52 (ssPv4(elem!0)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[517, 491, 4, 490])).
% 0.18/0.52 tff(519,plain,
% 0.18/0.52 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(520,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[519])).
% 0.18/0.52 tff(521,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(522,plain,
% 0.18/0.52 (^[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(W))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv2(U)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv2(U)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv2(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv2(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(523,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[522])).
% 0.18/0.52 tff(524,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 0.18/0.52 tff(525,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.18/0.52 tff(526,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[525, 521])).
% 0.18/0.52 tff(527,plain,(
% 0.18/0.52 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.18/0.52 inference(skolemize,[status(sab)],[526])).
% 0.18/0.52 tff(528,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[527, 520])).
% 0.18/0.52 tff(529,plain,
% 0.18/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(530,plain,
% 0.18/0.52 ((ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(531,plain,
% 0.18/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[530])).
% 0.18/0.52 tff(532,plain,
% 0.18/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.52 inference(transitivity,[status(thm)],[531, 529])).
% 0.18/0.52 tff(533,plain,
% 0.18/0.52 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(534,plain,
% 0.18/0.52 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.18/0.52 tff(535,plain,
% 0.18/0.52 (ssPv2(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[534, 528, 15])).
% 0.18/0.52 tff(536,plain,
% 0.18/0.52 (ssPv2(skf3(elem!0))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[535, 518, 2, 500])).
% 0.18/0.52 tff(537,plain,
% 0.18/0.52 (ssPv2(skf2(skf3(elem!0)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[187, 492, 4, 2])).
% 0.18/0.52 tff(538,plain,
% 0.18/0.52 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) <=> (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(539,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[538])).
% 0.18/0.52 tff(540,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(541,plain,
% 0.18/0.52 (^[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))) | (~ssPv4(V))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv4(V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv4(V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv3(X)) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv3(X)))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(542,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv3(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[541])).
% 0.18/0.52 tff(543,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv3(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.18/0.52 tff(544,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.18/0.52 tff(545,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[544, 540])).
% 0.18/0.52 tff(546,plain,(
% 0.18/0.52 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.18/0.52 inference(skolemize,[status(sab)],[545])).
% 0.18/0.52 tff(547,plain,
% 0.18/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[546, 539])).
% 0.18/0.52 tff(548,plain,
% 0.18/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(549,plain,
% 0.18/0.52 ((ssPv3(elem!0) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(550,plain,
% 0.18/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(elem!0) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), 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) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[549])).
% 0.18/0.52 tff(551,plain,
% 0.18/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(elem!0) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), 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) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[550, 548])).
% 0.18/0.52 tff(552,plain,
% 0.18/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(elem!0) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(553,plain,
% 0.35/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.35/0.52 tff(554,plain,
% 0.35/0.52 (ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[553, 547, 15, 65])).
% 0.35/0.52 tff(555,plain,
% 0.35/0.52 (~ssPv4(skf3(skf3(elem!0)))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[554, 491, 490, 492])).
% 0.35/0.52 tff(556,plain,
% 0.35/0.52 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))),
% 0.35/0.52 inference(bind,[status(th)],[])).
% 0.35/0.52 tff(557,plain,
% 0.35/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.35/0.52 inference(quant_intro,[status(thm)],[556])).
% 0.35/0.52 tff(558,plain,
% 0.35/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(559,plain,
% 0.35/0.52 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(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))) | (~ssRr(V, X))) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V))) | (~ssRr(V, X))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv2(X))) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv2(X))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv2(X))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv2(X))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv2(X))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv2(X))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv2(X))) | ssPv4(W)) | ssPv3(V)) <=> (((~ssRr(U, V)) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv3(V)) <=> ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv2(X))) | ssPv4(W)) | ssPv3(V)) <=> ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))))),
% 0.35/0.52 inference(bind,[status(th)],[])).
% 0.35/0.52 tff(560,plain,
% 0.35/0.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv2(X))) | ssPv4(W)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.35/0.52 inference(quant_intro,[status(thm)],[559])).
% 0.35/0.52 tff(561,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv2(X))) | ssPv4(W)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.35/0.52 tff(562,plain,
% 0.35/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.35/0.52 tff(563,plain,
% 0.35/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[562, 558])).
% 0.35/0.52 tff(564,plain,(
% 0.35/0.52 ![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.35/0.52 inference(skolemize,[status(sab)],[563])).
% 0.35/0.52 tff(565,plain,
% 0.35/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[564, 557])).
% 0.35/0.52 tff(566,plain,
% 0.35/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0)))))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(567,plain,
% 0.35/0.52 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0)))) <=> (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0)))))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(568,plain,
% 0.35/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0))))))),
% 0.35/0.52 inference(monotonicity,[status(thm)],[567])).
% 0.35/0.52 tff(569,plain,
% 0.35/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0)))))),
% 0.35/0.52 inference(transitivity,[status(thm)],[568, 566])).
% 0.35/0.52 tff(570,plain,
% 0.35/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(skf2(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(571,plain,
% 0.35/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0))))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.35/0.52 tff(572,plain,
% 0.35/0.52 (ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf2(skf3(elem!0))))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[571, 565, 65, 180])).
% 0.35/0.52 tff(573,plain,
% 0.35/0.52 (~ssPv3(skf3(skf3(elem!0)))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[572, 555, 4, 537])).
% 0.35/0.52 tff(574,plain,
% 0.35/0.52 ($false),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[223, 573, 536, 460, 492])).
% 0.35/0.52 tff(575,plain,(ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.52 tff(576,plain,
% 0.35/0.52 (ssPv1(skf3(elem!0))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[575, 4])).
% 0.35/0.52 tff(577,plain,
% 0.35/0.52 (~ssPv3(elem!0)),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[297, 3, 576, 4])).
% 0.35/0.52 tff(578,plain,
% 0.35/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(579,plain,
% 0.35/0.52 ((ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(580,plain,
% 0.35/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))))),
% 0.35/0.52 inference(monotonicity,[status(thm)],[579])).
% 0.35/0.52 tff(581,plain,
% 0.35/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.35/0.53 inference(transitivity,[status(thm)],[580, 578])).
% 0.35/0.53 tff(582,plain,
% 0.35/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(583,plain,
% 0.35/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.35/0.53 tff(584,plain,
% 0.35/0.53 ((~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[583, 198, 42])).
% 0.35/0.53 tff(585,plain,
% 0.35/0.53 (ssPv2(elem!0)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[584, 438, 416, 577])).
% 0.35/0.53 tff(586,assumption,(ssPv2(elem!0)), introduced(assumption)).
% 0.35/0.53 tff(587,assumption,(~ssPv2(skf3(elem!0))), introduced(assumption)).
% 0.35/0.53 tff(588,assumption,(~ssPv3(elem!0)), introduced(assumption)).
% 0.35/0.53 tff(589,plain,
% 0.35/0.53 (~ssPv4(elem!0)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[306, 587, 3, 588])).
% 0.35/0.53 tff(590,plain,
% 0.35/0.53 ($false),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[321, 589, 587, 586, 3])).
% 0.35/0.53 tff(591,plain,(ssPv2(skf3(elem!0)) | (~ssPv2(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.35/0.53 tff(592,plain,
% 0.35/0.53 (ssPv2(skf3(elem!0))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[591, 585, 3, 577])).
% 0.35/0.53 tff(593,plain,
% 0.35/0.53 ($false),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[377, 592, 585, 4, 438])).
% 0.35/0.53 tff(594,plain,(ssPv1(elem!0) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.53 tff(595,plain,
% 0.35/0.53 (ssPv1(elem!0)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[594, 4])).
% 0.35/0.53 tff(596,plain,
% 0.35/0.53 (~ssPv3(elem!0)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[489, 595, 4])).
% 0.35/0.53 tff(597,plain,
% 0.35/0.53 (ssPv4(skf3(elem!0))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[156, 1, 4, 595])).
% 0.35/0.53 tff(598,plain,
% 0.35/0.53 (^[V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))))),
% 0.35/0.53 inference(bind,[status(th)],[])).
% 0.35/0.53 tff(599,plain,
% 0.35/0.53 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.35/0.53 inference(quant_intro,[status(thm)],[598])).
% 0.35/0.53 tff(600,plain,
% 0.35/0.53 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(601,plain,
% 0.35/0.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv1(U)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv1(U))))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv1(U))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv1(U))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(V)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))))),
% 0.35/0.53 inference(bind,[status(th)],[])).
% 0.35/0.53 tff(602,plain,
% 0.35/0.53 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(V)) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.35/0.53 inference(quant_intro,[status(thm)],[601])).
% 0.35/0.53 tff(603,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.35/0.53 tff(604,plain,
% 0.35/0.53 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.35/0.53 tff(605,plain,
% 0.35/0.53 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[604, 600])).
% 0.35/0.53 tff(606,plain,(
% 0.35/0.53 ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.35/0.53 inference(skolemize,[status(sab)],[605])).
% 0.35/0.53 tff(607,plain,
% 0.35/0.53 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[606, 599])).
% 0.35/0.53 tff(608,plain,
% 0.35/0.53 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(609,plain,
% 0.35/0.53 (((~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(610,plain,
% 0.35/0.53 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0)))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[609])).
% 0.35/0.53 tff(611,plain,
% 0.35/0.53 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))),
% 0.35/0.53 inference(transitivity,[status(thm)],[610, 608])).
% 0.35/0.53 tff(612,plain,
% 0.35/0.53 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(613,plain,
% 0.35/0.53 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0)),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.35/0.53 tff(614,plain,
% 0.35/0.53 ((~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[613, 607, 15])).
% 0.35/0.53 tff(615,plain,
% 0.35/0.53 (~ssPv4(elem!0)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[614, 1, 576, 595])).
% 0.35/0.53 tff(616,plain,
% 0.35/0.53 ($false),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[517, 615, 597, 4, 596])).
% 0.35/0.53 tff(617,plain,(ssPv2(elem!0) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.53 tff(618,plain,
% 0.35/0.53 (ssPv2(elem!0)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[617, 4])).
% 0.35/0.53 tff(619,plain,
% 0.35/0.53 (ssPv2(skf3(elem!0))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[369, 618, 4, 595])).
% 0.35/0.53 tff(620,plain,
% 0.35/0.53 (~ssPv1(skf2(elem!0))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[377, 619, 4, 618])).
% 0.35/0.53 tff(621,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(622,plain,
% 0.35/0.53 ((ssPv1(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))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(623,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[622])).
% 0.35/0.53 tff(624,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.35/0.53 inference(transitivity,[status(thm)],[623, 621])).
% 0.35/0.53 tff(625,plain,
% 0.35/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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))) | (~ssPv3(skf2(elem!0))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(626,plain,
% 0.35/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.35/0.53 tff(627,plain,
% 0.35/0.53 ((~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[626, 129, 15, 42])).
% 0.35/0.53 tff(628,plain,
% 0.35/0.53 (~ssPv3(skf2(elem!0))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[627, 620, 618, 619])).
% 0.35/0.53 tff(629,plain,
% 0.35/0.53 ($false),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[395, 628, 620, 576, 595])).
% 0.35/0.53 tff(630,plain,(ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.53 tff(631,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(632,plain,
% 0.35/0.53 ((ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(633,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0)))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[632])).
% 0.35/0.53 tff(634,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.35/0.53 inference(transitivity,[status(thm)],[633, 631])).
% 0.35/0.53 tff(635,plain,
% 0.35/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(636,plain,
% 0.35/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.35/0.53 tff(637,plain,
% 0.35/0.53 (ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[636, 252, 15, 42])).
% 0.35/0.53 tff(638,plain,
% 0.35/0.53 (~ssPv4(skf2(elem!0))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[637, 586, 3, 2])).
% 0.35/0.53 tff(639,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(640,plain,
% 0.35/0.53 ((ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(641,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[640])).
% 0.35/0.53 tff(642,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.35/0.53 inference(transitivity,[status(thm)],[641, 639])).
% 0.35/0.53 tff(643,plain,
% 0.35/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(644,plain,
% 0.35/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.35/0.53 tff(645,plain,
% 0.35/0.53 (ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[644, 270, 15, 42])).
% 0.35/0.53 tff(646,plain,
% 0.35/0.53 ($false),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[645, 638, 586, 3, 2])).
% 0.35/0.53 tff(647,plain,((~ssPv2(elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.53 tff(648,plain,
% 0.35/0.53 (~ssPv2(elem!0)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[647, 2, 3])).
% 0.35/0.53 tff(649,plain,
% 0.35/0.53 (ssPv4(skf3(elem!0))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[340, 1, 5, 3])).
% 0.35/0.53 tff(650,plain,
% 0.35/0.53 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))))),
% 0.35/0.53 inference(bind,[status(th)],[])).
% 0.35/0.53 tff(651,plain,
% 0.35/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.35/0.53 inference(quant_intro,[status(thm)],[650])).
% 0.35/0.53 tff(652,plain,
% 0.35/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(653,plain,
% 0.35/0.53 (^[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))) | (~ssPv3(W))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv3(W))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssRr(V, X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssPv3(X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssPv3(X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv1(V)) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) | ssPv1(V)))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) | ssPv1(V)) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv1(V)) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))))),
% 0.35/0.53 inference(bind,[status(th)],[])).
% 0.35/0.53 tff(654,plain,
% 0.35/0.53 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.35/0.53 inference(quant_intro,[status(thm)],[653])).
% 0.35/0.53 tff(655,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.35/0.53 tff(656,plain,
% 0.35/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.35/0.53 tff(657,plain,
% 0.35/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[656, 652])).
% 0.35/0.53 tff(658,plain,(
% 0.35/0.53 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.35/0.53 inference(skolemize,[status(sab)],[657])).
% 0.35/0.53 tff(659,plain,
% 0.35/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[658, 651])).
% 0.35/0.53 tff(660,plain,
% 0.35/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(661,plain,
% 0.35/0.53 (((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(662,plain,
% 0.35/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0)))))),
% 0.35/0.54 inference(monotonicity,[status(thm)],[661])).
% 0.35/0.54 tff(663,plain,
% 0.35/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.35/0.54 inference(transitivity,[status(thm)],[662, 660])).
% 0.35/0.54 tff(664,plain,
% 0.35/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.35/0.54 inference(quant_inst,[status(thm)],[])).
% 0.35/0.54 tff(665,plain,
% 0.35/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0)))),
% 0.35/0.54 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.35/0.54 tff(666,plain,
% 0.35/0.54 (ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0)))),
% 0.35/0.54 inference(unit_resolution,[status(thm)],[665, 659, 15, 42])).
% 0.35/0.54 tff(667,plain,
% 0.35/0.54 (~ssPv3(skf2(elem!0))),
% 0.35/0.54 inference(unit_resolution,[status(thm)],[666, 649, 630, 3])).
% 0.35/0.54 tff(668,assumption,(~ssPv3(skf2(elem!0))), introduced(assumption)).
% 0.35/0.54 tff(669,plain,
% 0.35/0.54 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))))),
% 0.35/0.54 inference(bind,[status(th)],[])).
% 0.35/0.54 tff(670,plain,
% 0.35/0.54 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.35/0.54 inference(quant_intro,[status(thm)],[669])).
% 0.35/0.54 tff(671,plain,
% 0.35/0.54 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.35/0.54 inference(rewrite,[status(thm)],[])).
% 0.35/0.54 tff(672,plain,
% 0.35/0.54 (^[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)) | (~ssRr(V, W)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(U))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(U))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(U))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv3(U)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv3(U))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv3(U))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv3(U))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) | ssPv3(V)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))))),
% 0.35/0.54 inference(bind,[status(th)],[])).
% 0.35/0.54 tff(673,plain,
% 0.35/0.54 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.35/0.54 inference(quant_intro,[status(thm)],[672])).
% 0.35/0.54 tff(674,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause21')).
% 0.35/0.54 tff(675,plain,
% 0.35/0.54 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.35/0.54 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.35/0.54 tff(676,plain,
% 0.35/0.54 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.35/0.54 inference(modus_ponens,[status(thm)],[675, 671])).
% 0.35/0.54 tff(677,plain,(
% 0.35/0.54 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.35/0.54 inference(skolemize,[status(sab)],[676])).
% 0.35/0.54 tff(678,plain,
% 0.35/0.54 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.35/0.54 inference(modus_ponens,[status(thm)],[677, 670])).
% 0.35/0.54 tff(679,plain,
% 0.35/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.35/0.54 inference(rewrite,[status(thm)],[])).
% 0.35/0.54 tff(680,plain,
% 0.35/0.54 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.35/0.54 inference(rewrite,[status(thm)],[])).
% 0.35/0.54 tff(681,plain,
% 0.35/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.35/0.54 inference(monotonicity,[status(thm)],[680])).
% 0.35/0.54 tff(682,plain,
% 0.35/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.35/0.54 inference(transitivity,[status(thm)],[681, 679])).
% 0.35/0.54 tff(683,plain,
% 0.35/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.35/0.54 inference(quant_inst,[status(thm)],[])).
% 0.35/0.54 tff(684,plain,
% 0.35/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.35/0.54 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.35/0.54 tff(685,plain,
% 0.35/0.54 (ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.35/0.54 inference(unit_resolution,[status(thm)],[684, 678, 15, 42])).
% 0.35/0.54 tff(686,plain,
% 0.35/0.54 (~ssPv4(elem!0)),
% 0.35/0.54 inference(unit_resolution,[status(thm)],[685, 588, 630, 5])).
% 0.35/0.54 tff(687,plain,
% 0.35/0.54 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))),
% 0.35/0.54 inference(rewrite,[status(thm)],[])).
% 0.35/0.54 tff(688,plain,
% 0.35/0.54 ((ssPv4(elem!0) | ssPv3(elem!0) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))),
% 0.35/0.54 inference(rewrite,[status(thm)],[])).
% 0.35/0.54 tff(689,plain,
% 0.35/0.54 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)))),
% 0.35/0.54 inference(monotonicity,[status(thm)],[688])).
% 0.35/0.54 tff(690,plain,
% 0.35/0.54 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))),
% 0.35/0.54 inference(transitivity,[status(thm)],[689, 687])).
% 0.35/0.54 tff(691,plain,
% 0.35/0.54 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.35/0.54 inference(quant_inst,[status(thm)],[])).
% 0.35/0.54 tff(692,plain,
% 0.35/0.54 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)),
% 0.35/0.54 inference(modus_ponens,[status(thm)],[691, 690])).
% 0.35/0.54 tff(693,plain,
% 0.35/0.54 (ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)),
% 0.35/0.54 inference(unit_resolution,[status(thm)],[692, 25, 42])).
% 0.35/0.54 tff(694,plain,
% 0.35/0.54 ($false),
% 0.35/0.54 inference(unit_resolution,[status(thm)],[693, 686, 588, 3, 668])).
% 0.35/0.54 tff(695,plain,(ssPv3(elem!0) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.54 tff(696,plain,
% 0.35/0.54 (ssPv3(elem!0)),
% 0.35/0.54 inference(unit_resolution,[status(thm)],[695, 667, 3, 5])).
% 0.35/0.54 tff(697,plain,
% 0.35/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(698,plain,
% 0.37/0.54 ((ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(699,plain,
% 0.37/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0)))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[698])).
% 0.37/0.54 tff(700,plain,
% 0.37/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[699, 697])).
% 0.37/0.54 tff(701,plain,
% 0.37/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(702,plain,
% 0.37/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.37/0.54 tff(703,plain,
% 0.37/0.54 (ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[702, 52, 15, 65])).
% 0.37/0.54 tff(704,plain,
% 0.37/0.54 (ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[703, 1, 630, 2])).
% 0.37/0.54 tff(705,plain,
% 0.37/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(706,plain,
% 0.37/0.54 (((~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(707,plain,
% 0.37/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(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(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[706])).
% 0.37/0.54 tff(708,plain,
% 0.37/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(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(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[707, 705])).
% 0.37/0.54 tff(709,plain,
% 0.37/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(710,plain,
% 0.37/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.37/0.54 tff(711,plain,
% 0.37/0.54 (ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[710, 659, 15, 65])).
% 0.37/0.54 tff(712,plain,
% 0.37/0.54 (~ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[711, 696, 2, 704])).
% 0.37/0.54 tff(713,plain,
% 0.37/0.54 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv1(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv1(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(714,plain,
% 0.37/0.54 ((ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0))))) <=> (ssPv1(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(715,plain,
% 0.37/0.54 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv1(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[714])).
% 0.37/0.54 tff(716,plain,
% 0.37/0.54 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv1(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[715, 713])).
% 0.37/0.54 tff(717,plain,
% 0.37/0.54 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(718,plain,
% 0.37/0.54 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv1(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[717, 716])).
% 0.37/0.54 tff(719,plain,
% 0.37/0.54 (ssPv1(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[718, 93, 65])).
% 0.37/0.54 tff(720,plain,
% 0.37/0.54 (ssPv2(skf3(skf3(elem!0)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[719, 712, 2, 704])).
% 0.37/0.54 tff(721,plain,
% 0.37/0.54 (~ssPv2(skf3(elem!0))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[136, 720, 3, 696])).
% 0.37/0.54 tff(722,plain,
% 0.37/0.54 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(723,plain,
% 0.37/0.54 ((ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(724,plain,
% 0.37/0.54 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[723])).
% 0.37/0.54 tff(725,plain,
% 0.37/0.54 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[724, 722])).
% 0.37/0.54 tff(726,plain,
% 0.37/0.54 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(727,plain,
% 0.37/0.54 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.37/0.54 tff(728,plain,
% 0.37/0.54 (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[727, 75, 42])).
% 0.37/0.54 tff(729,plain,
% 0.37/0.54 (~ssPv4(skf2(elem!0))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[728, 418, 1, 668])).
% 0.37/0.54 tff(730,plain,
% 0.37/0.54 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(731,plain,
% 0.37/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[730])).
% 0.37/0.54 tff(732,plain,
% 0.37/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(733,plain,
% 0.37/0.54 (^[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)) | (~ssRr(W, V)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(U))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) | ssPv4(V)) <=> (((~ssRr(U, V)) | ssPv1(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) | ssPv4(V)))), rewrite((((~ssRr(U, V)) | ssPv1(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(734,plain,
% 0.37/0.54 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[733])).
% 0.37/0.54 tff(735,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause15')).
% 0.37/0.54 tff(736,plain,
% 0.37/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.37/0.54 tff(737,plain,
% 0.37/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[736, 732])).
% 0.37/0.54 tff(738,plain,(
% 0.37/0.54 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.54 inference(skolemize,[status(sab)],[737])).
% 0.37/0.55 tff(739,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[738, 731])).
% 0.37/0.55 tff(740,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(741,plain,
% 0.37/0.55 (((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(742,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0))))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[741])).
% 0.37/0.55 tff(743,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.37/0.55 inference(transitivity,[status(thm)],[742, 740])).
% 0.37/0.55 tff(744,plain,
% 0.37/0.55 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0) | (~ssPv3(elem!0)))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(745,plain,
% 0.37/0.55 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.37/0.55 tff(746,plain,
% 0.37/0.55 (ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[745, 739, 42])).
% 0.37/0.55 tff(747,plain,
% 0.37/0.55 (ssPv4(elem!0)),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[746, 729, 462, 418])).
% 0.37/0.55 tff(748,plain,
% 0.37/0.55 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(749,plain,
% 0.37/0.55 ((ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv1(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(750,plain,
% 0.37/0.55 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv1(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[749])).
% 0.37/0.55 tff(751,plain,
% 0.37/0.55 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv1(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(transitivity,[status(thm)],[750, 748])).
% 0.37/0.55 tff(752,plain,
% 0.37/0.55 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv1(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(753,plain,
% 0.37/0.55 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.37/0.55 tff(754,plain,
% 0.37/0.55 (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0)))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[753, 25, 420])).
% 0.37/0.55 tff(755,plain,
% 0.37/0.55 (ssPv3(skf2(skf2(elem!0)))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[754, 729, 668, 418])).
% 0.37/0.55 tff(756,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(757,plain,
% 0.37/0.55 (((~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(758,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[757])).
% 0.37/0.55 tff(759,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(transitivity,[status(thm)],[758, 756])).
% 0.37/0.55 tff(760,plain,
% 0.37/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(761,plain,
% 0.37/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.37/0.55 tff(762,plain,
% 0.37/0.55 (ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[761, 659, 42, 420])).
% 0.37/0.55 tff(763,plain,
% 0.37/0.55 ($false),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[762, 755, 747, 462, 418])).
% 0.37/0.55 tff(764,plain,(ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.55 tff(765,plain,
% 0.37/0.55 (ssPv1(skf2(elem!0))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[764, 696, 667, 1])).
% 0.37/0.55 tff(766,plain,
% 0.37/0.55 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(767,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[766])).
% 0.37/0.55 tff(768,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(769,plain,
% 0.37/0.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(770,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[769])).
% 0.37/0.55 tff(771,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause23')).
% 0.37/0.55 tff(772,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[771, 770])).
% 0.37/0.55 tff(773,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[772, 768])).
% 0.37/0.55 tff(774,plain,(
% 0.37/0.55 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.37/0.55 inference(skolemize,[status(sab)],[773])).
% 0.37/0.55 tff(775,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[774, 767])).
% 0.37/0.55 tff(776,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(777,plain,
% 0.37/0.55 (((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(778,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0)))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[777])).
% 0.37/0.55 tff(779,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))),
% 0.37/0.55 inference(transitivity,[status(thm)],[778, 776])).
% 0.37/0.55 tff(780,plain,
% 0.37/0.55 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(781,plain,
% 0.37/0.55 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0)),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[780, 779])).
% 0.37/0.55 tff(782,plain,
% 0.37/0.55 (ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0)),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[781, 775, 15, 42])).
% 0.37/0.55 tff(783,plain,
% 0.37/0.55 (~ssPv4(elem!0)),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[782, 765, 721, 1])).
% 0.37/0.55 tff(784,plain,
% 0.37/0.55 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(785,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[784])).
% 0.37/0.55 tff(786,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(787,plain,
% 0.37/0.55 (^[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))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(788,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[787])).
% 0.37/0.55 tff(789,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause25')).
% 0.37/0.55 tff(790,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.37/0.55 tff(791,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[790, 786])).
% 0.37/0.55 tff(792,plain,(
% 0.37/0.55 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.37/0.55 inference(skolemize,[status(sab)],[791])).
% 0.37/0.55 tff(793,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[792, 785])).
% 0.37/0.55 tff(794,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(795,plain,
% 0.37/0.55 (((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(796,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv1(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)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[795])).
% 0.37/0.55 tff(797,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv1(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)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(transitivity,[status(thm)],[796, 794])).
% 0.37/0.55 tff(798,plain,
% 0.37/0.55 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(799,plain,
% 0.37/0.55 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[798, 797])).
% 0.37/0.55 tff(800,plain,
% 0.37/0.55 ((~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[799, 793, 42, 420])).
% 0.37/0.55 tff(801,plain,
% 0.37/0.55 (~ssPv4(skf2(skf2(elem!0)))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[800, 765, 5, 1])).
% 0.37/0.55 tff(802,plain,
% 0.37/0.55 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) <=> (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(803,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[802])).
% 0.37/0.55 tff(804,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(805,plain,
% 0.37/0.55 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv1(W)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> (((~ssRr(U, V)) | (~ssPv1(W)) | (~ssRr(V, W))) | (~ssRr(V, X))))), rewrite((((~ssRr(U, V)) | (~ssPv1(W)) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) <=> ((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv4(X)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv4(X)) <=> (ssPv4(X) | ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) <=> (ssPv4(X) | ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) | ssPv2(V)) <=> ((ssPv4(X) | ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv2(V)))), rewrite(((ssPv4(X) | ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv2(V)) <=> (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) | ssPv2(V)) <=> (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(806,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[805])).
% 0.37/0.55 tff(807,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.37/0.55 tff(808,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.37/0.55 tff(809,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[808, 804])).
% 0.37/0.55 tff(810,plain,(
% 0.37/0.55 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.37/0.55 inference(skolemize,[status(sab)],[809])).
% 0.37/0.55 tff(811,plain,
% 0.37/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[810, 803])).
% 0.37/0.55 tff(812,plain,
% 0.37/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(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(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(813,plain,
% 0.37/0.56 ((ssPv4(skf2(skf2(elem!0))) | ssPv4(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(814,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv4(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[813])).
% 0.37/0.56 tff(815,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv4(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[814, 812])).
% 0.37/0.56 tff(816,plain,
% 0.37/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv4(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(817,plain,
% 0.37/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.37/0.56 tff(818,plain,
% 0.37/0.56 (ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[817, 811, 42, 420])).
% 0.37/0.56 tff(819,plain,
% 0.37/0.56 (~ssPv1(skf2(skf2(elem!0)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[818, 801, 5, 783])).
% 0.37/0.56 tff(820,plain,
% 0.37/0.56 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)))),
% 0.37/0.56 inference(bind,[status(th)],[])).
% 0.37/0.56 tff(821,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.37/0.56 inference(quant_intro,[status(thm)],[820])).
% 0.37/0.56 tff(822,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(823,plain,
% 0.37/0.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) | ssPv4(U)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv4(U)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv4(U)) <=> (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) | ssPv4(U)) <=> (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))))),
% 0.37/0.56 inference(bind,[status(th)],[])).
% 0.37/0.56 tff(824,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.37/0.56 inference(quant_intro,[status(thm)],[823])).
% 0.37/0.56 tff(825,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause16')).
% 0.37/0.56 tff(826,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.37/0.56 tff(827,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[826, 822])).
% 0.37/0.56 tff(828,plain,(
% 0.37/0.56 ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.37/0.56 inference(skolemize,[status(sab)],[827])).
% 0.37/0.56 tff(829,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[828, 821])).
% 0.37/0.56 tff(830,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(831,plain,
% 0.37/0.56 ((ssPv4(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(832,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[831])).
% 0.37/0.56 tff(833,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.37/0.56 inference(transitivity,[status(thm)],[832, 830])).
% 0.37/0.56 tff(834,plain,
% 0.37/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(835,plain,
% 0.37/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[834, 833])).
% 0.37/0.56 tff(836,plain,
% 0.37/0.56 ((~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[835, 829, 42])).
% 0.37/0.56 tff(837,plain,
% 0.37/0.56 (ssPv4(skf2(elem!0))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[836, 783, 3, 765])).
% 0.37/0.56 tff(838,plain,
% 0.37/0.56 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(839,plain,
% 0.37/0.56 ((ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(840,plain,
% 0.37/0.56 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[839])).
% 0.37/0.56 tff(841,plain,
% 0.37/0.56 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[840, 838])).
% 0.37/0.56 tff(842,plain,
% 0.37/0.56 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(843,plain,
% 0.37/0.56 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.37/0.56 tff(844,plain,
% 0.37/0.56 (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[843, 93, 420])).
% 0.37/0.56 tff(845,plain,
% 0.37/0.56 ($false),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[844, 837, 819, 5, 667])).
% 0.37/0.56 tff(846,plain,(ssPv2(elem!0) | ssPv2(skf2(elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.56 tff(847,plain,
% 0.37/0.56 (ssPv2(skf2(elem!0))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[846, 648, 3, 2])).
% 0.37/0.56 tff(848,plain,
% 0.37/0.56 (ssPv1(skf2(elem!0))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[437, 847, 3])).
% 0.37/0.56 tff(849,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(850,plain,
% 0.37/0.56 ((ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(851,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[850])).
% 0.37/0.56 tff(852,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[851, 849])).
% 0.37/0.56 tff(853,plain,
% 0.37/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(854,plain,
% 0.37/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[853, 852])).
% 0.37/0.56 tff(855,plain,
% 0.37/0.56 (ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[854, 528, 42])).
% 0.37/0.56 tff(856,plain,
% 0.37/0.56 (~ssPv4(skf2(elem!0))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[855, 847, 3, 648])).
% 0.37/0.56 tff(857,plain,
% 0.37/0.56 (ssPv4(elem!0)),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[836, 856, 3, 848])).
% 0.37/0.56 tff(858,plain,
% 0.37/0.56 (ssPv3(elem!0)),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[584, 848, 648, 847])).
% 0.37/0.56 tff(859,plain,
% 0.37/0.56 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))))),
% 0.37/0.56 inference(bind,[status(th)],[])).
% 0.37/0.56 tff(860,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.37/0.56 inference(quant_intro,[status(thm)],[859])).
% 0.37/0.56 tff(861,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(862,plain,
% 0.37/0.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))))),
% 0.37/0.56 inference(bind,[status(th)],[])).
% 0.37/0.56 tff(863,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.37/0.56 inference(quant_intro,[status(thm)],[862])).
% 0.37/0.56 tff(864,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause24')).
% 0.37/0.56 tff(865,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.37/0.56 tff(866,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[865, 861])).
% 0.37/0.56 tff(867,plain,(
% 0.37/0.56 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.37/0.56 inference(skolemize,[status(sab)],[866])).
% 0.37/0.56 tff(868,plain,
% 0.37/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[867, 860])).
% 0.37/0.56 tff(869,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(870,plain,
% 0.37/0.56 (((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(871,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[870])).
% 0.37/0.56 tff(872,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[871, 869])).
% 0.37/0.56 tff(873,plain,
% 0.37/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(874,plain,
% 0.37/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.37/0.56 tff(875,plain,
% 0.37/0.56 (ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[874, 868, 15, 42])).
% 0.37/0.56 tff(876,plain,
% 0.37/0.56 (ssPv2(skf3(elem!0))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[875, 858, 847, 648])).
% 0.37/0.56 tff(877,plain,
% 0.37/0.56 (ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[703, 648, 630, 2])).
% 0.37/0.56 tff(878,plain,
% 0.37/0.56 (~ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[711, 858, 2, 877])).
% 0.37/0.56 tff(879,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(880,plain,
% 0.37/0.56 ((ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(elem!0)))) <=> (ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(881,plain,
% 0.37/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[880])).
% 0.37/0.57 tff(882,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[881, 879])).
% 0.37/0.57 tff(883,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(884,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.37/0.57 tff(885,plain,
% 0.37/0.57 (ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[884, 290, 65])).
% 0.37/0.57 tff(886,plain,
% 0.37/0.57 (~ssPv1(skf3(skf3(elem!0)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[885, 878, 630, 2])).
% 0.37/0.57 tff(887,plain,
% 0.37/0.57 ($false),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[259, 886, 876, 2, 857])).
% 0.37/0.57 tff(888,plain,(ssPv1(skf3(elem!0)) | ssPv1(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.57 tff(889,plain,
% 0.37/0.57 (ssPv1(skf3(elem!0))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[888, 3])).
% 0.37/0.57 tff(890,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(891,plain,
% 0.37/0.57 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(892,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[891])).
% 0.37/0.57 tff(893,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.37/0.57 inference(transitivity,[status(thm)],[892, 890])).
% 0.37/0.57 tff(894,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(895,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[894, 893])).
% 0.37/0.57 tff(896,plain,
% 0.37/0.57 (ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[895, 234, 15])).
% 0.37/0.57 tff(897,plain,
% 0.37/0.57 (~ssPv2(elem!0)),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[896, 889, 630, 3])).
% 0.37/0.57 tff(898,plain,
% 0.37/0.57 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(899,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[898])).
% 0.37/0.57 tff(900,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(901,plain,
% 0.37/0.57 (^[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))) | (~ssPv3(W))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv3(W))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssRr(X, V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssRr(X, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssPv1(X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssPv1(X))) <=> ((~ssPv4(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) <=> ((~ssPv4(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) | ssPv2(V)) <=> (((~ssPv4(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | ssPv2(V)))), rewrite((((~ssPv4(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | ssPv2(V)) <=> ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) | ssPv2(V)) <=> ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(902,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[901])).
% 0.37/0.57 tff(903,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.37/0.57 tff(904,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[903, 902])).
% 0.37/0.57 tff(905,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[904, 900])).
% 0.37/0.57 tff(906,plain,(
% 0.37/0.57 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.37/0.57 inference(skolemize,[status(sab)],[905])).
% 0.37/0.57 tff(907,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[906, 899])).
% 0.37/0.57 tff(908,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(909,plain,
% 0.37/0.57 (((~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(910,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0)))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[909])).
% 0.37/0.57 tff(911,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0))),
% 0.37/0.57 inference(transitivity,[status(thm)],[910, 908])).
% 0.37/0.57 tff(912,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(913,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0)),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[912, 911])).
% 0.37/0.57 tff(914,plain,
% 0.37/0.57 ((~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0)),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[913, 907, 15])).
% 0.37/0.57 tff(915,plain,
% 0.37/0.57 (~ssPv4(skf3(elem!0))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[914, 897, 630, 889])).
% 0.37/0.57 tff(916,plain,
% 0.37/0.57 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(917,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[916])).
% 0.37/0.57 tff(918,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(919,plain,
% 0.37/0.57 (^[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(W, V))) <=> (((~ssPv1(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv4(X))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv4(X))) <=> ((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) <=> ((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) <=> (((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)))), rewrite((((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) | ssPv2(V)) <=> (((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv2(V)))), rewrite((((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv2(V)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) | ssPv2(V)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(920,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[919])).
% 0.37/0.57 tff(921,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.37/0.57 tff(922,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[921, 920])).
% 0.37/0.57 tff(923,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[922, 918])).
% 0.37/0.57 tff(924,plain,(
% 0.37/0.57 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.57 inference(skolemize,[status(sab)],[923])).
% 0.37/0.57 tff(925,plain,
% 0.37/0.57 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[924, 917])).
% 0.37/0.57 tff(926,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(927,plain,
% 0.37/0.57 (((~ssPv4(skf2(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(928,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssPv4(skf2(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[927])).
% 0.37/0.57 tff(929,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssPv4(skf2(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[928, 926])).
% 0.37/0.57 tff(930,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssPv4(skf2(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(931,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[930, 929])).
% 0.37/0.57 tff(932,plain,
% 0.37/0.57 ((~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[931, 925, 15, 42])).
% 0.37/0.57 tff(933,plain,
% 0.37/0.57 (~ssPv4(skf2(elem!0))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[932, 915, 897, 889])).
% 0.37/0.57 tff(934,plain,
% 0.37/0.57 (ssPv2(skf2(elem!0))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[340, 915, 897, 3])).
% 0.37/0.57 tff(935,plain,
% 0.37/0.57 (ssPv1(skf2(elem!0))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[437, 934, 3])).
% 0.37/0.57 tff(936,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(937,plain,
% 0.37/0.57 ((ssPv4(skf2(elem!0)) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(938,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(skf2(elem!0)) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[937])).
% 0.37/0.57 tff(939,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(skf2(elem!0)) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)))),
% 0.37/0.57 inference(transitivity,[status(thm)],[938, 936])).
% 0.37/0.57 tff(940,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(skf2(elem!0)) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(941,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.37/0.57 tff(942,plain,
% 0.37/0.57 ((~ssPv1(skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[941, 811, 15, 42])).
% 0.37/0.57 tff(943,plain,
% 0.37/0.57 ($false),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[942, 935, 933, 915, 897])).
% 0.37/0.57 tff(944,plain,(ssPv1(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.57 tff(945,assumption,(~ssPv3(skf3(skf3(elem!0)))), introduced(assumption)).
% 0.37/0.57 tff(946,plain,
% 0.37/0.57 (~ssPv1(skf3(skf3(elem!0)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[885, 945, 630, 2])).
% 0.37/0.57 tff(947,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(948,plain,
% 0.37/0.57 ((ssPv3(skf3(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(949,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (ssPv3(skf3(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[948])).
% 0.37/0.57 tff(950,plain,
% 0.37/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (ssPv3(skf3(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[949, 947])).
% 0.37/0.57 tff(951,plain,
% 0.37/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (ssPv3(skf3(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(952,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[951, 950])).
% 0.37/0.58 tff(953,plain,
% 0.37/0.58 (ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[952, 448, 15, 65])).
% 0.37/0.58 tff(954,plain,
% 0.37/0.58 ($false),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[953, 946, 945, 944, 2])).
% 0.37/0.58 tff(955,plain,(ssPv3(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.58 tff(956,plain,
% 0.37/0.58 (ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[955, 2])).
% 0.37/0.58 tff(957,plain,
% 0.37/0.58 (~ssPv3(elem!0)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[711, 704, 2, 956])).
% 0.37/0.58 tff(958,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(959,plain,
% 0.37/0.58 ((ssPv4(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0)) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(960,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0)))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[959])).
% 0.37/0.58 tff(961,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0))),
% 0.37/0.58 inference(transitivity,[status(thm)],[960, 958])).
% 0.37/0.58 tff(962,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(963,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0)),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[962, 961])).
% 0.37/0.58 tff(964,plain,
% 0.37/0.58 (ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[963, 829, 15])).
% 0.37/0.58 tff(965,plain,
% 0.37/0.58 (ssPv4(skf3(elem!0))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[964, 686, 2, 944])).
% 0.37/0.58 tff(966,plain,
% 0.37/0.58 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(967,plain,
% 0.37/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[966])).
% 0.37/0.58 tff(968,plain,
% 0.37/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(969,plain,
% 0.37/0.58 (^[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))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) | ssPv3(V)) <=> (((~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(970,plain,
% 0.37/0.58 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[969])).
% 0.37/0.58 tff(971,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause12')).
% 0.37/0.58 tff(972,plain,
% 0.37/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.37/0.58 tff(973,plain,
% 0.37/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[972, 968])).
% 0.37/0.58 tff(974,plain,(
% 0.37/0.58 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.37/0.58 inference(skolemize,[status(sab)],[973])).
% 0.37/0.58 tff(975,plain,
% 0.37/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[974, 967])).
% 0.37/0.58 tff(976,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(977,plain,
% 0.37/0.58 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(978,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[977])).
% 0.37/0.58 tff(979,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.37/0.58 inference(transitivity,[status(thm)],[978, 976])).
% 0.37/0.58 tff(980,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(981,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[980, 979])).
% 0.37/0.58 tff(982,plain,
% 0.37/0.58 ((~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[981, 975, 15, 42])).
% 0.37/0.58 tff(983,plain,
% 0.37/0.58 (~ssPv2(skf3(elem!0))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[982, 588, 5, 1])).
% 0.37/0.58 tff(984,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(985,plain,
% 0.37/0.58 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(986,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[985])).
% 0.37/0.58 tff(987,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[986, 984])).
% 0.37/0.58 tff(988,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(989,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.37/0.58 tff(990,plain,
% 0.37/0.58 (ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[989, 775, 15, 65])).
% 0.37/0.58 tff(991,plain,
% 0.37/0.58 (ssPv2(skf3(skf3(elem!0)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[990, 983, 944, 965])).
% 0.37/0.58 tff(992,plain,
% 0.37/0.58 ($false),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[554, 991, 965, 588, 704])).
% 0.37/0.58 tff(993,plain,(ssPv3(elem!0) | ssPv1(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.58 tff(994,plain,
% 0.37/0.58 (ssPv2(skf2(elem!0))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[993, 957, 2, 1])).
% 0.37/0.58 tff(995,plain,
% 0.37/0.58 (~ssPv1(skf2(elem!0))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[584, 994, 1, 957])).
% 0.37/0.58 tff(996,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(997,plain,
% 0.37/0.58 ((ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(998,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0)))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[997])).
% 0.37/0.58 tff(999,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0))),
% 0.37/0.58 inference(transitivity,[status(thm)],[998, 996])).
% 0.37/0.58 tff(1000,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(1001,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0)),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.37/0.58 tff(1002,plain,
% 0.37/0.58 (ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[1001, 290, 42])).
% 0.37/0.58 tff(1003,plain,
% 0.37/0.58 (~ssPv3(skf2(elem!0))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[1002, 995, 944, 957])).
% 0.37/0.58 tff(1004,plain,
% 0.37/0.58 (~ssPv4(skf2(elem!0))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[728, 995, 1, 1003])).
% 0.37/0.58 tff(1005,plain,
% 0.37/0.58 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(1006,plain,
% 0.37/0.58 (((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(1007,plain,
% 0.37/0.58 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[1006])).
% 0.37/0.58 tff(1008,plain,
% 0.37/0.58 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[1007, 1005])).
% 0.37/0.58 tff(1009,plain,
% 0.37/0.58 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(1010,plain,
% 0.37/0.58 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.37/0.58 tff(1011,plain,
% 0.37/0.58 (ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[1010, 317, 42])).
% 0.37/0.58 tff(1012,plain,
% 0.37/0.58 ($false),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[1011, 1004, 995, 994, 1])).
% 0.37/0.58 tff(1013,plain,(ssPv2(elem!0) | ssPv1(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.58 tff(1014,plain,
% 0.37/0.58 (ssPv2(elem!0)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[1013, 2])).
% 0.37/0.58 tff(1015,assumption,(~ssPv4(elem!0)), introduced(assumption)).
% 0.37/0.58 tff(1016,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(1017,plain,
% 0.37/0.58 (((~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0)) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(1018,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[1017])).
% 0.37/0.58 tff(1019,plain,
% 0.37/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[1018, 1016])).
% 0.37/0.58 tff(1020,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(1021,plain,
% 0.37/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 0.37/0.58 tff(1022,plain,
% 0.37/0.58 ((~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[1021, 925, 42, 420])).
% 0.37/0.58 tff(1023,plain,
% 0.37/0.58 (~ssPv4(skf2(skf2(elem!0)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[1022, 1015, 5, 944])).
% 0.37/0.58 tff(1024,plain,
% 0.37/0.58 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(1025,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[1024])).
% 0.37/0.59 tff(1026,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1027,plain,
% 0.37/0.59 (^[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(W, V))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv4(X)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) | ssPv2(V)) <=> ((ssPv4(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv2(V)))), rewrite(((ssPv4(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv2(V)) <=> (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) | ssPv2(V)) <=> (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(1028,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[1027])).
% 0.37/0.59 tff(1029,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.37/0.59 tff(1030,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.37/0.59 tff(1031,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1030, 1026])).
% 0.37/0.59 tff(1032,plain,(
% 0.37/0.59 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.59 inference(skolemize,[status(sab)],[1031])).
% 0.37/0.59 tff(1033,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1032, 1025])).
% 0.37/0.59 tff(1034,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1035,plain,
% 0.37/0.59 ((ssPv4(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0)) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1036,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[1035])).
% 0.37/0.59 tff(1037,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.37/0.59 tff(1038,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(1039,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.37/0.59 tff(1040,plain,
% 0.37/0.59 (ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(skf2(elem!0)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1039, 1033, 42, 420])).
% 0.37/0.59 tff(1041,plain,
% 0.37/0.59 ($false),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1040, 1023, 1015, 586, 5])).
% 0.37/0.59 tff(1042,plain,(ssPv4(elem!0) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.59 tff(1043,plain,
% 0.37/0.59 (ssPv4(elem!0)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1042, 5, 586])).
% 0.37/0.59 tff(1044,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1045,plain,
% 0.37/0.59 (((~ssPv4(elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1046,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[1045])).
% 0.37/0.59 tff(1047,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.37/0.59 inference(transitivity,[status(thm)],[1046, 1044])).
% 0.37/0.59 tff(1048,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(1049,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.37/0.59 tff(1050,plain,
% 0.37/0.59 ((~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1049, 907, 42])).
% 0.37/0.59 tff(1051,plain,
% 0.37/0.59 (~ssPv3(elem!0)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1050, 1043, 944, 5])).
% 0.37/0.59 tff(1052,plain,
% 0.37/0.59 ($false),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[685, 1051, 1043, 630, 5])).
% 0.37/0.59 tff(1053,plain,(ssPv2(skf2(elem!0)) | (~ssPv2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.59 tff(1054,plain,
% 0.37/0.59 (ssPv2(skf2(elem!0))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1053, 586])).
% 0.37/0.59 tff(1055,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1056,plain,
% 0.37/0.59 (((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1057,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf2(elem!0)))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[1056])).
% 0.37/0.59 tff(1058,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[1057, 1055])).
% 0.37/0.59 tff(1059,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(1060,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(U, V)) | ssPv3(V) | (~ssPv2(X)) | (~ssPv3(U)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.37/0.59 tff(1061,plain,
% 0.37/0.59 (ssPv4(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1060, 565, 15, 42])).
% 0.37/0.59 tff(1062,plain,
% 0.37/0.59 (ssPv4(skf3(elem!0))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1061, 588, 630, 1054])).
% 0.37/0.59 tff(1063,plain,
% 0.37/0.59 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(1064,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[1063])).
% 0.37/0.59 tff(1065,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1066,plain,
% 0.37/0.59 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(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(W))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssRr(U, X))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv1(X)) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv1(X)))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv1(X)) <=> (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv1(X)) <=> (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(1067,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv1(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[1066])).
% 0.37/0.59 tff(1068,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv1(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.37/0.59 tff(1069,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 0.37/0.59 tff(1070,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1069, 1065])).
% 0.37/0.59 tff(1071,plain,(
% 0.37/0.59 ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.59 inference(skolemize,[status(sab)],[1070])).
% 0.37/0.59 tff(1072,plain,
% 0.37/0.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1071, 1064])).
% 0.37/0.59 tff(1073,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1074,plain,
% 0.37/0.59 ((ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1075,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[1074])).
% 0.37/0.59 tff(1076,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[1075, 1073])).
% 0.37/0.59 tff(1077,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(1078,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv1(skf2(skf3(elem!0))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 0.37/0.59 tff(1079,plain,
% 0.37/0.59 ((~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv1(skf2(skf3(elem!0)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1078, 1072, 15, 180])).
% 0.37/0.59 tff(1080,plain,
% 0.37/0.59 (ssPv1(skf2(skf3(elem!0)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1079, 586, 630, 944])).
% 0.37/0.59 tff(1081,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1082,plain,
% 0.37/0.59 (((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0)) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1083,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[1082])).
% 0.37/0.59 tff(1084,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[1083, 1081])).
% 0.37/0.59 tff(1085,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(1086,plain,
% 0.37/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 0.37/0.59 tff(1087,plain,
% 0.37/0.59 (ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1086, 216, 42, 420])).
% 0.37/0.59 tff(1088,plain,
% 0.37/0.59 (~ssPv1(skf2(skf2(elem!0)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[1087, 588, 586, 1054])).
% 0.37/0.59 tff(1089,plain,
% 0.37/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(1090,plain,
% 0.37/0.59 ((ssPv1(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)))) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1091,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[1090])).
% 0.37/0.60 tff(1092,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[1091, 1089])).
% 0.37/0.60 tff(1093,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(1094,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 0.37/0.60 tff(1095,plain,
% 0.37/0.60 ((~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1094, 129, 42, 420])).
% 0.37/0.60 tff(1096,plain,
% 0.37/0.60 (~ssPv3(skf2(skf2(elem!0)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1095, 1088, 1054, 586])).
% 0.37/0.60 tff(1097,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1098,plain,
% 0.37/0.60 ((ssPv1(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)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1099,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(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)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[1098])).
% 0.37/0.60 tff(1100,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(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)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[1099, 1097])).
% 0.37/0.60 tff(1101,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(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)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(1102,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 0.37/0.60 tff(1103,plain,
% 0.37/0.60 ((~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1102, 388, 42, 420])).
% 0.37/0.60 tff(1104,plain,
% 0.37/0.60 (~ssPv1(skf2(elem!0))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1103, 1096, 944, 1088])).
% 0.37/0.60 tff(1105,plain,
% 0.37/0.60 (~ssPv3(skf2(elem!0))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1002, 1104, 944, 588])).
% 0.37/0.60 tff(1106,plain,
% 0.37/0.60 (ssPv4(skf2(elem!0))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[754, 1105, 1096, 1104])).
% 0.37/0.60 tff(1107,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1108,plain,
% 0.37/0.60 ((ssPv3(skf2(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1109,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[1108])).
% 0.37/0.60 tff(1110,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[1109, 1107])).
% 0.37/0.60 tff(1111,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(1112,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 0.37/0.60 tff(1113,plain,
% 0.37/0.60 ((~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1112, 547, 42, 420])).
% 0.37/0.60 tff(1114,plain,
% 0.37/0.60 (~ssPv4(elem!0)),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1113, 1106, 586, 1096])).
% 0.37/0.60 tff(1115,plain,
% 0.37/0.60 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U))))),
% 0.37/0.60 inference(bind,[status(th)],[])).
% 0.37/0.60 tff(1116,plain,
% 0.37/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.60 inference(quant_intro,[status(thm)],[1115])).
% 0.37/0.60 tff(1117,plain,
% 0.37/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1118,plain,
% 0.37/0.60 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(U))))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))))),
% 0.37/0.60 inference(bind,[status(th)],[])).
% 0.37/0.60 tff(1119,plain,
% 0.37/0.60 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.60 inference(quant_intro,[status(thm)],[1118])).
% 0.37/0.60 tff(1120,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) | ssPv4(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause30')).
% 0.37/0.60 tff(1121,plain,
% 0.37/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 0.37/0.60 tff(1122,plain,
% 0.37/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[1121, 1117])).
% 0.37/0.60 tff(1123,plain,(
% 0.37/0.60 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.60 inference(skolemize,[status(sab)],[1122])).
% 0.37/0.60 tff(1124,plain,
% 0.37/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[1123, 1116])).
% 0.37/0.60 tff(1125,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1126,plain,
% 0.37/0.60 (((~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1127,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0))))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[1126])).
% 0.37/0.60 tff(1128,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0)))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[1127, 1125])).
% 0.37/0.60 tff(1129,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), skf2(skf3(elem!0)))) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv3(skf3(elem!0))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(1130,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv1(skf2(skf3(elem!0)))) | (~ssRr(skf3(elem!0), skf2(skf3(elem!0))))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[1129, 1128])).
% 0.37/0.60 tff(1131,plain,
% 0.37/0.60 ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv1(skf2(skf3(elem!0))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1130, 1124, 15, 180])).
% 0.37/0.60 tff(1132,plain,
% 0.37/0.60 (~ssPv2(skf3(elem!0))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1131, 1114, 630, 1080])).
% 0.37/0.60 tff(1133,plain,
% 0.37/0.60 (ssPv2(skf3(skf3(elem!0)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[990, 1132, 944, 1062])).
% 0.37/0.60 tff(1134,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1135,plain,
% 0.37/0.60 ((ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1136,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0)))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[1135])).
% 0.37/0.60 tff(1137,plain,
% 0.37/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[1136, 1134])).
% 0.37/0.60 tff(1138,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(1139,plain,
% 0.37/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 0.37/0.60 tff(1140,plain,
% 0.37/0.60 (ssPv2(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1139, 1033, 15, 65])).
% 0.37/0.60 tff(1141,plain,
% 0.37/0.60 (ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1140, 1132, 1133, 1114])).
% 0.37/0.60 tff(1142,plain,
% 0.37/0.60 ($false),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[554, 1141, 1133, 588, 1062])).
% 0.37/0.60 tff(1143,plain,(ssPv3(elem!0) | (~ssPv2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.60 tff(1144,plain,
% 0.37/0.60 (ssPv3(elem!0)),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[1143, 1014])).
% 0.37/0.60 tff(1145,plain,
% 0.37/0.60 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V))) <=> (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V))))),
% 0.37/0.60 inference(bind,[status(th)],[])).
% 0.37/0.60 tff(1146,plain,
% 0.37/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))),
% 0.37/0.60 inference(quant_intro,[status(thm)],[1145])).
% 0.37/0.60 tff(1147,plain,
% 0.37/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(1148,plain,
% 0.37/0.60 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv1(X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) <=> (((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv3(V))))), rewrite((((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv3(V))) <=> ((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) <=> ((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V))))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) | ssPv4(U)) <=> (((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V))) | ssPv4(U)))), rewrite((((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))))),
% 0.37/0.61 inference(bind,[status(th)],[])).
% 0.37/0.61 tff(1149,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))),
% 0.37/0.61 inference(quant_intro,[status(thm)],[1148])).
% 0.37/0.61 tff(1150,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.37/0.61 tff(1151,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 0.37/0.61 tff(1152,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1151, 1147])).
% 0.37/0.61 tff(1153,plain,(
% 0.37/0.61 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))),
% 0.37/0.61 inference(skolemize,[status(sab)],[1152])).
% 0.37/0.61 tff(1154,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1153, 1146])).
% 0.37/0.61 tff(1155,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1156,plain,
% 0.37/0.61 ((ssPv4(skf3(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1157,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0)))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[1156])).
% 0.37/0.61 tff(1158,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))))),
% 0.37/0.61 inference(transitivity,[status(thm)],[1157, 1155])).
% 0.37/0.61 tff(1159,plain,
% 0.37/0.61 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(1160,plain,
% 0.37/0.61 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 0.37/0.61 tff(1161,plain,
% 0.37/0.61 ((~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1160, 1154, 15, 65])).
% 0.37/0.61 tff(1162,plain,
% 0.37/0.61 (ssPv4(skf3(skf3(elem!0)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1161, 1144, 630, 944])).
% 0.37/0.61 tff(1163,plain,
% 0.37/0.61 ($false),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[711, 1162, 1144, 2, 956])).
% 0.37/0.61 tff(1164,plain,(ssPv1(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.61 tff(1165,plain,
% 0.37/0.61 (~ssPv4(skf3(elem!0))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[914, 1, 630, 1164])).
% 0.37/0.61 tff(1166,plain,
% 0.37/0.61 (~ssPv4(skf2(elem!0))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[932, 1165, 1, 1164])).
% 0.37/0.61 tff(1167,plain,
% 0.37/0.61 (~ssPv1(skf2(elem!0))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[942, 1166, 1165, 1])).
% 0.37/0.61 tff(1168,plain,
% 0.37/0.61 (ssPv3(skf2(elem!0))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[395, 1167, 1164, 944])).
% 0.37/0.61 tff(1169,plain,
% 0.37/0.61 (~ssPv4(elem!0)),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[614, 1, 944, 1164])).
% 0.37/0.61 tff(1170,plain,
% 0.37/0.61 (~ssPv3(elem!0)),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[746, 1167, 1169, 1166])).
% 0.37/0.61 tff(1171,plain,
% 0.37/0.61 ($false),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1002, 1170, 1168, 944, 1167])).
% 0.37/0.61 tff(1172,plain,(ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.61 tff(1173,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(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] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1174,plain,
% 0.37/0.61 ((ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1175,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[1174])).
% 0.37/0.61 tff(1176,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.61 inference(transitivity,[status(thm)],[1175, 1173])).
% 0.37/0.61 tff(1177,plain,
% 0.37/0.61 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv1(elem!0)))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(1178,plain,
% 0.37/0.61 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 0.37/0.61 tff(1179,plain,
% 0.37/0.61 ((~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1178, 472, 15, 65])).
% 0.37/0.61 tff(1180,plain,
% 0.37/0.61 (ssPv3(skf3(skf3(elem!0)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1179, 1164, 630, 944])).
% 0.37/0.61 tff(1181,plain,
% 0.37/0.61 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))))),
% 0.37/0.61 inference(bind,[status(th)],[])).
% 0.37/0.61 tff(1182,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.61 inference(quant_intro,[status(thm)],[1181])).
% 0.37/0.61 tff(1183,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1184,plain,
% 0.37/0.61 (^[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(W))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))))),
% 0.37/0.61 inference(bind,[status(th)],[])).
% 0.37/0.61 tff(1185,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) | (~ssPv4(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.61 inference(quant_intro,[status(thm)],[1184])).
% 0.37/0.61 tff(1186,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) | (~ssPv4(U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.37/0.61 tff(1187,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 0.37/0.61 tff(1188,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1187, 1183])).
% 0.37/0.61 tff(1189,plain,(
% 0.37/0.61 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.61 inference(skolemize,[status(sab)],[1188])).
% 0.37/0.61 tff(1190,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1189, 1182])).
% 0.37/0.61 tff(1191,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1192,plain,
% 0.37/0.61 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1193,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[1192])).
% 0.37/0.61 tff(1194,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.37/0.61 inference(transitivity,[status(thm)],[1193, 1191])).
% 0.37/0.61 tff(1195,plain,
% 0.37/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(1196,plain,
% 0.37/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 0.37/0.61 tff(1197,plain,
% 0.37/0.61 ((~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1196, 1190, 15])).
% 0.37/0.61 tff(1198,plain,
% 0.37/0.61 (~ssPv4(skf3(elem!0))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1197, 1172, 1164, 944])).
% 0.37/0.61 tff(1199,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(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)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | (~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1200,plain,
% 0.37/0.61 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(skf3(elem!0))))) <=> ((~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1201,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[1200])).
% 0.37/0.61 tff(1202,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | (~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.61 inference(transitivity,[status(thm)],[1201, 1199])).
% 0.37/0.61 tff(1203,plain,
% 0.37/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(1204,plain,
% 0.37/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | (~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 0.37/0.61 tff(1205,plain,
% 0.37/0.61 ((~ssPv1(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1204, 1124, 65])).
% 0.37/0.61 tff(1206,plain,
% 0.37/0.61 (~ssPv2(skf3(skf3(elem!0)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1205, 1198, 1180, 1164])).
% 0.37/0.61 tff(1207,plain,
% 0.37/0.61 (ssPv2(skf2(elem!0))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1053, 1172])).
% 0.37/0.61 tff(1208,plain,
% 0.37/0.61 (ssPv3(elem!0)),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[1143, 1172])).
% 0.37/0.61 tff(1209,plain,
% 0.37/0.61 (ssPv1(skf2(elem!0))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[487, 1208, 944, 1207])).
% 0.37/0.61 tff(1210,plain,
% 0.37/0.61 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))),
% 0.37/0.61 inference(bind,[status(th)],[])).
% 0.37/0.61 tff(1211,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.37/0.61 inference(quant_intro,[status(thm)],[1210])).
% 0.37/0.61 tff(1212,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1213,plain,
% 0.37/0.61 (^[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(W, V))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> (((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(V))))), rewrite((((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))))),
% 0.37/0.61 inference(bind,[status(th)],[])).
% 0.37/0.61 tff(1214,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.37/0.61 inference(quant_intro,[status(thm)],[1213])).
% 0.37/0.61 tff(1215,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.37/0.61 tff(1216,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 0.37/0.61 tff(1217,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1216, 1212])).
% 0.37/0.61 tff(1218,plain,(
% 0.37/0.61 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.37/0.61 inference(skolemize,[status(sab)],[1217])).
% 0.37/0.61 tff(1219,plain,
% 0.37/0.61 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[1218, 1211])).
% 0.37/0.61 tff(1220,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1221,plain,
% 0.37/0.61 (((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(1222,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0)))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[1221])).
% 0.37/0.61 tff(1223,plain,
% 0.37/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.37/0.62 inference(transitivity,[status(thm)],[1222, 1220])).
% 0.37/0.62 tff(1224,plain,
% 0.37/0.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(1225,plain,
% 0.37/0.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.37/0.62 tff(1226,plain,
% 0.37/0.62 ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[1225, 1219, 15, 42])).
% 0.37/0.62 tff(1227,plain,
% 0.37/0.62 (~ssPv2(skf3(elem!0))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[1226, 1209, 1164, 944])).
% 0.37/0.62 tff(1228,plain,
% 0.37/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(1229,plain,
% 0.37/0.62 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(1230,plain,
% 0.37/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[1229])).
% 0.37/0.62 tff(1231,plain,
% 0.37/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.37/0.62 inference(transitivity,[status(thm)],[1230, 1228])).
% 0.37/0.62 tff(1232,plain,
% 0.37/0.62 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(1233,plain,
% 0.37/0.62 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 0.37/0.62 tff(1234,plain,
% 0.37/0.62 (ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf3(skf3(elem!0)))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[1233, 868, 15, 65])).
% 0.37/0.62 tff(1235,plain,
% 0.37/0.62 ($false),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[1234, 1227, 1206, 630, 1172])).
% 0.37/0.62 % SZS output end Proof
% 0.37/0.62 % E exiting
%------------------------------------------------------------------------------