%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN755-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:39:58 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.56s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN755-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:45:12 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.56 % SZS status Unsatisfiable
% 0.19/0.56 % SZS output start Proof
% 0.19/0.56 tff(ssPv3_type, type, (
% 0.19/0.56 ssPv3: $i > $o)).
% 0.19/0.56 tff(elem_0_type, type, (
% 0.19/0.56 elem_0: $i)).
% 0.19/0.56 tff(ssPv1_type, type, (
% 0.19/0.56 ssPv1: $i > $o)).
% 0.19/0.56 tff(skf1_type, type, (
% 0.19/0.56 skf1: $i > $i)).
% 0.19/0.56 tff(ssPv2_type, type, (
% 0.19/0.56 ssPv2: $i > $o)).
% 0.19/0.56 tff(ssPv4_type, type, (
% 0.19/0.56 ssPv4: $i > $o)).
% 0.19/0.56 tff(ssRr_type, type, (
% 0.19/0.56 ssRr: ( $i * $i ) > $o)).
% 0.19/0.56 tff(1,assumption,(~ssPv2(skf1(elem!0))), introduced(assumption)).
% 0.19/0.56 tff(2,assumption,(~ssPv4(skf1(elem!0))), introduced(assumption)).
% 0.19/0.56 tff(3,assumption,(~ssPv1(skf1(elem!0))), introduced(assumption)).
% 0.19/0.56 tff(4,assumption,(~ssPv4(skf1(skf1(elem!0)))), introduced(assumption)).
% 0.19/0.56 tff(5,plain,
% 0.19/0.56 (^[U: $i] : refl(ssRr(U, skf1(U)) <=> ssRr(U, skf1(U)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(6,plain,
% 0.19/0.56 (![U: $i] : ssRr(U, skf1(U)) <=> ![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.56 tff(7,plain,
% 0.19/0.56 (![U: $i] : ssRr(U, skf1(U)) <=> ![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(8,axiom,(![U: $i] : ssRr(U, skf1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.19/0.56 tff(9,plain,
% 0.19/0.56 (![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.56 tff(10,plain,(
% 0.19/0.56 ![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.56 inference(skolemize,[status(sab)],[9])).
% 0.19/0.56 tff(11,plain,
% 0.19/0.56 (![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.56 tff(12,plain,
% 0.19/0.56 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(elem!0), skf1(skf1(elem!0)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(13,plain,
% 0.19/0.56 (ssRr(skf1(elem!0), skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.56 tff(14,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(15,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.56 tff(16,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(17,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) | ssPv4(U)) <=> ((ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv4(U)))), rewrite(((ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(18,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.56 tff(19,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause12')).
% 0.19/0.56 tff(20,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.56 tff(21,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.56 tff(22,plain,(
% 0.19/0.56 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(skolemize,[status(sab)],[21])).
% 0.19/0.56 tff(23,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.19/0.56 tff(24,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(25,plain,
% 0.19/0.56 ((ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))) <=> (ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(26,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.56 tff(27,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.56 tff(28,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(29,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.56 tff(30,plain,
% 0.19/0.56 (ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[29, 23, 13])).
% 0.19/0.56 tff(31,plain,
% 0.19/0.56 (~ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[30, 4, 1, 2])).
% 0.19/0.56 tff(32,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) <=> (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(33,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.56 tff(34,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(35,plain,
% 0.19/0.56 (^[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)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv3(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) | ssPv2(U)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(36,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.56 tff(37,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause15')).
% 0.19/0.56 tff(38,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.56 tff(39,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.56 tff(40,plain,(
% 0.19/0.56 ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.56 inference(skolemize,[status(sab)],[39])).
% 0.19/0.56 tff(41,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.56 tff(42,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(43,plain,
% 0.19/0.56 ((ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0))))) <=> (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(44,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.56 tff(45,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[44, 42])).
% 0.19/0.56 tff(46,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(47,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.56 tff(48,plain,
% 0.19/0.56 (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[47, 41, 13])).
% 0.19/0.56 tff(49,plain,
% 0.19/0.56 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[48, 31, 3, 1])).
% 0.19/0.56 tff(50,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(51,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.56 tff(52,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(53,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv1(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> ((ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv2(U)))), rewrite(((ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(54,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.56 tff(55,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause16')).
% 0.19/0.56 tff(56,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.56 tff(57,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.56 tff(58,plain,(
% 0.19/0.56 ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.56 inference(skolemize,[status(sab)],[57])).
% 0.19/0.56 tff(59,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.56 tff(60,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(61,plain,
% 0.19/0.56 ((ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0)))) <=> (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(62,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.56 tff(63,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.56 tff(64,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(65,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.56 tff(66,plain,
% 0.19/0.56 (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[65, 59, 13])).
% 0.19/0.56 tff(67,plain,
% 0.19/0.56 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[66, 31, 3, 1])).
% 0.19/0.56 tff(68,plain,
% 0.19/0.56 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(69,plain,
% 0.19/0.56 (ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[68, 11])).
% 0.19/0.56 tff(70,plain,
% 0.19/0.56 (^[V: $i, U: $i] : refl((ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) <=> (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(71,plain,
% 0.19/0.56 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.56 tff(72,plain,
% 0.19/0.56 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(73,plain,
% 0.19/0.56 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | ssPv1(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) <=> ((ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) | ssPv2(U)))), rewrite(((ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) | ssPv3(U)) <=> ((ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) | ssPv3(U)))), rewrite(((ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) | ssPv3(U)) <=> (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) | ssPv3(U)) <=> (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(74,plain,
% 0.19/0.56 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) | ssPv3(U)) <=> ![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.56 tff(75,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.19/0.56 tff(76,plain,
% 0.19/0.56 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.56 tff(77,plain,
% 0.19/0.56 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.56 tff(78,plain,(
% 0.19/0.56 ![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.56 inference(skolemize,[status(sab)],[77])).
% 0.19/0.56 tff(79,plain,
% 0.19/0.56 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.56 tff(80,plain,
% 0.19/0.56 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(81,plain,
% 0.19/0.56 ((ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(82,plain,
% 0.19/0.56 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.56 tff(83,plain,
% 0.19/0.56 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.56 tff(84,plain,
% 0.19/0.56 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(85,plain,
% 0.19/0.56 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.56 tff(86,plain,
% 0.19/0.56 (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[85, 79, 69])).
% 0.19/0.56 tff(87,plain,
% 0.19/0.56 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[86, 67, 31, 49])).
% 0.19/0.56 tff(88,assumption,(~ssPv2(skf1(skf1(elem!0)))), introduced(assumption)).
% 0.19/0.56 tff(89,assumption,(~ssPv3(skf1(skf1(elem!0)))), introduced(assumption)).
% 0.19/0.56 tff(90,assumption,(~ssPv1(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 0.19/0.56 tff(91,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) <=> (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(92,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.56 tff(93,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(94,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv4(V) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) <=> (((~ssRr(U, V)) | ssPv4(V) | (~ssRr(U, W))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | ssPv4(V) | (~ssRr(U, W))) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) | ssPv3(U)) <=> ((ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) | ssPv3(U)))), rewrite(((ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) | ssPv3(U)) <=> (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) | ssPv3(U)) <=> (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(95,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.57 tff(96,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.19/0.57 tff(97,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.57 tff(98,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.57 tff(99,plain,(
% 0.19/0.57 ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[98])).
% 0.19/0.57 tff(100,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.19/0.57 tff(101,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(102,plain,
% 0.19/0.57 ((ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(103,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.57 tff(104,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[103, 101])).
% 0.19/0.57 tff(105,plain,
% 0.19/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(106,plain,
% 0.19/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.57 tff(107,plain,
% 0.19/0.57 (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[106, 100, 69])).
% 0.19/0.57 tff(108,plain,
% 0.19/0.57 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[107, 90, 88, 89])).
% 0.19/0.57 tff(109,plain,
% 0.19/0.57 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(110,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.57 tff(111,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(112,plain,
% 0.19/0.57 (^[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))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) | ssPv4(U)) <=> ((ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv4(U)))), rewrite(((ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(113,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.57 tff(114,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause24')).
% 0.19/0.57 tff(115,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.57 tff(116,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.57 tff(117,plain,(
% 0.19/0.57 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[116])).
% 0.19/0.57 tff(118,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.19/0.57 tff(119,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(120,plain,
% 0.19/0.57 ((ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(121,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[120])).
% 0.19/0.57 tff(122,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[121, 119])).
% 0.19/0.57 tff(123,plain,
% 0.19/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(124,plain,
% 0.19/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.57 tff(125,plain,
% 0.19/0.57 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[124, 118, 69])).
% 0.19/0.57 tff(126,plain,
% 0.19/0.57 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[125, 108, 4, 88])).
% 0.19/0.57 tff(127,plain,
% 0.19/0.57 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(128,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.57 tff(129,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(130,plain,
% 0.19/0.57 (^[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)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) | ssPv4(U)) <=> ((ssPv2(U) | (~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv4(U)))), rewrite(((ssPv2(U) | (~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(131,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.57 tff(132,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 0.19/0.57 tff(133,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.57 tff(134,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.19/0.57 tff(135,plain,(
% 0.19/0.57 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[134])).
% 0.19/0.57 tff(136,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.19/0.57 tff(137,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(138,plain,
% 0.19/0.57 ((ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(139,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[138])).
% 0.19/0.57 tff(140,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[139, 137])).
% 0.19/0.57 tff(141,plain,
% 0.19/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(142,plain,
% 0.19/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.57 tff(143,plain,
% 0.19/0.57 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[142, 136, 69])).
% 0.19/0.57 tff(144,plain,
% 0.19/0.57 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[143, 90, 4, 88])).
% 0.19/0.57 tff(145,plain,
% 0.19/0.57 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(146,plain,
% 0.19/0.57 (ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[145, 11])).
% 0.19/0.57 tff(147,plain,
% 0.19/0.57 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(148,plain,
% 0.19/0.57 ((ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(149,plain,
% 0.19/0.57 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[148])).
% 0.19/0.57 tff(150,plain,
% 0.19/0.57 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[149, 147])).
% 0.19/0.57 tff(151,plain,
% 0.19/0.57 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(152,plain,
% 0.19/0.57 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.57 tff(153,plain,
% 0.19/0.57 (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[152, 79, 146])).
% 0.19/0.57 tff(154,plain,
% 0.19/0.57 (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[153, 126, 90, 144])).
% 0.19/0.57 tff(155,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(156,plain,
% 0.19/0.57 ((ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(157,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[156])).
% 0.19/0.58 tff(158,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[157, 155])).
% 0.19/0.58 tff(159,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(160,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.58 tff(161,plain,
% 0.19/0.58 (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[160, 100, 146])).
% 0.19/0.58 tff(162,plain,
% 0.19/0.58 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[161, 154, 144, 126])).
% 0.19/0.58 tff(163,plain,
% 0.19/0.58 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(164,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[163])).
% 0.19/0.58 tff(165,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(166,plain,
% 0.19/0.58 (^[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))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(167,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[166])).
% 0.19/0.58 tff(168,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.19/0.58 tff(169,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.58 tff(170,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.19/0.58 tff(171,plain,(
% 0.19/0.58 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.58 inference(skolemize,[status(sab)],[170])).
% 0.19/0.58 tff(172,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.19/0.58 tff(173,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(174,plain,
% 0.19/0.58 ((ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(175,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.58 tff(176,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[175, 173])).
% 0.19/0.58 tff(177,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(178,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.58 tff(179,plain,
% 0.19/0.58 ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[178, 172, 146])).
% 0.19/0.58 tff(180,plain,
% 0.19/0.58 (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[179, 162, 108, 126])).
% 0.19/0.58 tff(181,plain,
% 0.19/0.58 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(182,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.58 tff(183,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(184,plain,
% 0.19/0.58 (^[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)) | ssPv3(U)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv3(U)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv3(U)) <=> (ssPv3(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)) | ssPv3(U)) <=> (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(185,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.58 tff(186,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause29')).
% 0.19/0.58 tff(187,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.58 tff(188,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.19/0.58 tff(189,plain,(
% 0.19/0.58 ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.58 inference(skolemize,[status(sab)],[188])).
% 0.19/0.58 tff(190,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.19/0.58 tff(191,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(192,plain,
% 0.19/0.58 ((ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(193,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[192])).
% 0.19/0.58 tff(194,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[193, 191])).
% 0.19/0.58 tff(195,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(196,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.58 tff(197,plain,
% 0.19/0.58 (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[196, 190, 146])).
% 0.19/0.58 tff(198,plain,
% 0.19/0.58 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[197, 162, 90, 126])).
% 0.19/0.58 tff(199,plain,
% 0.19/0.58 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) <=> (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(200,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[199])).
% 0.19/0.58 tff(201,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(202,plain,
% 0.19/0.58 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(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, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, X))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) <=> (((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv4(U))))), rewrite((((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv4(U))) <=> ((~ssPv4(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) <=> ((~ssPv4(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) <=> (((~ssPv4(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | ssPv3(W)))), rewrite((((~ssPv4(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | ssPv3(W)) <=> ((~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) <=> ((~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) | ssPv2(X)) <=> (((~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(X)))), rewrite((((~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(203,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) | ssPv2(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[202])).
% 0.19/0.58 tff(204,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) | ssPv2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.19/0.58 tff(205,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.58 tff(206,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.19/0.58 tff(207,plain,(
% 0.19/0.58 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.58 inference(skolemize,[status(sab)],[206])).
% 0.19/0.58 tff(208,plain,
% 0.19/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.19/0.58 tff(209,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(210,plain,
% 0.19/0.58 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(211,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[210])).
% 0.19/0.58 tff(212,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[211, 209])).
% 0.19/0.58 tff(213,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(214,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.58 tff(215,plain,
% 0.19/0.58 ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[214, 208, 146])).
% 0.19/0.58 tff(216,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[215, 198, 180, 108, 162])).
% 0.19/0.58 tff(217,plain,(ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(218,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[217, 87, 49, 4, 31])).
% 0.19/0.58 tff(219,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(220,plain,
% 0.19/0.58 (ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[219, 3, 1, 2])).
% 0.19/0.58 tff(221,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(222,plain,
% 0.19/0.58 ((ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0))))) <=> (ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(223,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[222])).
% 0.19/0.58 tff(224,plain,
% 0.19/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[223, 221])).
% 0.19/0.58 tff(225,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(226,plain,
% 0.19/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.19/0.59 tff(227,plain,
% 0.19/0.59 (ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[226, 118, 13])).
% 0.19/0.59 tff(228,plain,
% 0.19/0.59 (~ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[227, 220, 1, 2])).
% 0.19/0.59 tff(229,plain,
% 0.19/0.59 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[48, 228, 3, 1])).
% 0.19/0.59 tff(230,plain,
% 0.19/0.59 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[66, 228, 3, 1])).
% 0.19/0.59 tff(231,plain,
% 0.19/0.59 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[86, 230, 228, 229])).
% 0.19/0.59 tff(232,plain,
% 0.19/0.59 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[107, 231, 229, 228])).
% 0.19/0.59 tff(233,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(234,plain,
% 0.19/0.59 ((ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))) <=> (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(235,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[234])).
% 0.19/0.59 tff(236,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(transitivity,[status(thm)],[235, 233])).
% 0.19/0.59 tff(237,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(238,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.19/0.59 tff(239,plain,
% 0.19/0.59 (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[238, 190, 69])).
% 0.19/0.59 tff(240,plain,
% 0.19/0.59 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[239, 232, 230, 228])).
% 0.19/0.59 tff(241,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(242,plain,
% 0.19/0.59 ((ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))) <=> (ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(243,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[242])).
% 0.19/0.59 tff(244,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(transitivity,[status(thm)],[243, 241])).
% 0.19/0.59 tff(245,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(246,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.59 tff(247,plain,
% 0.19/0.59 (ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[246, 172, 69])).
% 0.19/0.59 tff(248,plain,
% 0.19/0.59 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[247, 232, 220, 228])).
% 0.19/0.59 tff(249,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(250,plain,
% 0.19/0.59 ((ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(251,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.59 tff(252,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(transitivity,[status(thm)],[251, 249])).
% 0.19/0.59 tff(253,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(254,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.59 tff(255,plain,
% 0.19/0.59 ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[254, 208, 69])).
% 0.19/0.59 tff(256,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[255, 248, 240, 220, 232])).
% 0.19/0.59 tff(257,plain,(ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(258,plain,
% 0.19/0.59 (ssPv1(skf1(elem!0))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[257, 2, 1])).
% 0.19/0.59 tff(259,assumption,(~ssPv3(skf1(elem!0))), introduced(assumption)).
% 0.19/0.59 tff(260,plain,
% 0.19/0.59 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(261,plain,
% 0.19/0.59 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(262,plain,
% 0.19/0.59 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.19/0.59 tff(263,plain,
% 0.19/0.59 (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[262, 79, 13])).
% 0.19/0.59 tff(264,plain,
% 0.19/0.59 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[263, 1, 3, 259])).
% 0.19/0.59 tff(265,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(266,plain,
% 0.19/0.59 ((ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(267,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[266])).
% 0.19/0.59 tff(268,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(transitivity,[status(thm)],[267, 265])).
% 0.19/0.59 tff(269,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(270,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.19/0.59 tff(271,plain,
% 0.19/0.59 (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[270, 100, 13])).
% 0.19/0.59 tff(272,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[271, 264, 1, 259, 4])).
% 0.19/0.59 tff(273,plain,(ssPv2(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(274,plain,
% 0.19/0.59 (ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[273, 1, 259, 3])).
% 0.19/0.59 tff(275,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(276,plain,
% 0.19/0.59 ((ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0))))) <=> (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(277,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[276])).
% 0.19/0.59 tff(278,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(transitivity,[status(thm)],[277, 275])).
% 0.19/0.59 tff(279,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(280,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.19/0.59 tff(281,plain,
% 0.19/0.59 (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[280, 190, 13])).
% 0.19/0.59 tff(282,plain,
% 0.19/0.59 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[281, 274, 3, 259])).
% 0.19/0.59 tff(283,assumption,(ssPv4(skf1(elem!0))), introduced(assumption)).
% 0.19/0.59 tff(284,assumption,(ssPv4(skf1(skf1(elem!0)))), introduced(assumption)).
% 0.19/0.59 tff(285,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(286,plain,
% 0.19/0.59 ((ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0))))) <=> ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(287,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[286])).
% 0.19/0.59 tff(288,plain,
% 0.19/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(transitivity,[status(thm)],[287, 285])).
% 0.19/0.59 tff(289,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(290,plain,
% 0.19/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.19/0.59 tff(291,plain,
% 0.19/0.59 ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[290, 172, 13])).
% 0.19/0.59 tff(292,plain,
% 0.19/0.59 (~ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[291, 284, 259, 283])).
% 0.19/0.60 tff(293,plain,
% 0.19/0.60 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[281, 284, 3, 259])).
% 0.19/0.60 tff(294,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(295,plain,
% 0.19/0.60 ((ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))) <=> ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(296,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.60 inference(monotonicity,[status(thm)],[295])).
% 0.19/0.60 tff(297,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.60 inference(transitivity,[status(thm)],[296, 294])).
% 0.19/0.60 tff(298,plain,
% 0.19/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(299,plain,
% 0.19/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.19/0.60 tff(300,plain,
% 0.19/0.60 ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[299, 208, 13])).
% 0.19/0.60 tff(301,plain,
% 0.19/0.60 ($false),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[300, 293, 284, 283, 292])).
% 0.19/0.60 tff(302,plain,((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.60 tff(303,plain,
% 0.19/0.60 (~ssPv4(skf1(elem!0))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[302, 274, 3, 259])).
% 0.19/0.60 tff(304,plain,
% 0.19/0.60 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) <=> (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))))),
% 0.19/0.60 inference(bind,[status(th)],[])).
% 0.19/0.60 tff(305,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.60 inference(quant_intro,[status(thm)],[304])).
% 0.19/0.60 tff(306,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(307,plain,
% 0.19/0.60 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(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, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv3(W))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv3(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | (~ssRr(U, X))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) <=> (((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | ssPv2(X)))), rewrite((((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | ssPv2(X)) <=> (ssPv2(X) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) <=> (ssPv2(X) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) | ssPv4(U)) <=> ((ssPv2(X) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | ssPv4(U)))), rewrite(((ssPv2(X) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | ssPv4(U)) <=> (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) | ssPv4(U)) <=> (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))))),
% 0.19/0.60 inference(bind,[status(th)],[])).
% 0.19/0.60 tff(308,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.60 inference(quant_intro,[status(thm)],[307])).
% 0.19/0.60 tff(309,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.19/0.60 tff(310,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.19/0.60 tff(311,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[310, 306])).
% 0.19/0.60 tff(312,plain,(
% 0.19/0.60 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.60 inference(skolemize,[status(sab)],[311])).
% 0.19/0.60 tff(313,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[312, 305])).
% 0.19/0.60 tff(314,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(315,plain,
% 0.19/0.60 ((ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0))))) <=> (ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(316,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.60 inference(monotonicity,[status(thm)],[315])).
% 0.19/0.60 tff(317,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.60 inference(transitivity,[status(thm)],[316, 314])).
% 0.19/0.60 tff(318,plain,
% 0.19/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(319,plain,
% 0.19/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.19/0.60 tff(320,plain,
% 0.19/0.60 (ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[319, 313, 13])).
% 0.19/0.60 tff(321,plain,
% 0.19/0.60 (~ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[320, 303, 282, 274])).
% 0.19/0.60 tff(322,plain,
% 0.19/0.60 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[263, 1, 259, 3])).
% 0.19/0.60 tff(323,plain,
% 0.19/0.60 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[86, 321, 322, 282])).
% 0.19/0.60 tff(324,plain,
% 0.19/0.60 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[107, 323, 282, 321])).
% 0.19/0.60 tff(325,plain,
% 0.19/0.60 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[247, 324, 274, 321])).
% 0.19/0.60 tff(326,plain,
% 0.19/0.60 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[239, 324, 322, 321])).
% 0.19/0.60 tff(327,plain,
% 0.19/0.60 ($false),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[255, 326, 325, 274, 324])).
% 0.19/0.60 tff(328,plain,(ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.60 tff(329,plain,
% 0.19/0.60 (ssPv2(skf1(elem!0))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[328, 3, 259])).
% 0.19/0.60 tff(330,plain,
% 0.19/0.60 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(elem!0, skf1(elem!0))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(331,plain,
% 0.19/0.60 (ssRr(elem!0, skf1(elem!0))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[330, 11])).
% 0.19/0.60 tff(332,plain,
% 0.19/0.60 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) <=> (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))),
% 0.19/0.60 inference(bind,[status(th)],[])).
% 0.19/0.60 tff(333,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.60 inference(quant_intro,[status(thm)],[332])).
% 0.19/0.60 tff(334,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(335,plain,
% 0.19/0.60 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssPv2(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> (((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> (((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssRr(U, X))))), rewrite((((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssRr(U, X))) <=> ((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> ((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) <=> (((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv3(W)))), rewrite((((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv3(W)) <=> ((~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) <=> ((~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) <=> (((~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv1(X)))), rewrite((((~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) | ssPv4(U)) <=> ((ssPv1(X) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv4(U)))), rewrite(((ssPv1(X) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv4(U)) <=> (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) | ssPv4(U)) <=> (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))))),
% 0.19/0.60 inference(bind,[status(th)],[])).
% 0.19/0.60 tff(336,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.60 inference(quant_intro,[status(thm)],[335])).
% 0.19/0.60 tff(337,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.19/0.60 tff(338,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.19/0.60 tff(339,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[338, 334])).
% 0.19/0.60 tff(340,plain,(
% 0.19/0.60 ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.60 inference(skolemize,[status(sab)],[339])).
% 0.19/0.60 tff(341,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[340, 333])).
% 0.19/0.60 tff(342,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ssPv4(elem!0) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(343,plain,
% 0.19/0.60 ((ssPv1(skf1(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))) <=> (ssPv4(elem!0) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(344,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.19/0.60 inference(monotonicity,[status(thm)],[343])).
% 0.19/0.60 tff(345,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ssPv4(elem!0) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.60 inference(transitivity,[status(thm)],[344, 342])).
% 0.19/0.60 tff(346,plain,
% 0.19/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(347,plain,
% 0.19/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ssPv4(elem!0) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.19/0.60 tff(348,plain,
% 0.19/0.60 (ssPv4(elem!0) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0)))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[347, 341, 331])).
% 0.19/0.60 tff(349,plain,
% 0.19/0.60 (ssPv4(elem!0)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[348, 329, 259, 3])).
% 0.19/0.60 tff(350,plain,
% 0.19/0.60 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))))),
% 0.19/0.60 inference(bind,[status(th)],[])).
% 0.19/0.60 tff(351,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.60 inference(quant_intro,[status(thm)],[350])).
% 0.19/0.60 tff(352,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(353,plain,
% 0.19/0.60 (^[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)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))))),
% 0.19/0.60 inference(bind,[status(th)],[])).
% 0.19/0.60 tff(354,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.60 inference(quant_intro,[status(thm)],[353])).
% 0.19/0.60 tff(355,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.19/0.60 tff(356,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.19/0.60 tff(357,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[356, 352])).
% 0.19/0.60 tff(358,plain,(
% 0.19/0.60 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.60 inference(skolemize,[status(sab)],[357])).
% 0.19/0.60 tff(359,plain,
% 0.19/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[358, 351])).
% 0.19/0.60 tff(360,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssPv2(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv2(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(361,plain,
% 0.19/0.60 (((~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(362,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssPv2(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0))))),
% 0.19/0.60 inference(monotonicity,[status(thm)],[361])).
% 0.19/0.60 tff(363,plain,
% 0.19/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv2(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.19/0.60 inference(transitivity,[status(thm)],[362, 360])).
% 0.19/0.60 tff(364,plain,
% 0.19/0.60 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))),
% 0.19/0.61 inference(quant_inst,[status(thm)],[])).
% 0.19/0.61 tff(365,plain,
% 0.19/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv2(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.19/0.61 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.19/0.61 tff(366,plain,
% 0.19/0.61 ((~ssPv2(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.19/0.61 inference(unit_resolution,[status(thm)],[365, 359, 331])).
% 0.19/0.61 tff(367,plain,
% 0.19/0.61 (~ssPv2(elem!0)),
% 0.19/0.61 inference(unit_resolution,[status(thm)],[366, 349, 3, 329])).
% 0.19/0.61 tff(368,assumption,(~ssPv3(elem!0)), introduced(assumption)).
% 0.19/0.61 tff(369,assumption,(~ssPv2(elem!0)), introduced(assumption)).
% 0.19/0.61 tff(370,plain,
% 0.19/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.61 inference(rewrite,[status(thm)],[])).
% 0.19/0.61 tff(371,plain,
% 0.19/0.61 ((ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))) <=> (ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.61 inference(rewrite,[status(thm)],[])).
% 0.19/0.61 tff(372,plain,
% 0.19/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.19/0.61 inference(monotonicity,[status(thm)],[371])).
% 0.19/0.61 tff(373,plain,
% 0.19/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.61 inference(transitivity,[status(thm)],[372, 370])).
% 0.19/0.61 tff(374,plain,
% 0.19/0.61 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.61 inference(quant_inst,[status(thm)],[])).
% 0.19/0.61 tff(375,plain,
% 0.19/0.61 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.19/0.61 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.19/0.61 tff(376,plain,
% 0.19/0.61 (ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0))),
% 0.19/0.61 inference(unit_resolution,[status(thm)],[375, 100, 331])).
% 0.19/0.61 tff(377,plain,
% 0.19/0.61 (ssPv4(skf1(elem!0))),
% 0.19/0.61 inference(unit_resolution,[status(thm)],[376, 369, 368, 3])).
% 0.19/0.61 tff(378,plain,
% 0.19/0.61 (~ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.61 inference(unit_resolution,[status(thm)],[302, 377, 3, 259])).
% 0.19/0.61 tff(379,plain,
% 0.19/0.61 (ssPv2(skf1(elem!0))),
% 0.19/0.61 inference(unit_resolution,[status(thm)],[273, 378, 259, 3])).
% 0.19/0.61 tff(380,plain,
% 0.19/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | ssPv1(elem!0) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ssPv2(elem!0) | ssPv1(elem!0) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.61 inference(rewrite,[status(thm)],[])).
% 0.19/0.61 tff(381,plain,
% 0.19/0.61 ((ssPv2(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0)))) <=> (ssPv2(elem!0) | ssPv1(elem!0) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.61 inference(rewrite,[status(thm)],[])).
% 0.19/0.61 tff(382,plain,
% 0.19/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | ssPv1(elem!0) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.19/0.61 inference(monotonicity,[status(thm)],[381])).
% 0.19/0.61 tff(383,plain,
% 0.19/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ssPv2(elem!0) | ssPv1(elem!0) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.61 inference(transitivity,[status(thm)],[382, 380])).
% 0.19/0.61 tff(384,plain,
% 0.19/0.61 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))),
% 0.19/0.61 inference(quant_inst,[status(thm)],[])).
% 0.19/0.61 tff(385,plain,
% 0.19/0.61 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ssPv2(elem!0) | ssPv1(elem!0) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.19/0.61 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.19/0.61 tff(386,plain,
% 0.19/0.61 (ssPv2(elem!0) | ssPv1(elem!0) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0)))),
% 0.19/0.61 inference(unit_resolution,[status(thm)],[385, 41, 331])).
% 0.19/0.61 tff(387,plain,
% 0.19/0.61 (ssPv1(elem!0)),
% 0.19/0.61 inference(unit_resolution,[status(thm)],[386, 379, 259, 369])).
% 0.19/0.61 tff(388,plain,
% 0.19/0.61 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))),
% 0.19/0.61 inference(bind,[status(th)],[])).
% 0.19/0.61 tff(389,plain,
% 0.19/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.61 inference(quant_intro,[status(thm)],[388])).
% 0.19/0.61 tff(390,plain,
% 0.19/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.61 inference(rewrite,[status(thm)],[])).
% 0.19/0.61 tff(391,plain,
% 0.19/0.61 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(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, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(W))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssRr(U, X))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) <=> (((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv3(X)) <=> (((~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | ssPv3(X)))), rewrite((((~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))))),
% 0.19/0.61 inference(bind,[status(th)],[])).
% 0.19/0.61 tff(392,plain,
% 0.19/0.61 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv3(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.61 inference(quant_intro,[status(thm)],[391])).
% 0.19/0.61 tff(393,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv3(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.19/0.61 tff(394,plain,
% 0.19/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.61 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.19/0.61 tff(395,plain,
% 0.19/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.61 inference(modus_ponens,[status(thm)],[394, 390])).
% 0.19/0.61 tff(396,plain,(
% 0.19/0.61 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.61 inference(skolemize,[status(sab)],[395])).
% 0.19/0.61 tff(397,plain,
% 0.19/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.61 inference(modus_ponens,[status(thm)],[396, 389])).
% 0.19/0.61 tff(398,plain,
% 0.19/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))),
% 0.19/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(399,plain,
% 0.45/0.61 ((ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(400,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0))))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[399])).
% 0.45/0.61 tff(401,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))),
% 0.45/0.61 inference(transitivity,[status(thm)],[400, 398])).
% 0.45/0.61 tff(402,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(403,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.45/0.61 tff(404,plain,
% 0.45/0.61 ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(elem!0))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[403, 397, 331])).
% 0.45/0.61 tff(405,plain,
% 0.45/0.61 ($false),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[404, 387, 379, 377, 259])).
% 0.45/0.61 tff(406,plain,(ssPv2(elem!0) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.61 tff(407,plain,
% 0.45/0.61 (ssPv2(elem!0)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[406, 259, 3, 368])).
% 0.45/0.61 tff(408,plain,
% 0.45/0.61 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(409,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[408])).
% 0.45/0.61 tff(410,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(411,plain,
% 0.45/0.61 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))) | ssPv3(V)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(412,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[411])).
% 0.45/0.61 tff(413,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause10')).
% 0.45/0.61 tff(414,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.45/0.61 tff(415,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[414, 410])).
% 0.45/0.61 tff(416,plain,(
% 0.45/0.61 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.61 inference(skolemize,[status(sab)],[415])).
% 0.45/0.61 tff(417,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[416, 409])).
% 0.45/0.61 tff(418,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(419,plain,
% 0.45/0.61 ((ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0))) <=> ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(420,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[419])).
% 0.45/0.61 tff(421,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.45/0.61 inference(transitivity,[status(thm)],[420, 418])).
% 0.45/0.61 tff(422,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(423,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.45/0.61 tff(424,plain,
% 0.45/0.61 ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[423, 417, 331])).
% 0.45/0.61 tff(425,plain,
% 0.45/0.61 (ssPv2(skf1(elem!0))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[424, 407, 368, 259])).
% 0.45/0.61 tff(426,plain,
% 0.45/0.61 (ssPv4(elem!0)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[348, 425, 259, 3])).
% 0.45/0.61 tff(427,plain,
% 0.45/0.61 ($false),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[366, 426, 425, 3, 407])).
% 0.45/0.61 tff(428,plain,(ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.61 tff(429,plain,
% 0.45/0.61 (ssPv3(elem!0)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[428, 3, 259])).
% 0.45/0.61 tff(430,plain,
% 0.45/0.61 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) <=> (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(431,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[430])).
% 0.45/0.61 tff(432,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(433,plain,
% 0.45/0.61 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssPv2(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> (((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> (((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssRr(U, X))))), rewrite((((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssRr(U, X))) <=> ((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> ((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> (((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv3(U))))), rewrite((((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) <=> (((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv4(W)))), rewrite((((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv4(W)) <=> ((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) | ssPv3(X)) <=> (((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) | ssPv3(X)))), rewrite((((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(434,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) | ssPv3(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[433])).
% 0.45/0.61 tff(435,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) | ssPv3(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.45/0.61 tff(436,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.45/0.61 tff(437,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[436, 432])).
% 0.45/0.61 tff(438,plain,(
% 0.45/0.61 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.45/0.61 inference(skolemize,[status(sab)],[437])).
% 0.45/0.61 tff(439,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[438, 431])).
% 0.45/0.61 tff(440,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | ((~ssPv3(elem!0)) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (~ssPv3(elem!0)) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(441,plain,
% 0.45/0.61 ((ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0))) <=> ((~ssPv3(elem!0)) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(442,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | ((~ssPv3(elem!0)) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[441])).
% 0.45/0.62 tff(443,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (~ssPv3(elem!0)) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[442, 440])).
% 0.45/0.62 tff(444,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(445,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (~ssPv3(elem!0)) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.45/0.62 tff(446,plain,
% 0.45/0.62 ((~ssPv3(elem!0)) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[445, 439, 331])).
% 0.45/0.62 tff(447,plain,
% 0.45/0.62 (ssPv4(skf1(elem!0))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[446, 329, 429, 259])).
% 0.45/0.62 tff(448,plain,
% 0.45/0.62 (~ssPv1(elem!0)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[404, 447, 329, 259])).
% 0.45/0.62 tff(449,plain,
% 0.45/0.62 ($false),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[386, 448, 367, 259, 329])).
% 0.45/0.62 tff(450,plain,(ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.62 tff(451,plain,
% 0.45/0.62 (ssPv1(skf1(elem!0))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[450, 259])).
% 0.45/0.62 tff(452,assumption,(ssPv1(skf1(elem!0))), introduced(assumption)).
% 0.45/0.62 tff(453,plain,
% 0.45/0.62 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(454,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[453])).
% 0.45/0.62 tff(455,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(456,plain,
% 0.45/0.62 (^[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)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(457,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[456])).
% 0.45/0.62 tff(458,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause21')).
% 0.45/0.62 tff(459,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.45/0.62 tff(460,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[459, 455])).
% 0.45/0.62 tff(461,plain,(
% 0.45/0.62 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.45/0.62 inference(skolemize,[status(sab)],[460])).
% 0.45/0.62 tff(462,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[461, 454])).
% 0.45/0.62 tff(463,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(464,plain,
% 0.45/0.62 ((ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(465,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[464])).
% 0.45/0.62 tff(466,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[465, 463])).
% 0.45/0.62 tff(467,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(468,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.45/0.62 tff(469,plain,
% 0.45/0.62 ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[468, 462, 13])).
% 0.45/0.62 tff(470,plain,
% 0.45/0.62 (~ssPv2(skf1(skf1(elem!0)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[469, 4, 452, 1])).
% 0.45/0.62 tff(471,plain,
% 0.45/0.62 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(472,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[471])).
% 0.45/0.62 tff(473,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(474,plain,
% 0.45/0.62 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(475,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[474])).
% 0.45/0.62 tff(476,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) | ssPv2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 0.45/0.62 tff(477,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.45/0.62 tff(478,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[477, 473])).
% 0.45/0.62 tff(479,plain,(
% 0.45/0.62 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.62 inference(skolemize,[status(sab)],[478])).
% 0.45/0.62 tff(480,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[479, 472])).
% 0.45/0.62 tff(481,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(482,plain,
% 0.45/0.62 ((ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))) <=> ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(483,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[482])).
% 0.45/0.62 tff(484,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[483, 481])).
% 0.45/0.62 tff(485,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(486,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.45/0.62 tff(487,plain,
% 0.45/0.62 ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[486, 480, 13])).
% 0.45/0.62 tff(488,plain,
% 0.45/0.62 (~ssPv3(skf1(skf1(elem!0)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[487, 470, 452, 1])).
% 0.45/0.62 tff(489,plain,
% 0.45/0.62 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[217, 4, 470, 488])).
% 0.45/0.62 tff(490,plain,
% 0.45/0.62 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W)))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(491,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[490])).
% 0.45/0.62 tff(492,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(493,plain,
% 0.45/0.62 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv3(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv4(U)))), rewrite(((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv4(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(494,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[493])).
% 0.45/0.62 tff(495,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause11')).
% 0.45/0.62 tff(496,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.45/0.62 tff(497,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[496, 492])).
% 0.45/0.62 tff(498,plain,(
% 0.45/0.62 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.45/0.62 inference(skolemize,[status(sab)],[497])).
% 0.45/0.62 tff(499,plain,
% 0.45/0.62 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[498, 491])).
% 0.45/0.62 tff(500,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(501,plain,
% 0.45/0.62 ((ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))) <=> (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(502,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[501])).
% 0.45/0.62 tff(503,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[502, 500])).
% 0.45/0.62 tff(504,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(505,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.45/0.62 tff(506,plain,
% 0.45/0.62 (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[505, 499, 69])).
% 0.45/0.62 tff(507,plain,
% 0.45/0.62 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[506, 489, 4, 488])).
% 0.45/0.62 tff(508,plain,
% 0.45/0.62 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[125, 507, 4, 470])).
% 0.45/0.62 tff(509,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(510,plain,
% 0.45/0.62 ((ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(511,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[510])).
% 0.45/0.62 tff(512,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[511, 509])).
% 0.45/0.62 tff(513,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(514,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.45/0.62 tff(515,plain,
% 0.45/0.62 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[514, 23, 69])).
% 0.45/0.62 tff(516,plain,
% 0.45/0.62 ($false),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[515, 508, 507, 4, 470])).
% 0.45/0.62 tff(517,plain,(ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.62 tff(518,plain,
% 0.45/0.62 (ssPv4(skf1(skf1(elem!0)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[517, 1, 451])).
% 0.45/0.63 tff(519,plain,
% 0.45/0.63 (ssPv1(skf1(skf1(elem!0)))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[271, 4, 259, 1])).
% 0.45/0.63 tff(520,plain,
% 0.45/0.63 (~ssPv3(skf1(skf1(elem!0)))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[30, 4, 2, 1])).
% 0.45/0.63 tff(521,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(522,plain,
% 0.45/0.63 ((ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0)))) <=> (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(523,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[522])).
% 0.45/0.63 tff(524,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.45/0.63 inference(transitivity,[status(thm)],[523, 521])).
% 0.45/0.63 tff(525,plain,
% 0.45/0.63 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(526,plain,
% 0.45/0.63 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.45/0.63 tff(527,plain,
% 0.45/0.63 (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0))))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[526, 499, 13])).
% 0.45/0.63 tff(528,plain,
% 0.45/0.63 ($false),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[527, 520, 519, 259, 2])).
% 0.45/0.63 tff(529,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.63 tff(530,plain,
% 0.45/0.63 (ssPv4(skf1(skf1(elem!0)))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[529, 2, 259, 1])).
% 0.45/0.63 tff(531,plain,
% 0.45/0.63 (~ssPv3(skf1(skf1(elem!0)))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[227, 530, 1, 2])).
% 0.45/0.63 tff(532,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(533,plain,
% 0.46/0.63 ((ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(534,plain,
% 0.46/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.46/0.63 inference(monotonicity,[status(thm)],[533])).
% 0.46/0.63 tff(535,plain,
% 0.46/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.46/0.63 inference(transitivity,[status(thm)],[534, 532])).
% 0.46/0.63 tff(536,plain,
% 0.46/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(537,plain,
% 0.46/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.46/0.63 tff(538,plain,
% 0.46/0.63 ((~ssPv1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[537, 397, 13])).
% 0.46/0.63 tff(539,plain,
% 0.46/0.63 (~ssPv2(skf1(skf1(elem!0)))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[538, 531, 451, 530])).
% 0.46/0.63 tff(540,plain,
% 0.46/0.63 (~ssPv1(skf1(skf1(elem!0)))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[527, 531, 259, 2])).
% 0.46/0.63 tff(541,plain,
% 0.46/0.63 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[86, 540, 531, 539])).
% 0.46/0.63 tff(542,plain,
% 0.46/0.63 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[107, 541, 539, 531])).
% 0.46/0.63 tff(543,plain,
% 0.46/0.63 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[247, 542, 530, 531])).
% 0.46/0.63 tff(544,plain,
% 0.46/0.63 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[239, 542, 540, 531])).
% 0.46/0.63 tff(545,plain,
% 0.46/0.63 ($false),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[255, 544, 543, 530, 542])).
% 0.46/0.63 tff(546,plain,(ssPv4(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.63 tff(547,plain,
% 0.46/0.63 (ssPv4(skf1(elem!0))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[546, 1, 259])).
% 0.46/0.63 tff(548,plain,
% 0.46/0.63 (~ssPv3(skf1(skf1(elem!0)))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[291, 518, 259, 547])).
% 0.46/0.63 tff(549,plain,
% 0.46/0.63 (ssPv2(skf1(skf1(elem!0)))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[300, 518, 547, 548])).
% 0.46/0.63 tff(550,plain,
% 0.46/0.63 ($false),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[538, 549, 548, 451, 518])).
% 0.46/0.63 tff(551,plain,(ssPv2(skf1(elem!0)) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.63 tff(552,plain,
% 0.46/0.63 (ssPv2(skf1(elem!0))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[551, 259])).
% 0.46/0.63 tff(553,plain,
% 0.46/0.63 (~ssPv1(elem!0)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[404, 283, 552, 259])).
% 0.46/0.63 tff(554,plain,
% 0.46/0.63 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))),
% 0.46/0.63 inference(bind,[status(th)],[])).
% 0.46/0.63 tff(555,plain,
% 0.46/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.46/0.63 inference(quant_intro,[status(thm)],[554])).
% 0.46/0.63 tff(556,plain,
% 0.46/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(557,plain,
% 0.46/0.63 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(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, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(W))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssRr(U, X))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) <=> (((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv1(X))))), rewrite((((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) | (~ssPv3(U))) <=> (((~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv3(U))))), rewrite((((~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(558,plain,
% 0.47/0.63 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[557])).
% 0.47/0.63 tff(559,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) | (~ssPv3(U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.47/0.63 tff(560,plain,
% 0.47/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.47/0.63 tff(561,plain,
% 0.47/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[560, 556])).
% 0.47/0.63 tff(562,plain,(
% 0.47/0.63 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.47/0.63 inference(skolemize,[status(sab)],[561])).
% 0.47/0.63 tff(563,plain,
% 0.47/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[562, 555])).
% 0.47/0.63 tff(564,plain,
% 0.47/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv3(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(565,plain,
% 0.47/0.63 (((~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv3(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(566,plain,
% 0.47/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[565])).
% 0.47/0.63 tff(567,plain,
% 0.47/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv3(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[566, 564])).
% 0.47/0.63 tff(568,plain,
% 0.47/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(569,plain,
% 0.47/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv3(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.47/0.63 tff(570,plain,
% 0.47/0.63 ((~ssPv3(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(elem!0)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[569, 563, 331])).
% 0.47/0.63 tff(571,plain,
% 0.47/0.63 (~ssPv3(elem!0)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[570, 283, 451, 552])).
% 0.47/0.63 tff(572,plain,
% 0.47/0.63 (^[V: $i, U: $i] : refl((ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V))) <=> (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(573,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[572])).
% 0.47/0.63 tff(574,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(575,plain,
% 0.47/0.63 (^[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(U)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(U))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(U))) | ssPv1(U)) | ssPv3(U)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V))) | ssPv3(U)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V))) | ssPv3(U)) <=> (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(U))) | ssPv1(U)) | ssPv3(U)) <=> (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(576,plain,
% 0.47/0.63 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(U))) | ssPv1(U)) | ssPv3(U)) <=> ![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[575])).
% 0.47/0.63 tff(577,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(U))) | ssPv1(U)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.47/0.63 tff(578,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.47/0.63 tff(579,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[578, 574])).
% 0.47/0.63 tff(580,plain,(
% 0.47/0.63 ![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))),
% 0.47/0.63 inference(skolemize,[status(sab)],[579])).
% 0.47/0.63 tff(581,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[580, 573])).
% 0.47/0.63 tff(582,plain,
% 0.47/0.63 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(583,plain,
% 0.47/0.63 ((ssPv3(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(skf1(elem!0)))) <=> ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(584,plain,
% 0.47/0.63 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))) | (ssPv3(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[583])).
% 0.47/0.63 tff(585,plain,
% 0.47/0.63 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))) | (ssPv3(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[584, 582])).
% 0.47/0.63 tff(586,plain,
% 0.47/0.63 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))) | (ssPv3(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(skf1(elem!0))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(587,plain,
% 0.47/0.63 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.47/0.63 tff(588,plain,
% 0.47/0.63 ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[587, 581, 331])).
% 0.47/0.63 tff(589,plain,
% 0.47/0.63 (~ssPv2(elem!0)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[588, 571, 553, 283])).
% 0.47/0.63 tff(590,plain,
% 0.47/0.63 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | ssPv1(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv1(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(591,plain,
% 0.47/0.63 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | ssPv1(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(592,plain,
% 0.47/0.63 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv1(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.47/0.63 tff(593,plain,
% 0.47/0.63 (ssPv3(elem!0) | ssPv2(elem!0) | ssPv1(elem!0) | (~ssPv1(skf1(elem!0)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[592, 79, 331])).
% 0.47/0.63 tff(594,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[593, 553, 571, 451, 589])).
% 0.47/0.63 tff(595,plain,((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(596,plain,
% 0.47/0.63 (~ssPv4(skf1(elem!0))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[595, 259])).
% 0.47/0.63 tff(597,plain,
% 0.47/0.63 (^[V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V))) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(598,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[597])).
% 0.47/0.63 tff(599,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(600,plain,
% 0.47/0.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv4(U)))), rewrite(((ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(601,plain,
% 0.47/0.63 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[600])).
% 0.47/0.63 tff(602,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.47/0.63 tff(603,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.47/0.63 tff(604,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[603, 599])).
% 0.47/0.63 tff(605,plain,(
% 0.47/0.63 ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.47/0.63 inference(skolemize,[status(sab)],[604])).
% 0.47/0.63 tff(606,plain,
% 0.47/0.63 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[605, 598])).
% 0.47/0.63 tff(607,plain,
% 0.47/0.63 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(608,plain,
% 0.47/0.63 ((ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0))))) <=> (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(609,plain,
% 0.47/0.64 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[608])).
% 0.47/0.64 tff(610,plain,
% 0.47/0.64 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[609, 607])).
% 0.47/0.64 tff(611,plain,
% 0.47/0.64 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(612,plain,
% 0.47/0.64 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[611, 610])).
% 0.47/0.64 tff(613,plain,
% 0.47/0.64 (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[612, 606, 13])).
% 0.47/0.64 tff(614,plain,
% 0.47/0.64 (~ssPv3(skf1(skf1(elem!0)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[613, 596, 259, 552])).
% 0.47/0.64 tff(615,plain,
% 0.47/0.64 (^[V: $i, U: $i] : refl((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U))) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(616,plain,
% 0.47/0.64 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[615])).
% 0.47/0.64 tff(617,plain,
% 0.47/0.64 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(618,plain,
% 0.47/0.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssPv2(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | ssPv3(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | ssPv4(U)))), rewrite(((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | ssPv4(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(619,plain,
% 0.47/0.64 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[618])).
% 0.47/0.64 tff(620,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.47/0.64 tff(621,plain,
% 0.47/0.64 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.47/0.64 tff(622,plain,
% 0.47/0.64 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[621, 617])).
% 0.47/0.64 tff(623,plain,(
% 0.47/0.64 ![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[622])).
% 0.47/0.64 tff(624,plain,
% 0.47/0.64 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[623, 616])).
% 0.47/0.64 tff(625,plain,
% 0.47/0.64 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(626,plain,
% 0.47/0.64 ((ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0)))) <=> (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(627,plain,
% 0.47/0.64 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[626])).
% 0.47/0.64 tff(628,plain,
% 0.47/0.64 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[627, 625])).
% 0.47/0.64 tff(629,plain,
% 0.47/0.64 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(630,plain,
% 0.47/0.64 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.47/0.64 tff(631,plain,
% 0.47/0.64 (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[630, 624, 13])).
% 0.47/0.64 tff(632,plain,
% 0.47/0.64 (~ssPv1(skf1(skf1(elem!0)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[631, 596, 259, 552])).
% 0.47/0.64 tff(633,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(634,plain,
% 0.47/0.64 ((ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(635,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[634])).
% 0.47/0.64 tff(636,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[635, 633])).
% 0.47/0.64 tff(637,plain,
% 0.47/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(638,plain,
% 0.47/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.47/0.64 tff(639,plain,
% 0.47/0.64 (ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[638, 341, 13])).
% 0.47/0.64 tff(640,plain,
% 0.47/0.64 (~ssPv2(skf1(skf1(elem!0)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[639, 632, 596, 614])).
% 0.47/0.64 tff(641,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(642,plain,
% 0.47/0.64 ((ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))) <=> (ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(643,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[642])).
% 0.47/0.64 tff(644,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[643, 641])).
% 0.47/0.64 tff(645,plain,
% 0.47/0.64 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(646,plain,
% 0.47/0.64 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.47/0.64 tff(647,plain,
% 0.47/0.64 (ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[646, 417, 13])).
% 0.47/0.64 tff(648,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[647, 640, 614, 259, 552])).
% 0.47/0.64 tff(649,plain,(ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(650,plain,
% 0.47/0.64 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(651,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[650])).
% 0.47/0.64 tff(652,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(653,plain,
% 0.47/0.64 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> (((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) <=> (((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssRr(U, X))))), rewrite((((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssRr(U, X))) <=> ((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) <=> ((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> (((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(X)) <=> (((~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(X)))), rewrite((((~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(654,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[653])).
% 0.47/0.64 tff(655,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.47/0.64 tff(656,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.47/0.64 tff(657,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[656, 652])).
% 0.47/0.64 tff(658,plain,(
% 0.47/0.64 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[657])).
% 0.47/0.64 tff(659,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[658, 651])).
% 0.47/0.64 tff(660,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(661,plain,
% 0.47/0.64 ((ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(662,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[661])).
% 0.47/0.64 tff(663,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[662, 660])).
% 0.47/0.64 tff(664,plain,
% 0.47/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(665,plain,
% 0.47/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.47/0.64 tff(666,plain,
% 0.47/0.64 ((~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[665, 659, 331])).
% 0.47/0.64 tff(667,plain,
% 0.47/0.64 ((~ssPv3(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[666, 649])).
% 0.47/0.64 tff(668,plain,
% 0.47/0.64 (~ssPv3(elem!0)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[667, 258, 2])).
% 0.47/0.64 tff(669,plain,
% 0.47/0.64 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(670,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[669])).
% 0.47/0.64 tff(671,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(672,plain,
% 0.47/0.64 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))) | ssPv2(W)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv3(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv3(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(673,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[672])).
% 0.47/0.64 tff(674,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause19')).
% 0.47/0.64 tff(675,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.47/0.64 tff(676,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[675, 671])).
% 0.47/0.64 tff(677,plain,(
% 0.47/0.64 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.47/0.64 inference(skolemize,[status(sab)],[676])).
% 0.47/0.64 tff(678,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[677, 670])).
% 0.47/0.64 tff(679,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(680,plain,
% 0.47/0.64 ((ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0))) <=> ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(681,plain,
% 0.47/0.64 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[680])).
% 0.47/0.65 tff(682,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[681, 679])).
% 0.47/0.65 tff(683,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(684,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.47/0.65 tff(685,plain,
% 0.47/0.65 ((~ssPv2(elem!0)) | ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[684, 678, 331])).
% 0.47/0.65 tff(686,plain,
% 0.47/0.65 (~ssPv2(elem!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[685, 258, 1, 668])).
% 0.47/0.65 tff(687,plain,
% 0.47/0.65 (ssPv1(elem!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[593, 686, 258, 668])).
% 0.47/0.65 tff(688,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | ssPv2(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(689,plain,
% 0.47/0.65 ((ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0))) <=> (ssPv2(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(690,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[689])).
% 0.47/0.65 tff(691,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | ssPv2(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[690, 688])).
% 0.47/0.65 tff(692,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(693,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | ssPv2(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.47/0.65 tff(694,plain,
% 0.47/0.65 (ssPv2(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv1(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[693, 480, 331])).
% 0.47/0.65 tff(695,plain,
% 0.47/0.65 (ssPv2(elem!0) | ssPv2(skf1(elem!0)) | (~ssPv1(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[694, 649])).
% 0.47/0.65 tff(696,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[695, 687, 686, 1])).
% 0.47/0.65 tff(697,plain,(ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(698,plain,
% 0.47/0.65 (ssPv4(skf1(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[697, 1])).
% 0.47/0.65 tff(699,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(700,plain,
% 0.47/0.65 ((ssPv2(skf1(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0)))) <=> (ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(701,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[700])).
% 0.47/0.65 tff(702,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[701, 699])).
% 0.47/0.65 tff(703,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(704,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.47/0.65 tff(705,plain,
% 0.47/0.65 (ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[704, 313, 331])).
% 0.47/0.65 tff(706,plain,
% 0.47/0.65 (ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[705, 649])).
% 0.47/0.65 tff(707,plain,
% 0.47/0.65 (ssPv4(elem!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[706, 698, 1])).
% 0.47/0.65 tff(708,assumption,(ssPv3(skf1(elem!0))), introduced(assumption)).
% 0.47/0.65 tff(709,plain,
% 0.47/0.65 (ssPv4(elem!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[705, 283, 708, 1])).
% 0.47/0.65 tff(710,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(711,plain,
% 0.47/0.65 ((ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0)))) <=> (ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(712,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[711])).
% 0.47/0.65 tff(713,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[712, 710])).
% 0.47/0.65 tff(714,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(715,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.47/0.65 tff(716,plain,
% 0.47/0.65 (ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[715, 172, 331])).
% 0.47/0.65 tff(717,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[716, 709, 283, 368, 708])).
% 0.47/0.65 tff(718,plain,((~ssPv4(skf1(elem!0))) | ssPv3(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(719,plain,
% 0.47/0.65 ((~ssPv4(skf1(elem!0))) | ssPv3(elem!0) | ssPv2(skf1(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[718, 649])).
% 0.47/0.65 tff(720,plain,
% 0.47/0.65 (ssPv3(elem!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[719, 698, 1])).
% 0.47/0.65 tff(721,plain,
% 0.47/0.65 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(722,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[721])).
% 0.47/0.65 tff(723,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(724,plain,
% 0.47/0.65 (^[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))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(725,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) | ssPv1(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[724])).
% 0.47/0.65 tff(726,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) | ssPv1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.47/0.65 tff(727,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.47/0.65 tff(728,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[727, 723])).
% 0.47/0.65 tff(729,plain,(
% 0.47/0.65 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[728])).
% 0.47/0.65 tff(730,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[729, 722])).
% 0.47/0.65 tff(731,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(732,plain,
% 0.47/0.65 ((ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0)))) <=> ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(733,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[732])).
% 0.47/0.65 tff(734,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[733, 731])).
% 0.47/0.65 tff(735,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(736,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.47/0.65 tff(737,plain,
% 0.47/0.65 ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[736, 730, 331])).
% 0.47/0.65 tff(738,plain,
% 0.47/0.65 ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf1(elem!0)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[737, 649])).
% 0.47/0.65 tff(739,plain,
% 0.47/0.65 (ssPv1(elem!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[738, 720, 698])).
% 0.47/0.65 tff(740,plain,
% 0.47/0.65 (ssPv2(elem!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[695, 739, 1])).
% 0.47/0.65 tff(741,plain,
% 0.47/0.65 (^[V: $i, U: $i] : refl(((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(742,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U))) <=> ![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[741])).
% 0.47/0.65 tff(743,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U))) <=> ![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(744,plain,
% 0.47/0.65 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssPv2(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | (~ssPv3(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | (~ssPv3(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(U)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(U))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) | (~ssPv4(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(U))) | (~ssPv4(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(U))) | (~ssPv4(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) | (~ssPv4(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(745,plain,
% 0.47/0.65 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) | (~ssPv4(U))) <=> ![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[744])).
% 0.47/0.65 tff(746,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) | (~ssPv4(U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.47/0.65 tff(747,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.47/0.65 tff(748,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[747, 743])).
% 0.47/0.65 tff(749,plain,(
% 0.47/0.65 ![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[748])).
% 0.47/0.65 tff(750,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[749, 742])).
% 0.47/0.65 tff(751,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(752,plain,
% 0.47/0.65 (((~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(elem!0))) <=> ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(753,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[752])).
% 0.47/0.65 tff(754,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[753, 751])).
% 0.47/0.65 tff(755,plain,
% 0.47/0.65 ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(elem!0)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(756,plain,
% 0.47/0.65 ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.47/0.65 tff(757,plain,
% 0.47/0.65 ((~ssPv2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[756, 750, 331])).
% 0.47/0.65 tff(758,plain,
% 0.47/0.65 (~ssPv1(skf1(elem!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[757, 740, 720, 707])).
% 0.47/0.65 tff(759,plain,
% 0.47/0.65 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(760,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[759])).
% 0.47/0.65 tff(761,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(762,plain,
% 0.47/0.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(763,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) | ssPv1(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[762])).
% 0.47/0.65 tff(764,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) | ssPv1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause27')).
% 0.47/0.65 tff(765,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[764, 763])).
% 0.47/0.65 tff(766,plain,
% 0.47/0.65 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[765, 761])).
% 0.47/0.66 tff(767,plain,(
% 0.47/0.66 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(skolemize,[status(sab)],[766])).
% 0.47/0.66 tff(768,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[767, 760])).
% 0.47/0.66 tff(769,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(770,plain,
% 0.47/0.66 ((ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))) <=> ((~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(771,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[770])).
% 0.47/0.66 tff(772,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[771, 769])).
% 0.47/0.66 tff(773,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(774,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.47/0.66 tff(775,plain,
% 0.47/0.66 ((~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[774, 768, 13])).
% 0.47/0.66 tff(776,plain,
% 0.47/0.66 (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[775, 649])).
% 0.47/0.66 tff(777,plain,
% 0.47/0.66 (~ssPv3(skf1(skf1(elem!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[776, 4, 758])).
% 0.47/0.66 tff(778,plain,
% 0.47/0.66 (~ssPv2(skf1(skf1(elem!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[48, 777, 758, 1])).
% 0.47/0.66 tff(779,plain,
% 0.47/0.66 (~ssPv1(skf1(skf1(elem!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[66, 777, 758, 1])).
% 0.47/0.66 tff(780,plain,
% 0.47/0.66 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[86, 779, 777, 778])).
% 0.47/0.66 tff(781,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[217, 780, 778, 4, 777])).
% 0.47/0.66 tff(782,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(783,plain,
% 0.47/0.66 (ssPv4(skf1(skf1(elem!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[782, 1])).
% 0.47/0.66 tff(784,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(785,plain,
% 0.47/0.66 ((ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0))))) <=> ((~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(786,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[785])).
% 0.47/0.66 tff(787,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[786, 784])).
% 0.47/0.66 tff(788,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(789,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.47/0.66 tff(790,plain,
% 0.47/0.66 ((~ssPv3(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[789, 730, 13])).
% 0.47/0.66 tff(791,plain,
% 0.47/0.66 (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[790, 649])).
% 0.47/0.66 tff(792,plain,
% 0.47/0.66 (~ssPv3(skf1(skf1(elem!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[791, 783, 758])).
% 0.47/0.66 tff(793,plain,
% 0.47/0.66 (ssPv2(skf1(skf1(elem!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[300, 783, 698, 792])).
% 0.47/0.66 tff(794,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[48, 793, 792, 758, 1])).
% 0.47/0.66 tff(795,plain,(ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(796,plain,
% 0.47/0.66 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) <=> ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(797,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[796])).
% 0.47/0.66 tff(798,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(799,plain,
% 0.47/0.66 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> (((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv2(W))))), rewrite((((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv2(W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> (((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | (~ssRr(U, X))))), rewrite((((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) <=> (((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | (~ssPv1(U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv4(X)) <=> (((~ssPv1(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | ssPv4(X)))), rewrite((((~ssPv1(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | ssPv4(X)) <=> ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv4(X)) <=> ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(800,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv4(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[799])).
% 0.47/0.66 tff(801,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv4(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.47/0.66 tff(802,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.47/0.66 tff(803,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[802, 798])).
% 0.47/0.66 tff(804,plain,(
% 0.47/0.66 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[803])).
% 0.47/0.66 tff(805,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[804, 797])).
% 0.47/0.66 tff(806,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(807,plain,
% 0.47/0.66 (((~ssPv1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(808,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[807])).
% 0.47/0.66 tff(809,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[808, 806])).
% 0.47/0.66 tff(810,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(811,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[810, 809])).
% 0.47/0.66 tff(812,plain,
% 0.47/0.66 ((~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(elem!0))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[811, 805, 331])).
% 0.47/0.66 tff(813,plain,
% 0.47/0.66 (ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv1(elem!0))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[812, 649])).
% 0.47/0.66 tff(814,plain,
% 0.47/0.66 (~ssPv1(elem!0)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[813, 2, 795])).
% 0.47/0.66 tff(815,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(816,plain,
% 0.47/0.66 ((ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0))) <=> ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(817,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[816])).
% 0.47/0.66 tff(818,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[817, 815])).
% 0.47/0.66 tff(819,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(820,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[819, 818])).
% 0.47/0.66 tff(821,plain,
% 0.47/0.66 ((~ssPv3(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[820, 768, 331])).
% 0.47/0.66 tff(822,plain,
% 0.47/0.66 ((~ssPv3(elem!0)) | ssPv1(elem!0) | ssPv4(skf1(elem!0))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[821, 649])).
% 0.47/0.66 tff(823,plain,
% 0.47/0.66 (~ssPv3(elem!0)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[822, 814, 2])).
% 0.47/0.66 tff(824,plain,
% 0.47/0.66 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(825,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[824])).
% 0.47/0.66 tff(826,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(827,plain,
% 0.47/0.66 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(828,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) | ssPv1(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[827])).
% 0.47/0.66 tff(829,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) | ssPv1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 0.47/0.66 tff(830,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[829, 828])).
% 0.47/0.66 tff(831,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[830, 826])).
% 0.47/0.66 tff(832,plain,(
% 0.47/0.66 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(skolemize,[status(sab)],[831])).
% 0.47/0.66 tff(833,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[832, 825])).
% 0.47/0.66 tff(834,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssPv2(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssPv2(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(835,plain,
% 0.47/0.66 ((ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0))) <=> ((~ssPv2(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(836,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssPv2(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[835])).
% 0.47/0.66 tff(837,plain,
% 0.47/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssPv2(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[836, 834])).
% 0.47/0.66 tff(838,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(839,plain,
% 0.47/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssPv2(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[838, 837])).
% 0.47/0.66 tff(840,plain,
% 0.47/0.66 ((~ssPv2(elem!0)) | ssPv1(elem!0) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[839, 833, 331])).
% 0.47/0.66 tff(841,plain,
% 0.47/0.66 ((~ssPv2(elem!0)) | ssPv1(elem!0) | ssPv4(skf1(elem!0))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[840, 649])).
% 0.47/0.66 tff(842,plain,
% 0.47/0.66 (~ssPv2(elem!0)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[841, 814, 2])).
% 0.47/0.66 tff(843,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[376, 842, 823, 3, 2])).
% 0.47/0.66 tff(844,plain,(ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(845,plain,
% 0.47/0.66 (ssPv4(skf1(elem!0))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[844, 3])).
% 0.47/0.66 tff(846,plain,
% 0.47/0.66 (((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(847,plain,
% 0.47/0.66 (((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0)))) <=> ((~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(848,plain,
% 0.47/0.66 (((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[847])).
% 0.47/0.67 tff(849,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[848, 846])).
% 0.47/0.67 tff(850,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(851,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[850, 849])).
% 0.47/0.67 tff(852,plain,
% 0.47/0.67 ((~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[851, 750, 13])).
% 0.47/0.67 tff(853,plain,
% 0.47/0.67 ((~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[852, 649])).
% 0.47/0.67 tff(854,plain,
% 0.47/0.67 (~ssPv1(skf1(skf1(elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[853, 845, 795])).
% 0.47/0.67 tff(855,plain,
% 0.47/0.67 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(856,plain,
% 0.47/0.67 (((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(857,plain,
% 0.47/0.67 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[856])).
% 0.47/0.67 tff(858,plain,
% 0.47/0.67 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[857, 855])).
% 0.47/0.67 tff(859,plain,
% 0.47/0.67 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(860,plain,
% 0.47/0.67 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[859, 858])).
% 0.47/0.67 tff(861,plain,
% 0.47/0.67 ((~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[860, 359, 13])).
% 0.47/0.67 tff(862,plain,
% 0.47/0.67 (~ssPv2(skf1(skf1(elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[861, 854, 845, 795])).
% 0.47/0.67 tff(863,plain,
% 0.47/0.67 (~ssPv3(skf1(skf1(elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[776, 4, 3])).
% 0.47/0.67 tff(864,plain,
% 0.47/0.67 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[217, 4, 862, 863])).
% 0.47/0.67 tff(865,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[86, 864, 863, 854, 862])).
% 0.47/0.67 tff(866,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(867,plain,
% 0.47/0.67 (ssPv4(skf1(skf1(elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[866, 3])).
% 0.47/0.67 tff(868,plain,
% 0.47/0.67 (~ssPv3(skf1(skf1(elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[791, 867, 3])).
% 0.47/0.67 tff(869,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[300, 868, 867, 845, 862])).
% 0.47/0.67 tff(870,plain,(ssPv1(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(871,plain,
% 0.47/0.67 (~ssPv3(elem!0)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[667, 2, 870])).
% 0.47/0.67 tff(872,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[593, 842, 814, 870, 871])).
% 0.47/0.67 tff(873,plain,(ssPv4(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(874,plain,
% 0.47/0.67 (~ssPv3(elem!0)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[570, 873, 795, 870])).
% 0.47/0.67 tff(875,plain,
% 0.47/0.67 (ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[716, 649])).
% 0.47/0.67 tff(876,plain,
% 0.47/0.67 (~ssPv4(elem!0)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[875, 873, 874])).
% 0.47/0.67 tff(877,plain,
% 0.47/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv4(elem!0) | ssPv2(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv4(elem!0) | ssPv2(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(878,plain,
% 0.47/0.67 ((ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0)))) <=> (ssPv4(elem!0) | ssPv2(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(879,plain,
% 0.47/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv4(elem!0) | ssPv2(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[878])).
% 0.47/0.67 tff(880,plain,
% 0.47/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv4(elem!0) | ssPv2(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[879, 877])).
% 0.47/0.67 tff(881,plain,
% 0.47/0.67 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(882,plain,
% 0.47/0.67 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv4(elem!0) | ssPv2(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.47/0.67 tff(883,plain,
% 0.47/0.67 (ssPv4(elem!0) | ssPv2(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[882, 118, 331])).
% 0.47/0.67 tff(884,plain,
% 0.47/0.67 (ssPv4(elem!0) | ssPv2(elem!0) | (~ssPv4(skf1(elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[883, 649])).
% 0.47/0.67 tff(885,plain,
% 0.47/0.67 (ssPv2(elem!0)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[884, 876, 873])).
% 0.47/0.67 tff(886,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(887,plain,
% 0.47/0.67 ((ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0)))) <=> ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(888,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[887])).
% 0.47/0.67 tff(889,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[888, 886])).
% 0.47/0.67 tff(890,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(891,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.47/0.67 tff(892,plain,
% 0.47/0.67 ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[891, 606, 331])).
% 0.47/0.67 tff(893,plain,
% 0.47/0.67 ((~ssPv2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[892, 649])).
% 0.47/0.67 tff(894,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[893, 885, 876, 874])).
% 0.47/0.67 % SZS output end Proof
% 0.47/0.67 % E exiting
%------------------------------------------------------------------------------