%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MSC015-1.005 : TPTP v9.0.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:17:32 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MSC015-1.005 : TPTP v9.0.0. Released v3.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : Thu Jun 19 23:37:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(p_type, type, (
% 0.12/0.37 p: ( $i * $i * $i * $i * $i ) > $o)).
% 0.12/0.37 tff(s0_type, type, (
% 0.12/0.37 s0: $i)).
% 0.12/0.37 tff(s1_type, type, (
% 0.12/0.37 s1: $i)).
% 0.12/0.37 tff(1,assumption,(~p(s0, s1, s0, s1, s1)), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1)) <=> ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1)) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1)) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule1')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,(
% 0.12/0.37 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))),
% 0.12/0.37 inference(skolemize,[status(sab)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (p(s0, s0, s0, s0, s0) <=> p(s0, s0, s0, s0, s0)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(10,axiom,(p(s0, s0, s0, s0, s0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','init')).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (p(s0, s0, s0, s0, s0)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s0, s0, s0, s0)) | p(s0, s0, s0, s0, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s0, s0, s0, s0)) | p(s0, s0, s0, s0, s1))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s0, s0, s0, s0)) | p(s0, s0, s0, s0, s1))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s0, s0, s0, s0)) | p(s0, s0, s0, s0, s1)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (p(s0, s0, s0, s0, s1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[14, 11, 8])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (^[X0: $i, X2: $i, X1: $i] : refl(((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0)) <=> ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(19,axiom,(![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule2')).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.37 tff(21,plain,(
% 0.12/0.37 ![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))),
% 0.12/0.37 inference(skolemize,[status(sab)],[20])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s0, s0, s0, s0, s1)) | p(s0, s0, s0, s1, s0))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s0, s0, s0, s0, s1)) | p(s0, s0, s0, s1, s0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s0, s0, s0, s0, s1)) | p(s0, s0, s0, s1, s0))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s0, s0, s0, s0, s1)) | p(s0, s0, s0, s1, s0)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (p(s0, s0, s0, s1, s0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[25, 22, 15])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s0, s0, s1, s0)) | p(s0, s0, s0, s1, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s0, s0, s1, s0)) | p(s0, s0, s0, s1, s1))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s0, s0, s1, s0)) | p(s0, s0, s0, s1, s1))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s0, s0, s1, s0)) | p(s0, s0, s0, s1, s1)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (p(s0, s0, s0, s1, s1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[29, 8, 26])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (^[X0: $i, X1: $i] : refl(((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0)) <=> ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0)) <=> ![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0)) <=> ![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(34,axiom,(![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule3')).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.37 tff(36,plain,(
% 0.12/0.37 ![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))),
% 0.12/0.37 inference(skolemize,[status(sab)],[35])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | ((~p(s0, s0, s0, s1, s1)) | p(s0, s0, s1, s0, s0))) <=> ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | (~p(s0, s0, s0, s1, s1)) | p(s0, s0, s1, s0, s0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | ((~p(s0, s0, s0, s1, s1)) | p(s0, s0, s1, s0, s0))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | (~p(s0, s0, s0, s1, s1)) | p(s0, s0, s1, s0, s0)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (p(s0, s0, s1, s0, s0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[40, 37, 30])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s0, s1, s0, s0)) | p(s0, s0, s1, s0, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s0, s1, s0, s0)) | p(s0, s0, s1, s0, s1))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s0, s1, s0, s0)) | p(s0, s0, s1, s0, s1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s0, s1, s0, s0)) | p(s0, s0, s1, s0, s1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (p(s0, s0, s1, s0, s1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[44, 8, 41])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s0, s0, s1, s0, s1)) | p(s0, s0, s1, s1, s0))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s0, s0, s1, s0, s1)) | p(s0, s0, s1, s1, s0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s0, s0, s1, s0, s1)) | p(s0, s0, s1, s1, s0))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s0, s0, s1, s0, s1)) | p(s0, s0, s1, s1, s0)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (p(s0, s0, s1, s1, s0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[48, 22, 45])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s0, s1, s1, s0)) | p(s0, s0, s1, s1, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s0, s1, s1, s0)) | p(s0, s0, s1, s1, s1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s0, s1, s1, s0)) | p(s0, s0, s1, s1, s1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s0, s1, s1, s0)) | p(s0, s0, s1, s1, s1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (p(s0, s0, s1, s1, s1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[52, 8, 49])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (^[X0: $i] : refl(((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0)) <=> ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0)) <=> ![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0)) <=> ![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(57,axiom,(![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule4')).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.12/0.38 tff(59,plain,(
% 0.12/0.38 ![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))),
% 0.12/0.38 inference(skolemize,[status(sab)],[58])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (((~![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))) | ((~p(s0, s0, s1, s1, s1)) | p(s0, s1, s0, s0, s0))) <=> ((~![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))) | (~p(s0, s0, s1, s1, s1)) | p(s0, s1, s0, s0, s0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 ((~![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))) | ((~p(s0, s0, s1, s1, s1)) | p(s0, s1, s0, s0, s0))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 ((~![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))) | (~p(s0, s0, s1, s1, s1)) | p(s0, s1, s0, s0, s0)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 (p(s0, s1, s0, s0, s0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[63, 60, 53])).
% 0.12/0.38 tff(65,plain,
% 0.12/0.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s1, s0, s0, s0)) | p(s0, s1, s0, s0, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s1, s0, s0, s0)) | p(s0, s1, s0, s0, s1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s1, s0, s0, s0)) | p(s0, s1, s0, s0, s1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s1, s0, s0, s0)) | p(s0, s1, s0, s0, s1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (p(s0, s1, s0, s0, s1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[67, 8, 64])).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s0, s1, s0, s0, s1)) | p(s0, s1, s0, s1, s0))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s0, s1, s0, s0, s1)) | p(s0, s1, s0, s1, s0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s0, s1, s0, s0, s1)) | p(s0, s1, s0, s1, s0))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s0, s1, s0, s0, s1)) | p(s0, s1, s0, s1, s0)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.38 tff(72,plain,
% 0.12/0.38 (p(s0, s1, s0, s1, s0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[71, 22, 68])).
% 0.12/0.38 tff(73,plain,
% 0.12/0.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s1, s0, s1, s0)) | p(s0, s1, s0, s1, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s1, s0, s1, s0)) | p(s0, s1, s0, s1, s1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(74,plain,
% 0.12/0.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s1, s0, s1, s0)) | p(s0, s1, s0, s1, s1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(75,plain,
% 0.12/0.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s1, s0, s1, s0)) | p(s0, s1, s0, s1, s1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.12/0.38 tff(76,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[75, 8, 72, 1])).
% 0.12/0.38 tff(77,plain,(p(s0, s1, s0, s1, s1)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(78,plain,
% 0.12/0.38 (((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | ((~p(s0, s1, s0, s1, s1)) | p(s0, s1, s1, s0, s0))) <=> ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | (~p(s0, s1, s0, s1, s1)) | p(s0, s1, s1, s0, s0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(79,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | ((~p(s0, s1, s0, s1, s1)) | p(s0, s1, s1, s0, s0))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(80,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | (~p(s0, s1, s0, s1, s1)) | p(s0, s1, s1, s0, s0)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.12/0.38 tff(81,plain,
% 0.12/0.38 (p(s0, s1, s1, s0, s0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[80, 37, 77])).
% 0.12/0.38 tff(82,plain,
% 0.12/0.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s1, s1, s0, s0)) | p(s0, s1, s1, s0, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s1, s1, s0, s0)) | p(s0, s1, s1, s0, s1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(83,plain,
% 0.12/0.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s1, s1, s0, s0)) | p(s0, s1, s1, s0, s1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(84,plain,
% 0.12/0.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s1, s1, s0, s0)) | p(s0, s1, s1, s0, s1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (p(s0, s1, s1, s0, s1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[84, 8, 81])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s0, s1, s1, s0, s1)) | p(s0, s1, s1, s1, s0))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s0, s1, s1, s0, s1)) | p(s0, s1, s1, s1, s0))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s0, s1, s1, s0, s1)) | p(s0, s1, s1, s1, s0))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s0, s1, s1, s0, s1)) | p(s0, s1, s1, s1, s0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 (p(s0, s1, s1, s1, s0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[88, 22, 85])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s1, s1, s1, s0)) | p(s0, s1, s1, s1, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s1, s1, s1, s0)) | p(s0, s1, s1, s1, s1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s0, s1, s1, s1, s0)) | p(s0, s1, s1, s1, s1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s0, s1, s1, s1, s0)) | p(s0, s1, s1, s1, s1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (p(s0, s1, s1, s1, s1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[92, 8, 89])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 (((~p(s0, s1, s1, s1, s1)) | p(s1, s0, s0, s0, s0)) <=> ((~p(s0, s1, s1, s1, s1)) | p(s1, s0, s0, s0, s0))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(95,axiom,((~p(s0, s1, s1, s1, s1)) | p(s1, s0, s0, s0, s0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule5')).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 ((~p(s0, s1, s1, s1, s1)) | p(s1, s0, s0, s0, s0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 (p(s1, s0, s0, s0, s0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s0, s0, s0, s0)) | p(s1, s0, s0, s0, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s0, s0, s0, s0)) | p(s1, s0, s0, s0, s1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s0, s0, s0, s0)) | p(s1, s0, s0, s0, s1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s0, s0, s0, s0)) | p(s1, s0, s0, s0, s1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 (p(s1, s0, s0, s0, s1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[100, 8, 97])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s1, s0, s0, s0, s1)) | p(s1, s0, s0, s1, s0))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s1, s0, s0, s0, s1)) | p(s1, s0, s0, s1, s0))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s1, s0, s0, s0, s1)) | p(s1, s0, s0, s1, s0))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s1, s0, s0, s0, s1)) | p(s1, s0, s0, s1, s0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 (p(s1, s0, s0, s1, s0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[104, 22, 101])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s0, s0, s1, s0)) | p(s1, s0, s0, s1, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s0, s0, s1, s0)) | p(s1, s0, s0, s1, s1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s0, s0, s1, s0)) | p(s1, s0, s0, s1, s1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(108,plain,
% 0.12/0.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s0, s0, s1, s0)) | p(s1, s0, s0, s1, s1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.12/0.39 tff(109,plain,
% 0.12/0.39 (p(s1, s0, s0, s1, s1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[108, 8, 105])).
% 0.12/0.39 tff(110,plain,
% 0.12/0.39 (((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | ((~p(s1, s0, s0, s1, s1)) | p(s1, s0, s1, s0, s0))) <=> ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | (~p(s1, s0, s0, s1, s1)) | p(s1, s0, s1, s0, s0))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(111,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | ((~p(s1, s0, s0, s1, s1)) | p(s1, s0, s1, s0, s0))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(112,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | (~p(s1, s0, s0, s1, s1)) | p(s1, s0, s1, s0, s0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.12/0.39 tff(113,plain,
% 0.12/0.39 (p(s1, s0, s1, s0, s0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[112, 37, 109])).
% 0.12/0.39 tff(114,plain,
% 0.12/0.39 ((~p(s1, s1, s1, s1, s1)) <=> (~p(s1, s1, s1, s1, s1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(115,axiom,(~p(s1, s1, s1, s1, s1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goal')).
% 0.12/0.40 tff(116,plain,
% 0.12/0.40 (~p(s1, s1, s1, s1, s1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s1, s1, s1, s0)) | p(s1, s1, s1, s1, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s1, s1, s1, s0)) | p(s1, s1, s1, s1, s1))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(118,plain,
% 0.12/0.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s1, s1, s1, s0)) | p(s1, s1, s1, s1, s1))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(119,plain,
% 0.12/0.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s1, s1, s1, s0)) | p(s1, s1, s1, s1, s1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.12/0.40 tff(120,plain,
% 0.12/0.40 (~p(s1, s1, s1, s1, s0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[119, 8, 116])).
% 0.12/0.40 tff(121,plain,
% 0.12/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s1, s1, s1, s0, s1)) | p(s1, s1, s1, s1, s0))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s1, s1, s1, s0, s1)) | p(s1, s1, s1, s1, s0))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(122,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s1, s1, s1, s0, s1)) | p(s1, s1, s1, s1, s0))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s1, s1, s1, s0, s1)) | p(s1, s1, s1, s1, s0)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.12/0.40 tff(124,plain,
% 0.12/0.40 (~p(s1, s1, s1, s0, s1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[123, 22, 120])).
% 0.12/0.40 tff(125,plain,
% 0.12/0.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s1, s1, s0, s0)) | p(s1, s1, s1, s0, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s1, s1, s0, s0)) | p(s1, s1, s1, s0, s1))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(126,plain,
% 0.12/0.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s1, s1, s0, s0)) | p(s1, s1, s1, s0, s1))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(127,plain,
% 0.12/0.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s1, s1, s0, s0)) | p(s1, s1, s1, s0, s1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.12/0.40 tff(128,plain,
% 0.12/0.40 (~p(s1, s1, s1, s0, s0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[127, 8, 124])).
% 0.12/0.40 tff(129,plain,
% 0.12/0.40 (((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | ((~p(s1, s1, s0, s1, s1)) | p(s1, s1, s1, s0, s0))) <=> ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | (~p(s1, s1, s0, s1, s1)) | p(s1, s1, s1, s0, s0))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(130,plain,
% 0.12/0.40 ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | ((~p(s1, s1, s0, s1, s1)) | p(s1, s1, s1, s0, s0))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(131,plain,
% 0.12/0.40 ((~![X0: $i, X1: $i] : ((~p(X0, X1, s0, s1, s1)) | p(X0, X1, s1, s0, s0))) | (~p(s1, s1, s0, s1, s1)) | p(s1, s1, s1, s0, s0)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.12/0.40 tff(132,plain,
% 0.12/0.40 (~p(s1, s1, s0, s1, s1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[131, 37, 128])).
% 0.12/0.40 tff(133,plain,
% 0.12/0.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s1, s0, s1, s0)) | p(s1, s1, s0, s1, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s1, s0, s1, s0)) | p(s1, s1, s0, s1, s1))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(134,plain,
% 0.12/0.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s1, s0, s1, s0)) | p(s1, s1, s0, s1, s1))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(135,plain,
% 0.12/0.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s1, s0, s1, s0)) | p(s1, s1, s0, s1, s1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.12/0.40 tff(136,plain,
% 0.12/0.40 (~p(s1, s1, s0, s1, s0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[135, 8, 132])).
% 0.12/0.40 tff(137,plain,
% 0.12/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s1, s1, s0, s0, s1)) | p(s1, s1, s0, s1, s0))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s1, s1, s0, s0, s1)) | p(s1, s1, s0, s1, s0))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(138,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s1, s1, s0, s0, s1)) | p(s1, s1, s0, s1, s0))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(139,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s1, s1, s0, s0, s1)) | p(s1, s1, s0, s1, s0)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.12/0.40 tff(140,plain,
% 0.12/0.40 (~p(s1, s1, s0, s0, s1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[139, 22, 136])).
% 0.12/0.40 tff(141,plain,
% 0.12/0.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s1, s0, s0, s0)) | p(s1, s1, s0, s0, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s1, s0, s0, s0)) | p(s1, s1, s0, s0, s1))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(142,plain,
% 0.12/0.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s1, s0, s0, s0)) | p(s1, s1, s0, s0, s1))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(143,plain,
% 0.12/0.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s1, s0, s0, s0)) | p(s1, s1, s0, s0, s1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (~p(s1, s1, s0, s0, s0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[143, 8, 140])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (((~![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))) | ((~p(s1, s0, s1, s1, s1)) | p(s1, s1, s0, s0, s0))) <=> ((~![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))) | (~p(s1, s0, s1, s1, s1)) | p(s1, s1, s0, s0, s0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 ((~![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))) | ((~p(s1, s0, s1, s1, s1)) | p(s1, s1, s0, s0, s0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 ((~![X0: $i] : ((~p(X0, s0, s1, s1, s1)) | p(X0, s1, s0, s0, s0))) | (~p(s1, s0, s1, s1, s1)) | p(s1, s1, s0, s0, s0)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 (~p(s1, s0, s1, s1, s1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[147, 60, 144])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s0, s1, s1, s0)) | p(s1, s0, s1, s1, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s0, s1, s1, s0)) | p(s1, s0, s1, s1, s1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s0, s1, s1, s0)) | p(s1, s0, s1, s1, s1))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s0, s1, s1, s0)) | p(s1, s0, s1, s1, s1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (~p(s1, s0, s1, s1, s0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[151, 8, 148])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s1, s0, s1, s0, s1)) | p(s1, s0, s1, s1, s0))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s1, s0, s1, s0, s1)) | p(s1, s0, s1, s1, s0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | ((~p(s1, s0, s1, s0, s1)) | p(s1, s0, s1, s1, s0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 ((~![X0: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, s0, s1)) | p(X0, X1, X2, s1, s0))) | (~p(s1, s0, s1, s0, s1)) | p(s1, s0, s1, s1, s0)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.41 tff(156,plain,
% 0.19/0.41 (~p(s1, s0, s1, s0, s1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[155, 22, 152])).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s0, s1, s0, s0)) | p(s1, s0, s1, s0, s1))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s0, s1, s0, s0)) | p(s1, s0, s1, s0, s1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | ((~p(s1, s0, s1, s0, s0)) | p(s1, s0, s1, s0, s1))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p(X0, X1, X2, X3, s0)) | p(X0, X1, X2, X3, s1))) | (~p(s1, s0, s1, s0, s0)) | p(s1, s0, s1, s0, s1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[159, 8, 156, 113])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------