%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN648-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:45 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN648-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 12:39:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(p3_type, type, (
% 0.12/0.40 p3: ( $i * $i ) > $o)).
% 0.12/0.40 tff(f4_type, type, (
% 0.12/0.40 f4: ( $i * $i ) > $i)).
% 0.12/0.40 tff(c28_type, type, (
% 0.12/0.40 c28: $i)).
% 0.12/0.40 tff(c30_type, type, (
% 0.12/0.40 c30: $i)).
% 0.12/0.40 tff(c27_type, type, (
% 0.12/0.40 c27: $i)).
% 0.12/0.40 tff(p24_type, type, (
% 0.12/0.40 p24: ( $i * $i ) > $o)).
% 0.12/0.40 tff(f9_type, type, (
% 0.12/0.40 f9: ( $i * $i ) > $i)).
% 0.12/0.40 tff(f11_type, type, (
% 0.12/0.40 f11: ( $i * $i ) > $i)).
% 0.12/0.40 tff(f13_type, type, (
% 0.12/0.40 f13: ( $i * $i ) > $i)).
% 0.12/0.40 tff(f15_type, type, (
% 0.12/0.40 f15: ( $i * $i ) > $i)).
% 0.12/0.40 tff(c34_type, type, (
% 0.12/0.40 c34: $i)).
% 0.12/0.40 tff(f17_type, type, (
% 0.12/0.40 f17: ( $i * $i ) > $i)).
% 0.12/0.40 tff(f19_type, type, (
% 0.12/0.40 f19: ( $i * $i ) > $i)).
% 0.12/0.40 tff(f21_type, type, (
% 0.12/0.40 f21: ( $i * $i ) > $i)).
% 0.12/0.40 tff(f23_type, type, (
% 0.12/0.40 f23: ( $i * $i ) > $i)).
% 0.12/0.40 tff(c33_type, type, (
% 0.12/0.40 c33: $i)).
% 0.12/0.40 tff(f6_type, type, (
% 0.12/0.40 f6: ( $i * $i ) > $i)).
% 0.12/0.40 tff(c32_type, type, (
% 0.12/0.40 c32: $i)).
% 0.12/0.40 tff(p2_type, type, (
% 0.12/0.40 p2: ( $i * $i ) > $o)).
% 0.12/0.40 tff(c29_type, type, (
% 0.12/0.40 c29: $i)).
% 0.12/0.40 tff(p26_type, type, (
% 0.12/0.40 p26: ( $i * $i ) > $o)).
% 0.12/0.40 tff(c31_type, type, (
% 0.12/0.40 c31: $i)).
% 0.12/0.40 tff(1,assumption,(p3(f4(c27, c28), f4(c30, c28))), introduced(assumption)).
% 0.12/0.40 tff(2,assumption,(~p3(c28, c28)), introduced(assumption)).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[X65: $i] : refl(p3(X65, X65) <=> p3(X65, X65))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![X65: $i] : p3(X65, X65) <=> ![X65: $i] : p3(X65, X65)),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![X65: $i] : p3(X65, X65) <=> ![X65: $i] : p3(X65, X65)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(6,axiom,(![X65: $i] : p3(X65, X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_5')).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![X65: $i] : p3(X65, X65)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.40 tff(8,plain,(
% 0.12/0.40 ![X65: $i] : p3(X65, X65)),
% 0.12/0.40 inference(skolemize,[status(sab)],[7])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (![X65: $i] : p3(X65, X65)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 ((~![X65: $i] : p3(X65, X65)) | p3(c28, c28)),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.12/0.40 tff(12,plain,(p3(c28, c28)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(13,assumption,(~p2(c27, c27)), introduced(assumption)).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (^[X31: $i] : refl(p2(X31, X31) <=> p2(X31, X31))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![X31: $i] : p2(X31, X31) <=> ![X31: $i] : p2(X31, X31)),
% 0.12/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (![X31: $i] : p2(X31, X31) <=> ![X31: $i] : p2(X31, X31)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(17,axiom,(![X31: $i] : p2(X31, X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_9')).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (![X31: $i] : p2(X31, X31)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.40 tff(19,plain,(
% 0.12/0.40 ![X31: $i] : p2(X31, X31)),
% 0.12/0.40 inference(skolemize,[status(sab)],[18])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![X31: $i] : p2(X31, X31)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 ((~![X31: $i] : p2(X31, X31)) | p2(c27, c27)),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[21, 20, 13])).
% 0.12/0.40 tff(23,plain,(p2(c27, c27)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (^[X73: $i, X75: $i, X72: $i, X74: $i] : refl(((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75))) <=> ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75))) <=> ![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75))) <=> ![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (^[X73: $i, X75: $i, X72: $i, X74: $i] : trans(monotonicity(rewrite((p3(f4(X72, X73), f4(X74, X75)) | (~p2(X72, X74))) <=> ((~p2(X72, X74)) | p3(f4(X72, X73), f4(X74, X75)))), (((p3(f4(X72, X73), f4(X74, X75)) | (~p2(X72, X74))) | (~p3(X73, X75))) <=> (((~p2(X72, X74)) | p3(f4(X72, X73), f4(X74, X75))) | (~p3(X73, X75))))), rewrite((((~p2(X72, X74)) | p3(f4(X72, X73), f4(X74, X75))) | (~p3(X73, X75))) <=> ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))), (((p3(f4(X72, X73), f4(X74, X75)) | (~p2(X72, X74))) | (~p3(X73, X75))) <=> ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(28,plain,
% 0.12/0.41 (![X73: $i, X75: $i, X72: $i, X74: $i] : ((p3(f4(X72, X73), f4(X74, X75)) | (~p2(X72, X74))) | (~p3(X73, X75))) <=> ![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.41 tff(29,axiom,(![X73: $i, X75: $i, X72: $i, X74: $i] : ((p3(f4(X72, X73), f4(X74, X75)) | (~p2(X72, X74))) | (~p3(X73, X75)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_41')).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 (![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.41 tff(31,plain,
% 0.12/0.41 (![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.41 tff(32,plain,(
% 0.12/0.41 ![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[31])).
% 0.12/0.41 tff(33,plain,
% 0.12/0.41 (![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.12/0.41 tff(34,plain,
% 0.12/0.41 (((~![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))) | ((~p2(c27, c27)) | (~p3(c28, c28)) | p3(f4(c27, c28), f4(c27, c28)))) <=> ((~![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))) | (~p2(c27, c27)) | (~p3(c28, c28)) | p3(f4(c27, c28), f4(c27, c28)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(35,plain,
% 0.12/0.41 ((~![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))) | ((~p2(c27, c27)) | (~p3(c28, c28)) | p3(f4(c27, c28), f4(c27, c28)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(36,plain,
% 0.12/0.41 ((~![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))) | (~p2(c27, c27)) | (~p3(c28, c28)) | p3(f4(c27, c28), f4(c27, c28))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 ((~p2(c27, c27)) | (~p3(c28, c28)) | p3(f4(c27, c28), f4(c27, c28))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 (p3(f4(c27, c28), f4(c27, c28))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[37, 23, 12])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 (^[X31: $i, X32: $i, X33: $i] : refl(((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)) <=> ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(40,plain,
% 0.12/0.41 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)) <=> ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)) <=> ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(42,plain,
% 0.12/0.41 (^[X31: $i, X32: $i, X33: $i] : trans(monotonicity(rewrite((p2(X32, X33) | (~p2(X31, X32))) <=> ((~p2(X31, X32)) | p2(X32, X33))), (((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33))) <=> (((~p2(X31, X32)) | p2(X32, X33)) | (~p2(X31, X33))))), rewrite((((~p2(X31, X32)) | p2(X32, X33)) | (~p2(X31, X33))) <=> ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))), (((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33))) <=> ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(43,plain,
% 0.12/0.41 (![X31: $i, X32: $i, X33: $i] : ((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33))) <=> ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.12/0.41 tff(44,axiom,(![X31: $i, X32: $i, X33: $i] : ((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_25')).
% 0.12/0.41 tff(45,plain,
% 0.12/0.41 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.41 tff(46,plain,
% 0.12/0.41 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.12/0.41 tff(47,plain,(
% 0.12/0.41 ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.41 inference(skolemize,[status(sab)],[46])).
% 0.12/0.41 tff(48,plain,
% 0.12/0.41 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.12/0.41 tff(49,plain,
% 0.12/0.41 (p2(c27, c30) <=> p2(c27, c30)),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(50,axiom,(p2(c27, c30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_14')).
% 0.12/0.41 tff(51,plain,
% 0.12/0.41 (p2(c27, c30)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.41 tff(52,plain,
% 0.12/0.41 (((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(c27, c30)) | p2(c30, c30))) <=> ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | (~p2(c27, c30)) | p2(c30, c30))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 (((~p2(c27, c30)) | (~p2(c27, c30)) | p2(c30, c30)) <=> ((~p2(c27, c30)) | p2(c30, c30))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(c27, c30)) | (~p2(c27, c30)) | p2(c30, c30))) <=> ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(c27, c30)) | p2(c30, c30)))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.12/0.41 tff(55,plain,
% 0.12/0.41 (((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(c27, c30)) | (~p2(c27, c30)) | p2(c30, c30))) <=> ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | (~p2(c27, c30)) | p2(c30, c30))),
% 0.12/0.41 inference(transitivity,[status(thm)],[54, 52])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(c27, c30)) | (~p2(c27, c30)) | p2(c30, c30))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(57,plain,
% 0.12/0.41 ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | (~p2(c27, c30)) | p2(c30, c30)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.41 tff(58,plain,
% 0.12/0.41 (p2(c30, c30)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[57, 51, 48])).
% 0.12/0.41 tff(59,plain,
% 0.12/0.41 (^[X53: $i, X55: $i, X52: $i, X54: $i] : refl(((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(60,plain,
% 0.12/0.41 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (^[X53: $i, X55: $i, X52: $i, X54: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X52, X54))) <=> ((~p3(X52, X54)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))), ((((p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X52, X54))) | (~p2(X55, X53))) <=> (((~p3(X52, X54)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p2(X55, X53))))), rewrite((((~p3(X52, X54)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p2(X55, X53))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))), ((((p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X52, X54))) | (~p2(X55, X53))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))))), (((((p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) <=> (((~p3(X52, X54)) | (~p2(X55, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p26(c31, X53))))), rewrite((((~p3(X52, X54)) | (~p2(X55, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p26(c31, X53))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))), (((((p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))))), ((((((p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28)))) <=> (((~p3(X52, X54)) | (~p2(X55, X53)) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28)))))), rewrite((((~p3(X52, X54)) | (~p2(X55, X53)) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28)))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))), ((((((p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28)))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (![X53: $i, X55: $i, X52: $i, X54: $i] : (((((p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28)))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.42 tff(64,axiom,(![X53: $i, X55: $i, X52: $i, X54: $i] : (((((p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p24_44')).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.42 tff(67,plain,(
% 0.20/0.42 ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[66])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ((~p24(f4(c27, c28), c29)) <=> (~p24(f4(c27, c28), c29))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(70,axiom,(~p24(f4(c27, c28), c29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p24_16')).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (~p24(f4(c27, c28), c29)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (p26(c31, c30) <=> p26(c31, c30)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(73,axiom,(p26(c31, c30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p26_15')).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (p26(c31, c30)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) | (p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28))))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) | p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (((~p3(f4(c27, c28), f4(c27, c28))) | (~p2(c30, c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p26(c31, c30)) | p24(f4(c27, c28), c29) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) <=> (p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) | ((~p3(f4(c27, c28), f4(c27, c28))) | (~p2(c30, c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p26(c31, c30)) | p24(f4(c27, c28), c29) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) | (p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) | ((~p3(f4(c27, c28), f4(c27, c28))) | (~p2(c30, c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p26(c31, c30)) | p24(f4(c27, c28), c29) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) | p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) | ((~p3(f4(c27, c28), f4(c27, c28))) | (~p2(c30, c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p26(c31, c30)) | p24(f4(c27, c28), c29) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29) | p24(f4(f6(c32, X53), f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) | p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)) | (~p3(f4(c27, c28), f4(c30, c28)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[80, 74, 71, 68, 58, 38])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[81, 1])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (^[X57: $i, X56: $i] : refl(((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57)) <=> ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57)) <=> ![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57)) <=> ![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (^[X57: $i, X56: $i] : rewrite((p24(f4(c30, X56), X57) | (~p24(f4(f6(c32, c30), X56), X57))) <=> ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (![X57: $i, X56: $i] : (p24(f4(c30, X56), X57) | (~p24(f4(f6(c32, c30), X56), X57))) <=> ![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.43 tff(88,axiom,(![X57: $i, X56: $i] : (p24(f4(c30, X56), X57) | (~p24(f4(f6(c32, c30), X56), X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p24_30')).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.43 tff(91,plain,(
% 0.20/0.43 ![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))),
% 0.20/0.43 inference(skolemize,[status(sab)],[90])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (((~![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))) | ((~p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)))) <=> ((~![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))) | (~p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ((~![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))) | ((~p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 ((~![X57: $i, X56: $i] : ((~p24(f4(f6(c32, c30), X56), X57)) | p24(f4(c30, X56), X57))) | (~p24(f4(f6(c32, c30), f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[95, 92, 82])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (^[X53: $i, X55: $i, X52: $i, X54: $i] : refl(((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29)) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29)) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29)) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (^[X53: $i, X55: $i, X52: $i, X54: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p24(X52, c29) | (~p3(X52, X54))) <=> ((~p3(X52, X54)) | p24(X52, c29))), (((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) <=> (((~p3(X52, X54)) | p24(X52, c29)) | (~p2(X55, X53))))), rewrite((((~p3(X52, X54)) | p24(X52, c29)) | (~p2(X55, X53))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | p24(X52, c29))), (((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | p24(X52, c29)))), ((((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) <=> (((~p3(X52, X54)) | (~p2(X55, X53)) | p24(X52, c29)) | (~p26(c31, X53))))), rewrite((((~p3(X52, X54)) | (~p2(X55, X53)) | p24(X52, c29)) | (~p26(c31, X53))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p26(c31, X53)) | p24(X52, c29))), ((((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p26(c31, X53)) | p24(X52, c29)))), (((((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28)))) <=> (((~p3(X52, X54)) | (~p2(X55, X53)) | (~p26(c31, X53)) | p24(X52, c29)) | (~p3(X54, f4(X55, c28)))))), rewrite((((~p3(X52, X54)) | (~p2(X55, X53)) | (~p26(c31, X53)) | p24(X52, c29)) | (~p3(X54, f4(X55, c28)))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))), (((((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28)))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29)))), ((((((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28)))) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) <=> (((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))))), rewrite((((~p3(X52, X54)) | (~p2(X55, X53)) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))), ((((((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28)))) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) <=> ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![X53: $i, X55: $i, X52: $i, X54: $i] : (((((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28)))) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53)))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.43 tff(102,axiom,(![X53: $i, X55: $i, X52: $i, X54: $i] : (((((p24(X52, c29) | (~p3(X52, X54))) | (~p2(X55, X53))) | (~p26(c31, X53))) | (~p3(X54, f4(X55, c28)))) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p24_43')).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.43 tff(105,plain,(
% 0.20/0.43 ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))),
% 0.20/0.43 inference(skolemize,[status(sab)],[104])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))) | (p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28))))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))) | p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (((~p3(f4(c27, c28), f4(c27, c28))) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p26(c31, c30)) | p24(f4(c27, c28), c29)) <=> (p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))) | ((~p3(f4(c27, c28), f4(c27, c28))) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p26(c31, c30)) | p24(f4(c27, c28), c29))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))) | (p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[108])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))) | ((~p3(f4(c27, c28), f4(c27, c28))) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p26(c31, c30)) | p24(f4(c27, c28), c29))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))) | p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[109, 107])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))) | ((~p3(f4(c27, c28), f4(c27, c28))) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p26(c31, c30)) | p24(f4(c27, c28), c29))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p3(X52, X54)) | (~p2(X55, X53)) | (~p24(f4(X53, f17(f19(f21(f23(c33, X52), X54), X55), X53)), f9(f11(f13(f15(c34, X52), X54), X55), X53))) | (~p3(X54, f4(X55, c28))) | (~p26(c31, X53)) | p24(X52, c29))) | p24(f4(c27, c28), c29) | (~p26(c31, c30)) | (~p2(c30, c30)) | (~p24(f4(c30, f17(f19(f21(f23(c33, f4(c27, c28)), f4(c27, c28)), c30), c30)), f9(f11(f13(f15(c34, f4(c27, c28)), f4(c27, c28)), c30), c30))) | (~p3(f4(c27, c28), f4(c30, c28))) | (~p3(f4(c27, c28), f4(c27, c28)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[112, 74, 71, 106, 58, 38, 1, 96])).
% 0.20/0.44 tff(114,plain,(~p3(f4(c27, c28), f4(c30, c28))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (((~![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))) | ((~p2(c27, c30)) | (~p3(c28, c28)) | p3(f4(c27, c28), f4(c30, c28)))) <=> ((~![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))) | (~p2(c27, c30)) | (~p3(c28, c28)) | p3(f4(c27, c28), f4(c30, c28)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 ((~![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))) | ((~p2(c27, c30)) | (~p3(c28, c28)) | p3(f4(c27, c28), f4(c30, c28)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 ((~![X73: $i, X75: $i, X72: $i, X74: $i] : ((~p2(X72, X74)) | (~p3(X73, X75)) | p3(f4(X72, X73), f4(X74, X75)))) | (~p2(c27, c30)) | (~p3(c28, c28)) | p3(f4(c27, c28), f4(c30, c28))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[117, 51, 33, 12, 114])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------