%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN643-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN643-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 12:39:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(p4_type, type, (
% 0.21/0.38 p4: ( $i * $i ) > $o)).
% 0.21/0.38 tff(f5_type, type, (
% 0.21/0.38 f5: $i > $i)).
% 0.21/0.38 tff(f10_type, type, (
% 0.21/0.38 f10: ( $i * $i ) > $i)).
% 0.21/0.38 tff(f3_type, type, (
% 0.21/0.38 f3: $i > $i)).
% 0.21/0.38 tff(c18_type, type, (
% 0.21/0.38 c18: $i)).
% 0.21/0.38 tff(c19_type, type, (
% 0.21/0.38 c19: $i)).
% 0.21/0.38 tff(f9_type, type, (
% 0.21/0.38 f9: ( $i * $i ) > $i)).
% 0.21/0.38 tff(p2_type, type, (
% 0.21/0.38 p2: ( $i * $i ) > $o)).
% 0.21/0.38 tff(p15_type, type, (
% 0.21/0.38 p15: $i > $o)).
% 0.21/0.38 tff(1,assumption,(~p2(c18, c18)), introduced(assumption)).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (^[X27: $i] : refl(p2(X27, X27) <=> p2(X27, X27))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (![X27: $i] : p2(X27, X27) <=> ![X27: $i] : p2(X27, X27)),
% 0.21/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (![X27: $i] : p2(X27, X27) <=> ![X27: $i] : p2(X27, X27)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(5,axiom,(![X27: $i] : p2(X27, X27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_6')).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (![X27: $i] : p2(X27, X27)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.38 tff(7,plain,(
% 0.21/0.38 ![X27: $i] : p2(X27, X27)),
% 0.21/0.38 inference(skolemize,[status(sab)],[6])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 (![X27: $i] : p2(X27, X27)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 ((~![X27: $i] : p2(X27, X27)) | p2(c18, c18)),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.38 tff(11,plain,(p2(c18, c18)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (^[X35: $i, X34: $i] : refl(((~p2(X34, X35)) | p2(f3(X34), f3(X35))) <=> ((~p2(X34, X35)) | p2(f3(X34), f3(X35))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35))) <=> ![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35))) <=> ![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (^[X35: $i, X34: $i] : rewrite((p2(f3(X34), f3(X35)) | (~p2(X34, X35))) <=> ((~p2(X34, X35)) | p2(f3(X34), f3(X35))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (![X35: $i, X34: $i] : (p2(f3(X34), f3(X35)) | (~p2(X34, X35))) <=> ![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.38 tff(17,axiom,(![X35: $i, X34: $i] : (p2(f3(X34), f3(X35)) | (~p2(X34, X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_20')).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 (![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.38 tff(20,plain,(
% 0.21/0.38 ![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[19])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 (![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (((~![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))) | ((~p2(c18, c18)) | p2(f3(c18), f3(c18)))) <=> ((~![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))) | (~p2(c18, c18)) | p2(f3(c18), f3(c18)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 ((~![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))) | ((~p2(c18, c18)) | p2(f3(c18), f3(c18)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 ((~![X35: $i, X34: $i] : ((~p2(X34, X35)) | p2(f3(X34), f3(X35)))) | (~p2(c18, c18)) | p2(f3(c18), f3(c18))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 ((~p2(c18, c18)) | p2(f3(c18), f3(c18))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 (p2(f3(c18), f3(c18))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[25, 11])).
% 0.21/0.38 tff(27,assumption,(~p2(f3(c19), f3(c19))), introduced(assumption)).
% 0.21/0.38 tff(28,plain,
% 0.21/0.38 ((~![X27: $i] : p2(X27, X27)) | p2(f3(c19), f3(c19))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[28, 8, 27])).
% 0.21/0.38 tff(30,plain,(p2(f3(c19), f3(c19))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 (^[X31: $i, X32: $i, X30: $i, X33: $i] : refl(((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33))) <=> ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 (![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33))) <=> ![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 (![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33))) <=> ![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (^[X31: $i, X32: $i, X30: $i, X33: $i] : trans(monotonicity(rewrite((p2(f10(X30, X31), f10(X32, X33)) | (~p2(X30, X32))) <=> ((~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))), (((p2(f10(X30, X31), f10(X32, X33)) | (~p2(X30, X32))) | (~p2(X31, X33))) <=> (((~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33))) | (~p2(X31, X33))))), rewrite((((~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33))) | (~p2(X31, X33))) <=> ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))), (((p2(f10(X30, X31), f10(X32, X33)) | (~p2(X30, X32))) | (~p2(X31, X33))) <=> ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 (![X31: $i, X32: $i, X30: $i, X33: $i] : ((p2(f10(X30, X31), f10(X32, X33)) | (~p2(X30, X32))) | (~p2(X31, X33))) <=> ![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.38 tff(36,axiom,(![X31: $i, X32: $i, X30: $i, X33: $i] : ((p2(f10(X30, X31), f10(X32, X33)) | (~p2(X30, X32))) | (~p2(X31, X33)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_34')).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 (![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.38 tff(38,plain,
% 0.21/0.38 (![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.38 tff(39,plain,(
% 0.21/0.38 ![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[38])).
% 0.21/0.38 tff(40,plain,
% 0.21/0.38 (![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.21/0.38 tff(41,plain,
% 0.21/0.38 (((~![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))) | ((~p2(f3(c18), f3(c18))) | (~p2(f3(c19), f3(c19))) | p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18))))) <=> ((~![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))) | (~p2(f3(c18), f3(c18))) | (~p2(f3(c19), f3(c19))) | p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(42,plain,
% 0.21/0.38 ((~![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))) | ((~p2(f3(c18), f3(c18))) | (~p2(f3(c19), f3(c19))) | p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(43,plain,
% 0.21/0.38 ((~![X31: $i, X32: $i, X30: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X30, X32)) | p2(f10(X30, X31), f10(X32, X33)))) | (~p2(f3(c18), f3(c18))) | (~p2(f3(c19), f3(c19))) | p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.38 tff(44,plain,
% 0.21/0.39 ((~p2(f3(c18), f3(c18))) | (~p2(f3(c19), f3(c19))) | p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[44, 30, 26])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (^[X39: $i, X40: $i] : refl(((~p2(X39, X40)) | p4(f5(X39), f5(X40))) <=> ((~p2(X39, X40)) | p4(f5(X39), f5(X40))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40))) <=> ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40))) <=> ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (^[X39: $i, X40: $i] : rewrite((p4(f5(X39), f5(X40)) | (~p2(X39, X40))) <=> ((~p2(X39, X40)) | p4(f5(X39), f5(X40))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (![X39: $i, X40: $i] : (p4(f5(X39), f5(X40)) | (~p2(X39, X40))) <=> ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.39 tff(51,axiom,(![X39: $i, X40: $i] : (p4(f5(X39), f5(X40)) | (~p2(X39, X40)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_19')).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.39 tff(54,plain,(
% 0.21/0.39 ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[53])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))) | ((~p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18)))) | p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18)))))) <=> ((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))) | (~p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18)))) | p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 ((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))) | ((~p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18)))) | p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 ((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p4(f5(X39), f5(X40)))) | (~p2(f10(f3(c19), f3(c18)), f10(f3(c19), f3(c18)))) | p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 (p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[58, 55, 45])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 (^[X14: $i, X15: $i] : refl(((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15)))) <=> ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 (![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15)))) <=> ![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 (![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15)))) <=> ![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (^[X14: $i, X15: $i] : trans(monotonicity(rewrite((p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))) | (~p15(X14))) <=> ((~p15(X14)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))), (((p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))) | (~p15(X14))) | (~p15(X15))) <=> (((~p15(X14)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15)))) | (~p15(X15))))), rewrite((((~p15(X14)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15)))) | (~p15(X15))) <=> ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))), (((p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))) | (~p15(X14))) | (~p15(X15))) <=> ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 (![X14: $i, X15: $i] : ((p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))) | (~p15(X14))) | (~p15(X15))) <=> ![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.39 tff(65,axiom,(![X14: $i, X15: $i] : ((p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))) | (~p15(X14))) | (~p15(X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_37')).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 (![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.39 tff(67,plain,
% 0.21/0.39 (![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.39 tff(68,plain,(
% 0.21/0.39 ![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[67])).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 (![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.39 tff(70,plain,
% 0.21/0.39 (p15(f3(c18)) <=> p15(f3(c18))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(71,axiom,(p15(f3(c18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f3_is_p15_2')).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 (p15(f3(c18))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.39 tff(73,plain,
% 0.21/0.39 (p15(f3(c19)) <=> p15(f3(c19))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(74,axiom,(p15(f3(c19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f3_is_p15_1')).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 (p15(f3(c19))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.39 tff(76,plain,
% 0.21/0.39 (((~![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))) | ((~p15(f3(c19))) | (~p15(f3(c18))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18)))))) <=> ((~![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))) | (~p15(f3(c19))) | (~p15(f3(c18))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(77,plain,
% 0.21/0.39 ((~![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))) | ((~p15(f3(c19))) | (~p15(f3(c18))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(78,plain,
% 0.21/0.39 ((~![X14: $i, X15: $i] : ((~p15(X14)) | (~p15(X15)) | p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))))) | (~p15(f3(c19))) | (~p15(f3(c18))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.39 tff(79,plain,
% 0.21/0.39 (p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[78, 75, 72, 69])).
% 0.21/0.39 tff(80,plain,
% 0.21/0.39 (^[X38: $i, X37: $i, X36: $i] : refl(((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38)) <=> ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(81,plain,
% 0.21/0.39 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38)) <=> ![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.39 tff(82,plain,
% 0.21/0.39 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38)) <=> ![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(83,plain,
% 0.21/0.39 (^[X38: $i, X37: $i, X36: $i] : trans(monotonicity(rewrite((p4(X37, X38) | (~p4(X36, X37))) <=> ((~p4(X36, X37)) | p4(X37, X38))), (((p4(X37, X38) | (~p4(X36, X37))) | (~p4(X36, X38))) <=> (((~p4(X36, X37)) | p4(X37, X38)) | (~p4(X36, X38))))), rewrite((((~p4(X36, X37)) | p4(X37, X38)) | (~p4(X36, X38))) <=> ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))), (((p4(X37, X38) | (~p4(X36, X37))) | (~p4(X36, X38))) <=> ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(84,plain,
% 0.21/0.39 (![X38: $i, X37: $i, X36: $i] : ((p4(X37, X38) | (~p4(X36, X37))) | (~p4(X36, X38))) <=> ![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.39 tff(85,axiom,(![X38: $i, X37: $i, X36: $i] : ((p4(X37, X38) | (~p4(X36, X37))) | (~p4(X36, X38)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_24')).
% 0.21/0.39 tff(86,plain,
% 0.21/0.39 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.39 tff(87,plain,
% 0.21/0.39 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.21/0.39 tff(88,plain,(
% 0.21/0.39 ![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.21/0.39 inference(skolemize,[status(sab)],[87])).
% 0.21/0.39 tff(89,plain,
% 0.21/0.39 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.21/0.39 tff(90,plain,
% 0.21/0.39 (((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | ((~p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18))))) | (~p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18))))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | (~p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18))))) | (~p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18))))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(91,plain,
% 0.21/0.39 ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | ((~p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18))))) | (~p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18))))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(92,plain,
% 0.21/0.39 ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | (~p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18))))) | (~p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18))))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.39 tff(93,plain,
% 0.21/0.39 (p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[92, 89, 79, 59])).
% 0.21/0.39 tff(94,plain,
% 0.21/0.39 (^[X43: $i, X42: $i, X41: $i, X44: $i] : refl(((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44))) <=> ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(95,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44))) <=> ![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.39 tff(96,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44))) <=> ![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(97,plain,
% 0.21/0.39 (^[X43: $i, X42: $i, X41: $i, X44: $i] : trans(monotonicity(rewrite((p4(f9(X41, X42), f9(X43, X44)) | (~p4(X42, X44))) <=> ((~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))), (((p4(f9(X41, X42), f9(X43, X44)) | (~p4(X42, X44))) | (~p4(X41, X43))) <=> (((~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44))) | (~p4(X41, X43))))), rewrite((((~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44))) | (~p4(X41, X43))) <=> ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))), (((p4(f9(X41, X42), f9(X43, X44)) | (~p4(X42, X44))) | (~p4(X41, X43))) <=> ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(98,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X44: $i] : ((p4(f9(X41, X42), f9(X43, X44)) | (~p4(X42, X44))) | (~p4(X41, X43))) <=> ![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.39 tff(99,axiom,(![X43: $i, X42: $i, X41: $i, X44: $i] : ((p4(f9(X41, X42), f9(X43, X44)) | (~p4(X42, X44))) | (~p4(X41, X43)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_35')).
% 0.21/0.39 tff(100,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.39 tff(101,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.21/0.39 tff(102,plain,(
% 0.21/0.39 ![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[101])).
% 0.21/0.39 tff(103,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.21/0.39 tff(104,plain,
% 0.21/0.39 (p4(f5(f3(c19)), f5(c19)) <=> p4(f5(f3(c19)), f5(c19))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(105,axiom,(p4(f5(f3(c19)), f5(c19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_11')).
% 0.21/0.39 tff(106,plain,
% 0.21/0.39 (p4(f5(f3(c19)), f5(c19))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.39 tff(107,plain,
% 0.21/0.39 (p4(f5(f3(c18)), f5(c18)) <=> p4(f5(f3(c18)), f5(c18))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(108,axiom,(p4(f5(f3(c18)), f5(c18))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_10')).
% 0.21/0.39 tff(109,plain,
% 0.21/0.39 (p4(f5(f3(c18)), f5(c18))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.39 tff(110,plain,
% 0.21/0.39 (((~![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))) | ((~p4(f5(f3(c18)), f5(c18))) | (~p4(f5(f3(c19)), f5(c19))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18))))) <=> ((~![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))) | (~p4(f5(f3(c18)), f5(c18))) | (~p4(f5(f3(c19)), f5(c19))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(111,plain,
% 0.21/0.39 (((~p4(f5(f3(c19)), f5(c19))) | (~p4(f5(f3(c18)), f5(c18))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) <=> ((~p4(f5(f3(c18)), f5(c18))) | (~p4(f5(f3(c19)), f5(c19))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(112,plain,
% 0.21/0.39 (((~![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))) | ((~p4(f5(f3(c19)), f5(c19))) | (~p4(f5(f3(c18)), f5(c18))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18))))) <=> ((~![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))) | ((~p4(f5(f3(c18)), f5(c18))) | (~p4(f5(f3(c19)), f5(c19))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.39 tff(113,plain,
% 0.21/0.39 (((~![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))) | ((~p4(f5(f3(c19)), f5(c19))) | (~p4(f5(f3(c18)), f5(c18))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18))))) <=> ((~![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))) | (~p4(f5(f3(c18)), f5(c18))) | (~p4(f5(f3(c19)), f5(c19))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[112, 110])).
% 0.21/0.39 tff(114,plain,
% 0.21/0.39 ((~![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))) | ((~p4(f5(f3(c19)), f5(c19))) | (~p4(f5(f3(c18)), f5(c18))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(115,plain,
% 0.21/0.40 ((~![X43: $i, X42: $i, X41: $i, X44: $i] : ((~p4(X41, X43)) | (~p4(X42, X44)) | p4(f9(X41, X42), f9(X43, X44)))) | (~p4(f5(f3(c18)), f5(c18))) | (~p4(f5(f3(c19)), f5(c19))) | p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 (p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[115, 109, 106, 103])).
% 0.21/0.40 tff(117,plain,
% 0.21/0.40 ((~p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))) <=> (~p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(118,axiom,(~p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p4_28')).
% 0.21/0.40 tff(119,plain,
% 0.21/0.40 (~p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.40 tff(120,plain,
% 0.21/0.40 (((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | (p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(121,plain,
% 0.21/0.40 (((~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))) <=> (p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(122,plain,
% 0.21/0.40 (((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | ((~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | (p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[121])).
% 0.21/0.40 tff(123,plain,
% 0.21/0.40 (((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | ((~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[122, 120])).
% 0.21/0.40 tff(124,plain,
% 0.21/0.40 ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | ((~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(125,plain,
% 0.21/0.40 ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18)))) | (~p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.40 tff(126,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[125, 89, 119, 116, 93])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------