%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:40 PM UTC 2026
% Result : Theorem 0.38s 0.64s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 09:53:05 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.38/0.64 % SZS status Theorem
% 0.38/0.64 % SZS output start Proof
% 0.38/0.64 tff(p1_type, type, (
% 0.38/0.64 p1: $i > $o)).
% 0.38/0.64 tff(tptp_fun_Y_6_type, type, (
% 0.38/0.64 tptp_fun_Y_6: $i > $i)).
% 0.38/0.64 tff(tptp_fun_Y_3_type, type, (
% 0.38/0.64 tptp_fun_Y_3: $i)).
% 0.38/0.64 tff(p2_type, type, (
% 0.38/0.64 p2: $i > $o)).
% 0.38/0.64 tff(r1_type, type, (
% 0.38/0.64 r1: ( $i * $i ) > $o)).
% 0.38/0.64 tff(tptp_fun_Y_5_type, type, (
% 0.38/0.64 tptp_fun_Y_5: $i > $i)).
% 0.38/0.64 tff(p3_type, type, (
% 0.38/0.64 p3: $i > $o)).
% 0.38/0.64 tff(tptp_fun_Y_4_type, type, (
% 0.38/0.64 tptp_fun_Y_4: $i > $i)).
% 0.38/0.64 tff(tptp_fun_X_0_type, type, (
% 0.38/0.64 tptp_fun_X_0: $i)).
% 0.38/0.64 tff(tptp_fun_Y_1_type, type, (
% 0.38/0.64 tptp_fun_Y_1: $i)).
% 0.38/0.64 tff(tptp_fun_X_2_type, type, (
% 0.38/0.64 tptp_fun_X_2: $i)).
% 0.38/0.64 tff(1,assumption,(~p1(tptp_fun_Y_6(Y!3))), introduced(assumption)).
% 0.38/0.64 tff(2,assumption,(~r1(Y!3, Y!3)), introduced(assumption)).
% 0.38/0.64 tff(3,plain,
% 0.38/0.64 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.38/0.64 inference(bind,[status(th)],[])).
% 0.38/0.64 tff(4,plain,
% 0.38/0.64 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.38/0.64 inference(quant_intro,[status(thm)],[3])).
% 0.38/0.64 tff(5,plain,
% 0.38/0.64 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.38/0.64 inference(rewrite,[status(thm)],[])).
% 0.38/0.64 tff(6,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.38/0.64 tff(7,plain,
% 0.38/0.64 (![X: $i] : r1(X, X)),
% 0.38/0.64 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.38/0.64 tff(8,plain,(
% 0.38/0.64 ![X: $i] : r1(X, X)),
% 0.38/0.64 inference(skolemize,[status(sab)],[7])).
% 0.38/0.64 tff(9,plain,
% 0.38/0.64 (![X: $i] : r1(X, X)),
% 0.38/0.64 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.38/0.64 tff(10,plain,
% 0.38/0.64 ((~![X: $i] : r1(X, X)) | r1(Y!3, Y!3)),
% 0.38/0.64 inference(quant_inst,[status(thm)],[])).
% 0.38/0.64 tff(11,plain,
% 0.38/0.64 ($false),
% 0.38/0.64 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.38/0.64 tff(12,plain,(r1(Y!3, Y!3)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.64 tff(13,plain,
% 0.38/0.64 (^[X: $i] : rewrite(((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))) <=> ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))))),
% 0.38/0.64 inference(bind,[status(th)],[])).
% 0.38/0.64 tff(14,plain,
% 0.38/0.64 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))) <=> ![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.38/0.64 inference(quant_intro,[status(thm)],[13])).
% 0.38/0.64 tff(15,plain,
% 0.38/0.64 (^[X: $i] : refl(((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))) <=> ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))))),
% 0.38/0.64 inference(bind,[status(th)],[])).
% 0.38/0.64 tff(16,plain,
% 0.38/0.64 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))) <=> ![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X))))))),
% 0.38/0.64 inference(quant_intro,[status(thm)],[15])).
% 0.38/0.64 tff(17,plain,
% 0.38/0.64 (^[X: $i] : rewrite(((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))) <=> ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))))),
% 0.38/0.64 inference(bind,[status(th)],[])).
% 0.38/0.64 tff(18,plain,
% 0.38/0.64 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))) <=> ![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X))))))),
% 0.38/0.64 inference(quant_intro,[status(thm)],[17])).
% 0.38/0.64 tff(19,plain,
% 0.38/0.64 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))) <=> ![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X))))))),
% 0.38/0.64 inference(transitivity,[status(thm)],[18, 16])).
% 0.38/0.64 tff(20,plain,
% 0.38/0.64 (^[X: $i] : rewrite(((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))) <=> ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X)))))))),
% 0.38/0.64 inference(bind,[status(th)],[])).
% 0.38/0.64 tff(21,plain,
% 0.38/0.64 (![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))) <=> ![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X))))))),
% 0.38/0.64 inference(quant_intro,[status(thm)],[20])).
% 0.38/0.64 tff(22,plain,
% 0.38/0.64 (((r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1)) & (r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))) <=> (r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1) & r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))),
% 0.38/0.64 inference(rewrite,[status(thm)],[])).
% 0.38/0.64 tff(23,plain,
% 0.38/0.64 ((r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X))))))))) <=> (r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))),
% 0.38/0.64 inference(rewrite,[status(thm)],[])).
% 0.38/0.64 tff(24,plain,
% 0.38/0.64 ((~((~r1(Y!1, X!2)) | (~p1(X!2)))) <=> (~((~r1(Y!1, X!2)) | (~p1(X!2))))),
% 0.38/0.64 inference(rewrite,[status(thm)],[])).
% 0.38/0.64 tff(25,plain,
% 0.38/0.64 ((r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1)) <=> (r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1))),
% 0.38/0.64 inference(monotonicity,[status(thm)],[24])).
% 0.38/0.64 tff(26,plain,
% 0.38/0.64 (((r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1)) & (r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))) <=> ((r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1)) & (r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X))))))))))),
% 0.38/0.64 inference(monotonicity,[status(thm)],[25, 23])).
% 0.38/0.64 tff(27,plain,
% 0.38/0.64 (((r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1)) & (r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))) <=> (r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1) & r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X)))))))))),
% 0.38/0.64 inference(transitivity,[status(thm)],[26, 22])).
% 0.38/0.64 tff(28,plain,
% 0.38/0.64 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.38/0.64 inference(rewrite,[status(thm)],[])).
% 0.38/0.64 tff(29,plain,
% 0.38/0.64 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.38/0.64 inference(rewrite,[status(thm)],[])).
% 0.38/0.64 tff(30,plain,
% 0.38/0.64 ((~?[X: $i] : (~(![Y: $i] : (((~r1(X, Y)) | (~p3(Y))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(((![Y: $i] : ((~r1(X, Y)) | $false) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | ![Y: $i] : (((~r1(X, Y)) | ((~p1(Y)) & (~p2(Y)))) | (p2(Y) & p1(Y))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y))))))))))))),
% 0.38/0.64 inference(rewrite,[status(thm)],[])).
% 0.38/0.64 tff(31,plain,
% 0.38/0.64 ((~(~?[X: $i] : (~(![Y: $i] : (((~r1(X, Y)) | (~p3(Y))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(((![Y: $i] : ((~r1(X, Y)) | $false) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | ![Y: $i] : (((~r1(X, Y)) | ((~p1(Y)) & (~p2(Y)))) | (p2(Y) & p1(Y)))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))))),
% 0.38/0.64 inference(monotonicity,[status(thm)],[30])).
% 0.38/0.64 tff(32,plain,
% 0.38/0.64 ((~(~?[X: $i] : (~(![Y: $i] : (((~r1(X, Y)) | (~p3(Y))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(((![Y: $i] : ((~r1(X, Y)) | $false) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | ![Y: $i] : (((~r1(X, Y)) | ((~p1(Y)) & (~p2(Y)))) | (p2(Y) & p1(Y)))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.38/0.64 inference(transitivity,[status(thm)],[31, 29])).
% 0.38/0.64 tff(33,axiom,(~(~?[X: $i] : (~(![Y: $i] : (((~r1(X, Y)) | (~p3(Y))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(((![Y: $i] : ((~r1(X, Y)) | $false) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | ![Y: $i] : (((~r1(X, Y)) | ((~p1(Y)) & (~p2(Y)))) | (p2(Y) & p1(Y)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.38/0.64 tff(34,plain,
% 0.38/0.64 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.38/0.65 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.38/0.65 tff(35,plain,
% 0.38/0.65 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X))) | (~p3(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y)))))) | ![Y: $i] : (~r1(X, Y)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & p1(Y)) | ((~p1(Y)) & (~p2(Y)))))))))))),
% 0.38/0.65 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.38/0.65 tff(36,plain,
% 0.38/0.65 (r1(X!0, Y!1) & (~((~r1(Y!1, X!2)) | (~p1(X!2)))) & p3(Y!1) & r1(X!0, Y!3) & ![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X))))))))),
% 0.38/0.65 inference(modus_ponens,[status(thm)],[35, 27])).
% 0.38/0.65 tff(37,plain,
% 0.38/0.65 (![X: $i] : ((~r1(Y!3, X)) | ((~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)))) & ![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p1(Y))) | ((~p2(Y)) & p1(Y))))) & r1(X, tptp_fun_Y_5(X)) & (~((~r1(X, tptp_fun_Y_6(X))) | (p2(tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X))) | ((~p1(tptp_fun_Y_6(X))) & (~p2(tptp_fun_Y_6(X))))))))),
% 0.38/0.65 inference(and_elim,[status(thm)],[36])).
% 0.38/0.65 tff(38,plain,
% 0.38/0.65 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X))))))),
% 0.38/0.65 inference(modus_ponens,[status(thm)],[37, 21])).
% 0.38/0.65 tff(39,plain,
% 0.38/0.65 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(X, tptp_fun_Y_5(X))))))),
% 0.38/0.65 inference(modus_ponens,[status(thm)],[38, 19])).
% 0.38/0.65 tff(40,plain,
% 0.38/0.65 (![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.38/0.65 inference(modus_ponens,[status(thm)],[39, 14])).
% 0.38/0.65 tff(41,plain,
% 0.38/0.65 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, Y!3)) | (~((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))))))),
% 0.38/0.65 inference(rewrite,[status(thm)],[])).
% 0.38/0.65 tff(42,plain,
% 0.38/0.65 (((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y))))))))))) <=> ((~r1(Y!3, Y!3)) | (~((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))))))),
% 0.38/0.65 inference(rewrite,[status(thm)],[])).
% 0.38/0.65 tff(43,plain,
% 0.38/0.65 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3)))))))),
% 0.38/0.65 inference(monotonicity,[status(thm)],[42])).
% 0.38/0.65 tff(44,plain,
% 0.38/0.65 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, Y!3)) | (~((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))))))),
% 0.38/0.65 inference(transitivity,[status(thm)],[43, 41])).
% 0.38/0.65 tff(45,plain,
% 0.38/0.65 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | ((~r1(Y!3, Y!3)) | (~((~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))),
% 0.38/0.65 inference(quant_inst,[status(thm)],[])).
% 0.38/0.65 tff(46,plain,
% 0.38/0.65 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | p3(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_6(X))) | (~((~p1(tptp_fun_Y_6(X))) | (~p2(tptp_fun_Y_6(X))))) | (~(p1(tptp_fun_Y_6(X)) | p2(tptp_fun_Y_6(X)))) | (~r1(X, tptp_fun_Y_5(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))))))) | (~r1(Y!3, Y!3)) | (~((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3)))))),
% 0.38/0.65 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.38/0.65 tff(47,plain,
% 0.38/0.65 ((~r1(Y!3, Y!3)) | (~((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3)))))),
% 0.38/0.65 inference(unit_resolution,[status(thm)],[46, 40])).
% 0.38/0.65 tff(48,plain,
% 0.38/0.65 (~((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3))))),
% 0.38/0.65 inference(unit_resolution,[status(thm)],[47, 12])).
% 0.38/0.65 tff(49,plain,
% 0.38/0.65 (((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3)))) | (p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))),
% 0.38/0.65 inference(tautology,[status(thm)],[])).
% 0.38/0.65 tff(50,plain,
% 0.38/0.65 (p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3))),
% 0.38/0.65 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.38/0.65 tff(51,plain,
% 0.38/0.65 ((~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3))),
% 0.38/0.65 inference(tautology,[status(thm)],[])).
% 0.38/0.65 tff(52,plain,
% 0.38/0.65 (p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3))),
% 0.38/0.65 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.38/0.65 tff(53,plain,
% 0.38/0.65 (p2(tptp_fun_Y_6(Y!3))),
% 0.38/0.65 inference(unit_resolution,[status(thm)],[52, 1])).
% 0.38/0.65 tff(54,plain,
% 0.38/0.65 (((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3)))) | ![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))),
% 0.38/0.65 inference(tautology,[status(thm)],[])).
% 0.38/0.65 tff(55,plain,
% 0.38/0.65 (![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))),
% 0.38/0.65 inference(unit_resolution,[status(thm)],[54, 48])).
% 0.38/0.65 tff(56,plain,
% 0.38/0.65 (((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3)))) | r1(Y!3, tptp_fun_Y_6(Y!3))),
% 0.38/0.65 inference(tautology,[status(thm)],[])).
% 0.38/0.65 tff(57,plain,
% 0.38/0.65 (r1(Y!3, tptp_fun_Y_6(Y!3))),
% 0.38/0.65 inference(unit_resolution,[status(thm)],[56, 48])).
% 0.38/0.65 tff(58,plain,
% 0.38/0.65 (((~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | ((~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~(p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3))))))))) <=> ((~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~(p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3))))))))),
% 0.38/0.66 inference(rewrite,[status(thm)],[])).
% 0.38/0.66 tff(59,plain,
% 0.38/0.66 ((~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | ((~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~(p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3))))))))),
% 0.38/0.66 inference(quant_inst,[status(thm)],[])).
% 0.38/0.66 tff(60,plain,
% 0.38/0.66 ((~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~((~(p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3)))))))),
% 0.38/0.66 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.38/0.66 tff(61,plain,
% 0.38/0.66 (~((~(p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3))))))),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[60, 57, 55])).
% 0.38/0.66 tff(62,plain,
% 0.38/0.66 (((~(p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3)))))) | (p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3))))),
% 0.38/0.66 inference(tautology,[status(thm)],[])).
% 0.38/0.66 tff(63,plain,
% 0.38/0.66 (p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3)))),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.38/0.66 tff(64,plain,
% 0.38/0.66 ((~(p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3))))) | p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3)))),
% 0.38/0.66 inference(tautology,[status(thm)],[])).
% 0.38/0.66 tff(65,plain,
% 0.38/0.66 (p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3)))),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.38/0.66 tff(66,plain,
% 0.38/0.66 ($false),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[65, 53, 1])).
% 0.38/0.66 tff(67,plain,(p1(tptp_fun_Y_6(Y!3))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.66 tff(68,plain,
% 0.38/0.66 (((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p1(tptp_fun_Y_6(Y!3)) | p2(tptp_fun_Y_6(Y!3)))) | (~r1(Y!3, tptp_fun_Y_4(Y!3))) | p3(tptp_fun_Y_4(Y!3)) | (~r1(Y!3, tptp_fun_Y_6(Y!3))) | (~![Y: $i] : ((~r1(Y!3, Y)) | (~((~(p1(Y) | (~p2(Y)))) | (~(p2(Y) | (~p1(Y)))))))) | (~r1(Y!3, tptp_fun_Y_5(Y!3)))) | ((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))),
% 0.38/0.66 inference(tautology,[status(thm)],[])).
% 0.38/0.66 tff(69,plain,
% 0.38/0.66 ((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3)))),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[68, 48])).
% 0.38/0.66 tff(70,plain,
% 0.38/0.66 ((~((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3))))) | (~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3)))),
% 0.38/0.66 inference(tautology,[status(thm)],[])).
% 0.38/0.66 tff(71,plain,
% 0.38/0.66 ((~p1(tptp_fun_Y_6(Y!3))) | (~p2(tptp_fun_Y_6(Y!3)))),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.38/0.66 tff(72,plain,
% 0.38/0.66 (~p2(tptp_fun_Y_6(Y!3))),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[71, 67])).
% 0.38/0.66 tff(73,plain,
% 0.38/0.66 (((~(p1(tptp_fun_Y_6(Y!3)) | (~p2(tptp_fun_Y_6(Y!3))))) | (~(p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3)))))) | (p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3))))),
% 0.38/0.66 inference(tautology,[status(thm)],[])).
% 0.38/0.66 tff(74,plain,
% 0.38/0.66 (p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3)))),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[73, 61])).
% 0.38/0.66 tff(75,plain,
% 0.38/0.66 ((~(p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3))))) | p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3)))),
% 0.38/0.66 inference(tautology,[status(thm)],[])).
% 0.38/0.66 tff(76,plain,
% 0.38/0.66 (p2(tptp_fun_Y_6(Y!3)) | (~p1(tptp_fun_Y_6(Y!3)))),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.38/0.66 tff(77,plain,
% 0.38/0.66 ($false),
% 0.38/0.66 inference(unit_resolution,[status(thm)],[76, 72, 67])).
% 0.38/0.66 % SZS output end Proof
% 0.38/0.66 % E exiting
%------------------------------------------------------------------------------