%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN352+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:52 AM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN352+1 : TPTP v9.0.0. Released v2.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:35:50 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(big_f_type, type, (
% 0.13/0.37 big_f: ( $i * $i ) > $o)).
% 0.13/0.37 tff(tptp_fun_Z_2_type, type, (
% 0.13/0.37 tptp_fun_Z_2: ( $i * $i ) > $i)).
% 0.13/0.37 tff(elem_3_type, type, (
% 0.13/0.37 elem_3: $i)).
% 0.13/0.37 tff(tptp_fun_X2_0_type, type, (
% 0.13/0.37 tptp_fun_X2_0: $i)).
% 0.13/0.37 tff(tptp_fun_X1_1_type, type, (
% 0.13/0.37 tptp_fun_X1_1: $i)).
% 0.13/0.37 tff(1,plain,
% 0.13/0.37 (^[Y1: $i, Y2: $i] : refl((~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1)))))) <=> (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1)))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 (![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1)))))) <=> ![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.37 tff(3,plain,
% 0.13/0.37 (^[Y1: $i, Y2: $i] : rewrite((~((~big_f(X1!1, X2!0)) | (big_f(Y1, Y2) & (big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1)))))) <=> (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1)))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(4,plain,
% 0.13/0.37 (![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (big_f(Y1, Y2) & (big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1)))))) <=> ![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 (^[Y1: $i, Y2: $i] : rewrite((~((big_f(Y1, Y2) & (big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) | big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)))) | (~big_f(X1!1, X2!0)))) <=> (~((~big_f(X1!1, X2!0)) | (big_f(Y1, Y2) & (big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1)))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(6,plain,
% 0.13/0.37 (![Y1: $i, Y2: $i] : (~((big_f(Y1, Y2) & (big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) | big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)))) | (~big_f(X1!1, X2!0)))) <=> ![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (big_f(Y1, Y2) & (big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 ((~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2, Z) <=> big_f(Y1, Z)))) | big_f(Z, Z))) | (~(big_f(X2, Z) | big_f(Y2, Z) | (~big_f(Y1, Y2)))) | (~big_f(X1, X2)))) <=> (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2, Z) <=> big_f(Y1, Z)))) | big_f(Z, Z))) | (~(big_f(X2, Z) | big_f(Y2, Z) | (~big_f(Y1, Y2)))) | (~big_f(X1, X2))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(8,plain,
% 0.13/0.37 ((~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(X1, X2) => ((big_f(Y1, Y2) => (big_f(X2, Z) | big_f(Y2, Z))) => (((big_f(Y1, Y2) => (big_f(X2, Z) <=> big_f(Y1, Z))) => big_f(Z, Z)) => (big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))))))) <=> (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2, Z) <=> big_f(Y1, Z)))) | big_f(Z, Z))) | (~(big_f(X2, Z) | big_f(Y2, Z) | (~big_f(Y1, Y2)))) | (~big_f(X1, X2))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(9,axiom,(~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(X1, X2) => ((big_f(Y1, Y2) => (big_f(X2, Z) | big_f(Y2, Z))) => (((big_f(Y1, Y2) => (big_f(X2, Z) <=> big_f(Y1, Z))) => big_f(Z, Z)) => (big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_18_4')).
% 0.13/0.37 tff(10,plain,
% 0.13/0.37 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2, Z) <=> big_f(Y1, Z)))) | big_f(Z, Z))) | (~(big_f(X2, Z) | big_f(Y2, Z) | (~big_f(Y1, Y2)))) | (~big_f(X1, X2)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.37 tff(11,plain,
% 0.13/0.37 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2, Z) <=> big_f(Y1, Z)))) | big_f(Z, Z))) | (~(big_f(X2, Z) | big_f(Y2, Z) | (~big_f(Y1, Y2)))) | (~big_f(X1, X2)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.13/0.37 tff(12,plain,
% 0.13/0.37 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2, Z) <=> big_f(Y1, Z)))) | big_f(Z, Z))) | (~(big_f(X2, Z) | big_f(Y2, Z) | (~big_f(Y1, Y2)))) | (~big_f(X1, X2)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.13/0.37 tff(13,plain,
% 0.13/0.37 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2, Z) <=> big_f(Y1, Z)))) | big_f(Z, Z))) | (~(big_f(X2, Z) | big_f(Y2, Z) | (~big_f(Y1, Y2)))) | (~big_f(X1, X2)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.13/0.37 tff(14,plain,(
% 0.13/0.37 $oeq((~?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(Y1, Y2) & (big_f(Y1, Z) <=> big_f(Y2, Z))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, Z) <=> big_f(Y1, Z)))) | big_f(Z, Z))) | (~(big_f(X2!0, Z) | big_f(Y2, Z) | (~big_f(Y1, Y2)))) | (~big_f(X1!1, X2!0)))), ![Y1: $i, Y2: $i] : (~((big_f(Y1, Y2) & (big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) | big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)))) | (~big_f(X1!1, X2!0)))))),
% 0.13/0.38 inference(transitivity,[status(sab)],[13])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (big_f(Y1, Y2) & (big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(elem!3, elem!3) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(elem!3, elem!3) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 ((~((~big_f(X1!1, X2!0)) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | (~(big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)) | (~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)))))) <=> (~((~big_f(X1!1, X2!0)) | big_f(elem!3, elem!3) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | (~(big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)) | (~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(elem!3, elem!3) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[19])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | (~(big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)) | (~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(elem!3, elem!3) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[20, 18])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | (~(big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)) | (~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3))))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(elem!3, elem!3) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (~((~big_f(X1!1, X2!0)) | big_f(elem!3, elem!3) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[23, 17])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (((~big_f(X1!1, X2!0)) | big_f(elem!3, elem!3) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | ((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 ((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (((~big_f(X1!1, X2!0)) | big_f(elem!3, elem!3) | (~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | (~big_f(elem!3, elem!3))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (~big_f(elem!3, elem!3)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | big_f(elem!3, elem!3)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 ((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 ((~((~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))) | (~((~big_f(elem!3, elem!3)) | (big_f(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3))))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[31, 30, 26])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (((~big_f(X1!1, X2!0)) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ((~big_f(X1!1, X2!0)) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~((~big_f(X1!1, X2!0)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))) | (~(big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))) <=> (~((~big_f(X1!1, X2!0)) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))) | (~(big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[36])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))) | (~(big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[37, 35])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))) | (~(big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 ((~![Y1: $i, Y2: $i] : (~((~big_f(X1!1, X2!0)) | (~((~((~big_f(Y1, Y2)) | (big_f(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y1, tptp_fun_Z_2(Y2, Y1))))) | big_f(tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))) | (~((~big_f(Y1, Y2)) | (~(big_f(Y1, tptp_fun_Z_2(Y2, Y1)) <=> big_f(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(Y2, tptp_fun_Z_2(Y2, Y1)) | (~big_f(Y1, Y2)) | big_f(X2!0, tptp_fun_Z_2(Y2, Y1))))))) | (~((~big_f(X1!1, X2!0)) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)) | (~((~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | (big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) <=> big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))) | (~((~big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))) | big_f(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[40, 17, 34])).
% 0.13/0.40 % SZS output end Proof
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------