%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN350+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:38:51 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN350+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 12:32:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(big_f_type, type, (
% 0.19/0.44 big_f: ( $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_Z_1_type, type, (
% 0.19/0.44 tptp_fun_Z_1: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_X_0_type, type, (
% 0.19/0.44 tptp_fun_X_0: $i)).
% 0.19/0.44 tff(elem_2_type, type, (
% 0.19/0.44 elem_2: $i)).
% 0.19/0.44 tff(1,assumption,(~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))), introduced(assumption)).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) | big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 ((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (^[Y1: $i, Y2: $i] : refl((~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) <=> (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![Y1: $i, Y2: $i] : (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) <=> ![Y1: $i, Y2: $i] : (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (^[Y1: $i, Y2: $i] : rewrite((~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> (big_f(Y2, tptp_fun_Z_1(Y2, Y1)) & ((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))))) <=> (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (![Y1: $i, Y2: $i] : (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> (big_f(Y2, tptp_fun_Z_1(Y2, Y1)) & ((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))))) <=> ![Y1: $i, Y2: $i] : (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 ((~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((~(big_f(X, Z) <=> big_f(Z, X))) | (big_f(X, Z) <=> (big_f(Y2, Z) & ((~big_f(Y1, Z)) | big_f(Y1, Y2)))))) <=> (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((~(big_f(X, Z) <=> big_f(Z, X))) | (big_f(X, Z) <=> (big_f(Y2, Z) & ((~big_f(Y1, Z)) | big_f(Y1, Y2))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 ((~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X, Z) <=> big_f(Z, X)) => (big_f(X, Z) <=> (big_f(Y2, Z) & (big_f(Y1, Z) => big_f(Y1, Y2)))))) <=> (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((~(big_f(X, Z) <=> big_f(Z, X))) | (big_f(X, Z) <=> (big_f(Y2, Z) & ((~big_f(Y1, Z)) | big_f(Y1, Y2))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(10,axiom,(~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X, Z) <=> big_f(Z, X)) => (big_f(X, Z) <=> (big_f(Y2, Z) & (big_f(Y1, Z) => big_f(Y1, Y2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_18_2')).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((~(big_f(X, Z) <=> big_f(Z, X))) | (big_f(X, Z) <=> (big_f(Y2, Z) & ((~big_f(Y1, Z)) | big_f(Y1, Y2)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((~(big_f(X, Z) <=> big_f(Z, X))) | (big_f(X, Z) <=> (big_f(Y2, Z) & ((~big_f(Y1, Z)) | big_f(Y1, Y2)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((~(big_f(X, Z) <=> big_f(Z, X))) | (big_f(X, Z) <=> (big_f(Y2, Z) & ((~big_f(Y1, Z)) | big_f(Y1, Y2)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((~(big_f(X, Z) <=> big_f(Z, X))) | (big_f(X, Z) <=> (big_f(Y2, Z) & ((~big_f(Y1, Z)) | big_f(Y1, Y2)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.19/0.45 tff(15,plain,(
% 0.19/0.45 $oeq((~?[Y1: $i, Y2: $i] : ![Z: $i] : ((~(big_f(X!0, Z) <=> big_f(Z, X!0))) | (big_f(X!0, Z) <=> (big_f(Y2, Z) & ((~big_f(Y1, Z)) | big_f(Y1, Y2)))))), ![Y1: $i, Y2: $i] : (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> (big_f(Y2, tptp_fun_Z_1(Y2, Y1)) & ((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))))))),
% 0.19/0.45 inference(transitivity,[status(sab)],[14])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (![Y1: $i, Y2: $i] : (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (![Y1: $i, Y2: $i] : (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[16, 5])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 ((~![Y1: $i, Y2: $i] : (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1))))))) | (~((~(big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))), X!0))) | (~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (~((~(big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))), X!0))) | (~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (((~(big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))), X!0))) | (~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))))) | (((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 ((~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))))) | (~((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))))) | big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 ((~((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))))) | big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[23, 3, 1])).
% 0.19/0.45 tff(25,plain,(big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 ((~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))))) | ((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[26, 21])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 ((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[27, 25])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 ((~((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[29, 28, 25])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 ((~![Y1: $i, Y2: $i] : (~((~(big_f(X!0, tptp_fun_Z_1(Y2, Y1)) <=> big_f(tptp_fun_Z_1(Y2, Y1), X!0))) | (~(((~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | big_f(Y1, Y2)))) <=> big_f(X!0, tptp_fun_Z_1(Y2, Y1))))))) | (~((~(big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))) | (~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (~((~(big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))) | (~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[33, 17])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (((~(big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))) | (~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))))) | (big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 ((~(big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 ((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0)))) | big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 ((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (((~(big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))) <=> big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)), X!0))) | (~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))))) | (((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 (((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[42, 34])).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 ((~(((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0)))) <=> big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0))))) | (~((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0))))) | big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 ((~((~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | (~((~big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0), X!0))))) | big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, elem!2), X!0))), X!0), X!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[45, 41, 39])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------