TSTP Solution File: SYN326+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN326+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 : Thu Sep 29 23:54:44 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN326+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 02:37:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(big_f_type, type, (
% 0.13/0.39 big_f: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.39 tptp_fun_Z_0: $i > $i)).
% 0.13/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.39 tptp_fun_Y_1: $i > $i)).
% 0.13/0.39 tff(elem_2_type, type, (
% 0.13/0.39 elem_2: $i)).
% 0.13/0.39 tff(big_g_type, type, (
% 0.13/0.39 big_g: $i > $o)).
% 0.13/0.39 tff(big_h_type, type, (
% 0.13/0.39 big_h: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[X: $i] : refl((~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X))))) <=> (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X))))) <=> ![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ((~?[X: $i] : ![Y: $i, Z: $i] : (((big_f(Y, Z) => (big_g(Y) => big_h(X))) => big_f(X, X)) => (((big_f(Z, X) => big_g(X)) => big_h(Z)) => (big_f(X, Y) => big_f(Z, Z))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,axiom,(~?[X: $i] : ![Y: $i, Z: $i] : (((big_f(Y, Z) => (big_g(Y) => big_h(X))) => big_f(X, X)) => (((big_f(Z, X) => big_g(X)) => big_h(Z)) => (big_f(X, Y) => big_f(Z, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_12_1')).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (^[X: $i] : sk($oeq((~![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))), (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(14,plain,(
% 0.13/0.39 ![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))),
% 0.13/0.39 inference(nnf-neg,[status(sab)],[12, 13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 ((~![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (~(big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ((big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Z_0(elem!2)) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(elem!2))))))) | (~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Z_0(elem!2)) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(elem!2))))))) | (~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[20, 15])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Z_0(elem!2)) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(elem!2))))))) | (~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))))) | ((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((~![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))) | (~(big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)) | (~big_f(elem!2, tptp_fun_Y_1(elem!2))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~(big_g(elem!2) | (~big_f(tptp_fun_Z_0(elem!2), elem!2)))))) | (~((~(big_h(elem!2) | (~big_g(tptp_fun_Y_1(elem!2))) | (~big_f(tptp_fun_Y_1(elem!2), tptp_fun_Z_0(elem!2))))) | big_f(elem!2, elem!2)))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (~(big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)) | (~big_f(elem!2, tptp_fun_Y_1(elem!2))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~(big_g(elem!2) | (~big_f(tptp_fun_Z_0(elem!2), elem!2)))))) | (~((~(big_h(elem!2) | (~big_g(tptp_fun_Y_1(elem!2))) | (~big_f(tptp_fun_Y_1(elem!2), tptp_fun_Z_0(elem!2))))) | big_f(elem!2, elem!2))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[24, 15])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)) | (~big_f(elem!2, tptp_fun_Y_1(elem!2))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~(big_g(elem!2) | (~big_f(tptp_fun_Z_0(elem!2), elem!2)))))) | (~((~(big_h(elem!2) | (~big_g(tptp_fun_Y_1(elem!2))) | (~big_f(tptp_fun_Y_1(elem!2), tptp_fun_Z_0(elem!2))))) | big_f(elem!2, elem!2)))) | (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 23])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 ((big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))) | big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[36, 19])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 17])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ((~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 41, 39])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | ((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 15, 45])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------