TSTP Solution File: SYN319+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN319+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 23:54:41 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN319+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 02:53:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(big_h_type, type, (
% 0.14/0.40 big_h: $i > $o)).
% 0.14/0.40 tff(tptp_fun_Z2_0_type, type, (
% 0.14/0.40 tptp_fun_Z2_0: ( $i * $i ) > $i)).
% 0.14/0.40 tff(elem_2_type, type, (
% 0.14/0.40 elem_2: $i)).
% 0.14/0.40 tff(big_g_type, type, (
% 0.14/0.40 big_g: $i > $o)).
% 0.14/0.40 tff(big_f_type, type, (
% 0.14/0.40 big_f: $i > $o)).
% 0.14/0.40 tff(tptp_fun_Z1_1_type, type, (
% 0.14/0.40 tptp_fun_Z1_1: ( $i * $i ) > $i)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : refl((~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))))) <=> (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))))) <=> ![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : rewrite((~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(tptp_fun_Z2_0(Y, X)) & (big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X)))))))) <=> (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(tptp_fun_Z2_0(Y, X)) & (big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X)))))))) <=> ![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 ((~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))) <=> (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1)))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 ((~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : (((big_f(Y) => big_g(Z1)) => (big_g(X) & (~big_f(Z1)))) => (((big_f(X) | big_g(X)) => big_h(X)) => (big_h(Z2) & (big_h(Y) => ((big_f(Z2) | big_g(Z2)) => big_h(Z2))))))) <=> (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1)))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(7,axiom,(~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : (((big_f(Y) => big_g(Z1)) => (big_g(X) & (~big_f(Z1)))) => (((big_f(X) | big_g(X)) => big_h(X)) => (big_h(Z2) & (big_h(Y) => ((big_f(Z2) | big_g(Z2)) => big_h(Z2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_2_5')).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : sk($oeq((~![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))), (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(tptp_fun_Z2_0(Y, X)) & (big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X))))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(16,plain,(
% 0.14/0.40 ![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(tptp_fun_Z2_0(Y, X)) & (big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X))))))))),
% 0.14/0.40 inference(nnf-neg,[status(sab)],[14, 15])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[16, 4])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[17, 2])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 ((~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~(big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))) <=> (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~(big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))))))))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~(big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))))))))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[21, 19])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~(big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))))))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))) | ((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 ((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 ((~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~(big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))) <=> (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~(big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~(big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[30, 28])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~(big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(33,plain,
% 0.14/0.42 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.42 tff(34,plain,
% 0.14/0.42 (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[33, 18])).
% 0.14/0.42 tff(35,plain,
% 0.14/0.42 (((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))) | (big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(36,plain,
% 0.14/0.42 (big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.14/0.42 tff(37,assumption,(~big_h(tptp_fun_Z2_0(elem!2, elem!2))), introduced(assumption)).
% 0.14/0.42 tff(38,plain,
% 0.14/0.42 ((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(39,plain,
% 0.14/0.42 ((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.14/0.42 tff(40,plain,
% 0.14/0.42 (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.14/0.42 tff(41,plain,
% 0.14/0.42 ((big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(42,plain,
% 0.14/0.42 (~big_f(tptp_fun_Z2_0(elem!2, elem!2))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.14/0.42 tff(43,plain,
% 0.14/0.42 ((big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2)))) | big_f(tptp_fun_Z2_0(elem!2, elem!2))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(44,plain,
% 0.14/0.42 (big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.14/0.42 tff(45,plain,
% 0.14/0.42 ((big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(46,plain,
% 0.14/0.42 (~big_g(tptp_fun_Z2_0(elem!2, elem!2))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[45, 40])).
% 0.14/0.42 tff(47,plain,
% 0.14/0.42 ((big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | big_g(tptp_fun_Z2_0(elem!2, elem!2))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(48,plain,
% 0.14/0.42 (big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.14/0.42 tff(49,plain,
% 0.14/0.42 ((~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(50,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[49, 48, 44, 27])).
% 0.14/0.42 tff(51,plain,(big_h(tptp_fun_Z2_0(elem!2, elem!2))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(52,plain,
% 0.14/0.42 (((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(53,plain,
% 0.14/0.42 ((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.14/0.42 tff(54,plain,
% 0.14/0.42 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 ((~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))))) <=> (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[56, 54])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~(big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[59, 18])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))))))) | ((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 ((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 ((~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 ((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[64, 53, 51])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------