TSTP Solution File: SYN370+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN370+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Thu Sep 29 23:55:01 EDT 2022
% Result : Theorem 0.12s 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 : SYN370+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 02:41:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(big_p_type, type, (
% 0.12/0.39 big_p: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(f_type, type, (
% 0.12/0.39 f: $i > $i)).
% 0.12/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.39 tptp_fun_Y_0: $i > $i)).
% 0.12/0.39 tff(a_type, type, (
% 0.12/0.39 a: $i)).
% 0.12/0.39 tff(h_type, type, (
% 0.12/0.39 h: $i > $i)).
% 0.12/0.39 tff(elem_1_type, type, (
% 0.12/0.39 elem_1: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (![V: $i] : ![Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))) <=> ![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))),
% 0.12/0.39 inference(pull_quant,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))) <=> (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 ((~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((big_p(a, Y, h(Y)) | big_p(V, Y, f(Y))) => big_p(V, Y, Z))) <=> (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(4,axiom,(~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((big_p(a, Y, h(Y)) | big_p(V, Y, f(Y))) => big_p(V, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2121')).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (~?[V: $i] : ![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (^[V: $i] : trans(sk($oeq((~![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))), (~?[Z: $i] : ((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))))), nnf_neg(proof_bind(^[Z: $i] : refl($oeq((~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))), (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))))), $oeq((~?[Z: $i] : ((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))), ![Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z))))), $oeq((~![Y: $i] : ?[Z: $i] : ((~(big_p(a, Y, h(Y)) | big_p(V, Y, f(Y)))) | big_p(V, Y, Z))), ![Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(13,plain,(
% 0.12/0.40 ![V: $i] : ![Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))),
% 0.12/0.40 inference(nnf-neg,[status(sab)],[11, 12])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))))) <=> ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 ((~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) <=> (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))))) <=> ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))))) <=> ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[20, 14])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))) | (~big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (~big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1)))) <=> ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 ((~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1))) <=> (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1)))) <=> ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1)))) <=> ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[29, 14])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), elem!1)) | (big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 ((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[34, 23])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))) | (~big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 ((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))))) <=> ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) <=> (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))))) <=> ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))))) <=> ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[40, 38])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![V: $i, Z: $i] : (~((~(big_p(a, tptp_fun_Y_0(V), h(tptp_fun_Y_0(V))) | big_p(V, tptp_fun_Y_0(V), f(tptp_fun_Y_0(V))))) | big_p(V, tptp_fun_Y_0(V), Z)))) | (~((~(big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a))) | big_p(a, tptp_fun_Y_0(a), h(tptp_fun_Y_0(a))))) | big_p(a, tptp_fun_Y_0(a), f(tptp_fun_Y_0(a)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 14, 37])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------