TSTP Solution File: ITP019+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP019+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 04:15:20 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP019+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.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 : Thu Sep 1 03:14:47 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.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(s_type, type, (
% 0.19/0.40 s: ( $i * $i ) > $i)).
% 0.19/0.40 tff(c_2Ecomplex_2Ecomplex__of__num_2E1_type, type, (
% 0.19/0.40 c_2Ecomplex_2Ecomplex__of__num_2E1: $i > $i)).
% 0.19/0.40 tff(c_2Enum_2E0_2E0_type, type, (
% 0.19/0.40 c_2Enum_2E0_2E0: $i)).
% 0.19/0.40 tff(tyop_2Enum_2Enum_type, type, (
% 0.19/0.40 tyop_2Enum_2Enum: $i)).
% 0.19/0.40 tff(tyop_2Epair_2Eprod_type, type, (
% 0.19/0.40 tyop_2Epair_2Eprod: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tyop_2Erealax_2Ereal_type, type, (
% 0.19/0.40 tyop_2Erealax_2Ereal: $i)).
% 0.19/0.40 tff(tptp_fun_V0z_2E0_3_type, type, (
% 0.19/0.40 tptp_fun_V0z_2E0_3: $i)).
% 0.19/0.40 tff(c_2Ecomplex_2Ecomplex__inv_2E1_type, type, (
% 0.19/0.40 c_2Ecomplex_2Ecomplex__inv_2E1: $i > $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 ((~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))) <=> (~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))) <=> (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 ((~![V0z_2E0: $i] : ((~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) => (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))) <=> (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,axiom,(~![V0z_2E0: $i] : ((~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) => (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ecomplex_2ECOMPLEX__INV__NZ')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.19/0.41 tff(13,plain,(
% 0.19/0.41 ~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[12])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[14])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))),
% 0.19/0.41 inference(or_elim,[status(thm)],[14])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) | (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[17, 16, 15])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (^[V0z_2E0: $i] : refl(((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) <=> ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) <=> ![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) <=> ![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,axiom,(![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ecomplex_2ECOMPLEX__INV__EQ__0')).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,(
% 0.19/0.41 ![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[23])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))) | ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[26, 25, 18])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------