TSTP Solution File: KRS179+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS179+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 17:45:06 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS179+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n010.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 09:33:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(status_type, type, (
% 0.20/0.39 status: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_S2_29_type, type, (
% 0.20/0.39 tptp_fun_S2_29: $i)).
% 0.20/0.39 tff(tptp_fun_C_2_type, type, (
% 0.20/0.39 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_S1_30_type, type, (
% 0.20/0.39 tptp_fun_S1_30: $i)).
% 0.20/0.39 tff(tptp_fun_S3_28_type, type, (
% 0.20/0.39 tptp_fun_S3_28: $i)).
% 0.20/0.39 tff(tptp_fun_Ax_3_type, type, (
% 0.20/0.39 tptp_fun_Ax_3: ( $i * $i ) > $i)).
% 0.20/0.39 tff(isa_type, type, (
% 0.20/0.39 isa: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (^[S1: $i, S2: $i] : refl((~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))), ((((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))) <=> (((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))), rewrite((((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))), ((((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (^[S1: $i, S2: $i] : rewrite((![Ax: $i, C: $i] : (status(Ax, C, S1) => status(Ax, C, S2)) <=> isa(S1, S2)) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => status(Ax, C, S2)) <=> isa(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.40 tff(13,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => status(Ax, C, S2)) <=> isa(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','isa')).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.40 tff(16,plain,(
% 0.20/0.40 ![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))) | (~((~((~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))) | isa(S1!30, S3!28))) | (~((~isa(S1!30, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S3!28))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (~((~((~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))) | isa(S1!30, S3!28))) | (~((~isa(S1!30, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S3!28)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~((~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))) | isa(S1!30, S3!28))) | (~((~isa(S1!30, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S3!28))))) | ((~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))) | isa(S1!30, S3!28))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))) | isa(S1!30, S3!28)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3))) <=> (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((~![S1: $i, S2: $i, S3: $i] : ((isa(S1, S2) & isa(S2, S3)) => isa(S1, S3))) <=> (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,axiom,(~![S1: $i, S2: $i, S3: $i] : ((isa(S1, S2) & isa(S2, S3)) => isa(S1, S3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isa_transitive')).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & isa(S2, S3))) | isa(S1, S3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.20/0.40 tff(34,plain,(
% 0.20/0.40 ~((~(isa(S1!30, S2!29) & isa(S2!29, S3!28))) | isa(S1!30, S3!28))),
% 0.20/0.40 inference(skolemize,[status(sab)],[33])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (~isa(S1!30, S3!28)),
% 0.20/0.40 inference(or_elim,[status(thm)],[34])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ((~((~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))) | isa(S1!30, S3!28))) | (~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))) | isa(S1!30, S3!28)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((~((~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))) | isa(S1!30, S3!28))) | (~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (~((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[37, 23])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))) | (~((~((~((~status(tptp_fun_Ax_3(S2!29, S1!30), tptp_fun_C_2(S2!29, S1!30), S1!30)) | status(tptp_fun_Ax_3(S2!29, S1!30), tptp_fun_C_2(S2!29, S1!30), S2!29))) | isa(S1!30, S2!29))) | (~((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (~((~((~((~status(tptp_fun_Ax_3(S2!29, S1!30), tptp_fun_C_2(S2!29, S1!30), S1!30)) | status(tptp_fun_Ax_3(S2!29, S1!30), tptp_fun_C_2(S2!29, S1!30), S2!29))) | isa(S1!30, S2!29))) | (~((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[41, 19])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (((~((~((~status(tptp_fun_Ax_3(S2!29, S1!30), tptp_fun_C_2(S2!29, S1!30), S1!30)) | status(tptp_fun_Ax_3(S2!29, S1!30), tptp_fun_C_2(S2!29, S1!30), S2!29))) | isa(S1!30, S2!29))) | (~((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))))) | ((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 ((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (isa(S1!30, S2!29) & isa(S2!29, S3!28)),
% 0.20/0.40 inference(or_elim,[status(thm)],[34])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (isa(S1!30, S2!29)),
% 0.20/0.40 inference(and_elim,[status(thm)],[45])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((~((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))) | (~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ((~((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[48, 44])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))) | ((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S2!29))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))) | (~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S2!29))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))) | ((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S2!29))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))) | (~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S2!29)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S2!29)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[52, 49, 40])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28)) | (~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[54, 38])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S1)) | status(tptp_fun_Ax_3(S2, S1), tptp_fun_C_2(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))) | (~((~((~((~status(tptp_fun_Ax_3(S3!28, S2!29), tptp_fun_C_2(S3!28, S2!29), S2!29)) | status(tptp_fun_Ax_3(S3!28, S2!29), tptp_fun_C_2(S3!28, S2!29), S3!28))) | isa(S2!29, S3!28))) | (~((~isa(S2!29, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (~((~((~((~status(tptp_fun_Ax_3(S3!28, S2!29), tptp_fun_C_2(S3!28, S2!29), S2!29)) | status(tptp_fun_Ax_3(S3!28, S2!29), tptp_fun_C_2(S3!28, S2!29), S3!28))) | isa(S2!29, S3!28))) | (~((~isa(S2!29, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[56, 19])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~((~((~status(tptp_fun_Ax_3(S3!28, S2!29), tptp_fun_C_2(S3!28, S2!29), S2!29)) | status(tptp_fun_Ax_3(S3!28, S2!29), tptp_fun_C_2(S3!28, S2!29), S3!28))) | isa(S2!29, S3!28))) | (~((~isa(S2!29, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))))) | ((~isa(S2!29, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~isa(S2!29, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (isa(S2!29, S3!28)),
% 0.20/0.41 inference(and_elim,[status(thm)],[45])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 ((~((~isa(S2!29, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28)))) | (~isa(S2!29, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((~((~isa(S2!29, S3!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (((~![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))) | ((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S2!29)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))) | (~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S2!29)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))) | ((~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S2!29)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))) | (~status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S2!29)) | status(tptp_fun_Ax_3(S3!28, S1!30), tptp_fun_C_2(S3!28, S1!30), S3!28)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[66, 63, 55, 53])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------