%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS178+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 Jun 21 05:13:31 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS178+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:12:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(isa_type, type, (
% 0.19/0.37 isa: ( $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_S1_28_type, type, (
% 0.19/0.37 tptp_fun_S1_28: $i)).
% 0.19/0.37 tff(status_type, type, (
% 0.19/0.37 status: ( $i * $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_C_2_type, type, (
% 0.19/0.37 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_Ax_3_type, type, (
% 0.19/0.37 tptp_fun_Ax_3: ( $i * $i ) > $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 ((~![S1: $i] : isa(S1, S1)) <=> (~![S1: $i] : isa(S1, S1))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(2,axiom,(~![S1: $i] : isa(S1, S1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isa_reflexive')).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (~![S1: $i] : isa(S1, S1)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (~![S1: $i] : isa(S1, S1)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (~![S1: $i] : isa(S1, S1)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (~![S1: $i] : isa(S1, S1)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.37 tff(7,plain,(
% 0.19/0.37 ~isa(S1!28, S1!28)),
% 0.19/0.37 inference(skolemize,[status(sab)],[6])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (^[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)))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (![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))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (^[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)))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (![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))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (^[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)))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (![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))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![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))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[13, 11])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (^[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))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![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))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![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))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (^[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)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![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))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.37 tff(20,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')).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.37 tff(23,plain,(
% 0.19/0.37 ![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))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[22])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![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))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (![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))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (![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))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[25, 9])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (((~![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))))))) | isa(S1!28, S1!28)) <=> ((~![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))))))) | isa(S1!28, S1!28))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 ((~(~isa(S1!28, S1!28))) <=> isa(S1!28, S1!28)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (((~isa(S1!28, S1!28)) | $false) <=> (~isa(S1!28, S1!28))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 ((~$true) <=> $false),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (((~isa(S1!28, S1!28)) | $true) <=> $true),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (![Ax: $i, C: $i] : $true <=> $true),
% 0.19/0.37 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (![Ax: $i, C: $i] : $true <=> ![Ax: $i, C: $i] : $true),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (![Ax: $i, C: $i] : $true <=> $true),
% 0.19/0.37 inference(transitivity,[status(thm)],[33, 32])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (^[Ax: $i, C: $i] : rewrite(((~status(Ax, C, S1!28)) | status(Ax, C, S1!28)) <=> $true)),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28)) <=> ![Ax: $i, C: $i] : $true),
% 0.19/0.37 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28)) <=> $true),
% 0.19/0.37 inference(transitivity,[status(thm)],[36, 34])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28))) <=> ((~isa(S1!28, S1!28)) | $true)),
% 0.19/0.37 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28))) <=> $true),
% 0.19/0.37 inference(transitivity,[status(thm)],[38, 31])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 ((~((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28)))) <=> (~$true)),
% 0.19/0.37 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 ((~((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28)))) <=> $false),
% 0.19/0.38 inference(transitivity,[status(thm)],[40, 30])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 ((~((~((~status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28)) | status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28))) | isa(S1!28, S1!28))) <=> (~isa(S1!28, S1!28))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (((~((~((~status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28)) | status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28))) | isa(S1!28, S1!28))) | (~((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28))))) <=> ((~isa(S1!28, S1!28)) | $false)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[42, 41])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (((~((~((~status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28)) | status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28))) | isa(S1!28, S1!28))) | (~((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28))))) <=> (~isa(S1!28, S1!28))),
% 0.19/0.38 inference(transitivity,[status(thm)],[43, 29])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((~((~((~((~status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28)) | status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28))) | isa(S1!28, S1!28))) | (~((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28)))))) <=> (~(~isa(S1!28, S1!28)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 ((~((~((~((~status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28)) | status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28))) | isa(S1!28, S1!28))) | (~((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28)))))) <=> isa(S1!28, S1!28)),
% 0.19/0.38 inference(transitivity,[status(thm)],[45, 28])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (((~![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(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28)) | status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28))) | isa(S1!28, S1!28))) | (~((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28))))))) <=> ((~![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))))))) | isa(S1!28, S1!28))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (((~![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(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28)) | status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28))) | isa(S1!28, S1!28))) | (~((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28))))))) <=> ((~![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))))))) | isa(S1!28, S1!28))),
% 0.19/0.38 inference(transitivity,[status(thm)],[47, 27])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 ((~![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(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28)) | status(tptp_fun_Ax_3(S1!28, S1!28), tptp_fun_C_2(S1!28, S1!28), S1!28))) | isa(S1!28, S1!28))) | (~((~isa(S1!28, S1!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!28)) | status(Ax, C, S1!28))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 ((~![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: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))) | isa(S1!28, S1!28)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[50, 26, 7])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------