%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS181+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 05:13:32 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KRS181+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:12:27 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(status_type, type, (
% 0.12/0.37 status: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_S2_29_type, type, (
% 0.12/0.37 tptp_fun_S2_29: $i)).
% 0.12/0.37 tff(tptp_fun_C_4_type, type, (
% 0.12/0.37 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_S1_30_type, type, (
% 0.12/0.37 tptp_fun_S1_30: $i)).
% 0.12/0.37 tff(tptp_fun_S3_28_type, type, (
% 0.12/0.37 tptp_fun_S3_28: $i)).
% 0.12/0.37 tff(tptp_fun_Ax_5_type, type, (
% 0.12/0.37 tptp_fun_Ax_5: ( $i * $i ) > $i)).
% 0.12/0.37 tff(nota_type, type, (
% 0.12/0.37 nota: ( $i * $i ) > $o)).
% 0.12/0.37 tff(isa_type, type, (
% 0.12/0.37 isa: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_C_2_type, type, (
% 0.12/0.37 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_Ax_3_type, type, (
% 0.12/0.37 tptp_fun_Ax_3: ( $i * $i ) > $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[S1: $i, S2: $i] : refl((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[S1: $i, S2: $i] : rewrite((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) <=> (nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))), trans(monotonicity(rewrite((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) <=> (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))), (((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))), (((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))))), rewrite(((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2)))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(11,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','nota')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,(
% 0.12/0.38 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1) & (~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2))) | (~nota(S1, S2))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))) | (~((~(nota(S1!30, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S3!28)))) | (~((~nota(S1!30, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~((~(nota(S1!30, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S3!28)))) | (~((~nota(S1!30, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (((~(nota(S1!30, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S3!28)))) | (~((~nota(S1!30, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28)))))) | ((~nota(S1!30, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~nota(S1!30, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & nota(S1, S3))) | nota(S2, S3))) <=> (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & nota(S1, S3))) | nota(S2, S3)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![S1: $i, S2: $i, S3: $i] : ((isa(S1, S2) & nota(S1, S3)) => nota(S2, S3))) <=> (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & nota(S1, S3))) | nota(S2, S3)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,axiom,(~![S1: $i, S2: $i, S3: $i] : ((isa(S1, S2) & nota(S1, S3)) => nota(S2, S3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nota_isa_nota')).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & nota(S1, S3))) | nota(S2, S3))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & nota(S1, S3))) | nota(S2, S3))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & nota(S1, S3))) | nota(S2, S3))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~![S1: $i, S2: $i, S3: $i] : ((~(isa(S1, S2) & nota(S1, S3))) | nota(S2, S3))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.12/0.38 tff(28,plain,(
% 0.12/0.38 ~((~(isa(S1!30, S2!29) & nota(S1!30, S3!28))) | nota(S2!29, S3!28))),
% 0.12/0.38 inference(skolemize,[status(sab)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (isa(S1!30, S2!29) & nota(S1!30, S3!28)),
% 0.12/0.38 inference(or_elim,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (nota(S1!30, S3!28)),
% 0.12/0.38 inference(and_elim,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~((~nota(S1!30, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28))))) | (~nota(S1!30, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~((~nota(S1!30, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28))))) | (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (~((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 20])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (^[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)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![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))) | (~(![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (^[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)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![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))) | (~(![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (^[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)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![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))) | (~(![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (![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))) | (~(![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))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[41, 39])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (![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)) & (![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (![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))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (^[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)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![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))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.38 tff(48,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => status(Ax, C, S2)) <=> isa(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','isa')).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.12/0.38 tff(51,plain,(
% 0.12/0.38 ![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)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![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))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (![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))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[53, 37])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (((~![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!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))) | (~((~((~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)))))) <=> ((~![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!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))) | (~((~((~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))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 ((~((~((~((~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)))) | (~((~((~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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (((~![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))) | (~((~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))))))) <=> ((~![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!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))) | (~((~((~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))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (((~![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))) | (~((~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))))))) <=> ((~![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!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))) | (~((~((~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))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[57, 55])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 ((~![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))) | (~((~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))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 ((~![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))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))) | (~((~((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))) | (~((~((~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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (~((~((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))) | (~((~((~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))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[60, 54])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (((~((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29)))) | (~((~((~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)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~isa(S1!30, S2!29)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (isa(S1!30, S2!29)),
% 0.12/0.39 inference(and_elim,[status(thm)],[29])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~((~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))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~((~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))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))) | ((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S2!29))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))) | (~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S2!29))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))) | ((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S2!29))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!30)) | status(Ax, C, S2!29))) | (~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S2!29)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S2!29)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[70, 67, 35])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ((~![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S1)) | status(tptp_fun_Ax_5(S2, S1), tptp_fun_C_4(S2, S1), S2)))))))) | (~((~(nota(S2!29, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28)))) | (~((~nota(S2!29, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S2!29), tptp_fun_C_4(S3!28, S2!29), S2!29)) | status(tptp_fun_Ax_5(S3!28, S2!29), tptp_fun_C_4(S3!28, S2!29), S3!28)))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (~((~(nota(S2!29, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28)))) | (~((~nota(S2!29, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S2!29), tptp_fun_C_4(S3!28, S2!29), S2!29)) | status(tptp_fun_Ax_5(S3!28, S2!29), tptp_fun_C_4(S3!28, S2!29), S3!28))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[72, 16])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (((~(nota(S2!29, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28)))) | (~((~nota(S2!29, S3!28)) | (~((~status(tptp_fun_Ax_5(S3!28, S2!29), tptp_fun_C_4(S3!28, S2!29), S2!29)) | status(tptp_fun_Ax_5(S3!28, S2!29), tptp_fun_C_4(S3!28, S2!29), S3!28)))))) | (nota(S2!29, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (nota(S2!29, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (~nota(S2!29, S3!28)),
% 0.12/0.40 inference(or_elim,[status(thm)],[28])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 ((~(nota(S2!29, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28)))) | nota(S2!29, S3!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 ((~(nota(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))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S1!30)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28)) | (~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[80, 33])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (((~![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))) | ((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S2!29)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))) | (~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S2!29)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))) | ((~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S2!29)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S2!29)) | status(Ax, C, S3!28))) | (~status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S2!29)) | status(tptp_fun_Ax_5(S3!28, S1!30), tptp_fun_C_4(S3!28, S1!30), S3!28)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[84, 81, 79, 71])).
% 0.12/0.40 % SZS output end Proof
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------