%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS180+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS180+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 19:12:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(status_type, type, (
% 0.19/0.39 status: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_S2_28_type, type, (
% 0.19/0.39 tptp_fun_S2_28: $i)).
% 0.19/0.39 tff(tptp_fun_C_4_type, type, (
% 0.19/0.39 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_S1_29_type, type, (
% 0.19/0.39 tptp_fun_S1_29: $i)).
% 0.19/0.39 tff(tptp_fun_Ax_5_type, type, (
% 0.19/0.39 tptp_fun_Ax_5: ( $i * $i ) > $i)).
% 0.19/0.39 tff(nota_type, type, (
% 0.19/0.39 nota: ( $i * $i ) > $o)).
% 0.19/0.39 tff(xora_type, type, (
% 0.19/0.39 xora: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_C_8_type, type, (
% 0.19/0.39 tptp_fun_C_8: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Ax_9_type, type, (
% 0.19/0.39 tptp_fun_Ax_9: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_I1_12_type, type, (
% 0.19/0.39 tptp_fun_I1_12: $i)).
% 0.19/0.39 tff(isa_type, type, (
% 0.19/0.39 isa: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_C_2_type, type, (
% 0.19/0.39 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Ax_3_type, type, (
% 0.19/0.39 tptp_fun_Ax_3: ( $i * $i ) > $i)).
% 0.19/0.39 tff(nevera_type, type, (
% 0.19/0.39 nevera: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_C_6_type, type, (
% 0.19/0.39 tptp_fun_C_6: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Ax_7_type, type, (
% 0.19/0.39 tptp_fun_Ax_7: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![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))))))) <=> ![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![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))))))) <=> ![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![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))))))) <=> ![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)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 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/sandbox2/benchmark/Axioms/KRS001+1.ax','nota')).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.39 tff(13,plain,(
% 0.19/0.39 ![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))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 ((~![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(S1!29, S2!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~nota(S1!29, S2!28)) | (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~((~(nota(S1!29, S2!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~nota(S1!29, S2!28)) | (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (((~(nota(S1!29, S2!28) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~nota(S1!29, S2!28)) | (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28)))))) | ((~nota(S1!29, S2!28)) | (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~nota(S1!29, S2!28)) | (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.39 tff(21,assumption,((~(xora(S1!29, S2!28) | (status(tptp_fun_Ax_9(S2!28, S1!29), tptp_fun_C_8(S2!28, S1!29), S1!29) <=> status(tptp_fun_Ax_9(S2!28, S1!29), tptp_fun_C_8(S2!28, S1!29), S2!28)))) | (~((~xora(S1!29, S2!28)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28)))))), introduced(assumption)).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (^[S1: $i, S2: $i] : rewrite((~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~((~xora(S1, S2)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~((~xora(S1, S2)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[S1: $i, S2: $i] : refl((~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[S1: $i, S2: $i] : rewrite((~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))) <=> (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))), (((xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2))) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))) <=> ((xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2))) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))), rewrite(((xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2))) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))))), (((xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2))) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : ((xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2))) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (^[S1: $i, S2: $i] : rewrite((((status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)) | xora(S1, S2)) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))) <=> ((xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2))) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (((status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)) | xora(S1, S2)) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2)))) <=> ![S1: $i, S2: $i] : ((xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2))) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) <=> xora(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) <=> xora(S1, S2))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(34,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) <=> xora(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','xora')).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) <=> xora(S1, S2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.40 tff(36,plain,(
% 0.19/0.40 ![S1: $i, S2: $i] : (((status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)) | xora(S1, S2)) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[35])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : ((xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2))) & (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) | (~xora(S1, S2))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~((~xora(S1, S2)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 23])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S1) <=> status(tptp_fun_Ax_9(S2, S1), tptp_fun_C_8(S2, S1), S2)))) | (~((~xora(S1, S2)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2)))))))) | (~((~(xora(S1!29, S2!28) | (status(tptp_fun_Ax_9(S2!28, S1!29), tptp_fun_C_8(S2!28, S1!29), S1!29) <=> status(tptp_fun_Ax_9(S2!28, S1!29), tptp_fun_C_8(S2!28, S1!29), S2!28)))) | (~((~xora(S1!29, S2!28)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 40, 21])).
% 0.19/0.40 tff(43,plain,(~((~(xora(S1!29, S2!28) | (status(tptp_fun_Ax_9(S2!28, S1!29), tptp_fun_C_8(S2!28, S1!29), S1!29) <=> status(tptp_fun_Ax_9(S2!28, S1!29), tptp_fun_C_8(S2!28, S1!29), S2!28)))) | (~((~xora(S1!29, S2!28)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (((~(xora(S1!29, S2!28) | (status(tptp_fun_Ax_9(S2!28, S1!29), tptp_fun_C_8(S2!28, S1!29), S1!29) <=> status(tptp_fun_Ax_9(S2!28, S1!29), tptp_fun_C_8(S2!28, S1!29), S2!28)))) | (~((~xora(S1!29, S2!28)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28)))))) | ((~xora(S1!29, S2!28)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 ((~xora(S1!29, S2!28)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![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))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (^[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)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.40 tff(58,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')).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.40 tff(61,plain,(
% 0.19/0.40 ![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))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[60])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 47])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (((~![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))))))) | (~((~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~((~status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!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!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~((~status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 ((~((~((~((~status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28))) | (~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))))) <=> (~((~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~((~status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~![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(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28))) | (~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!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!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~((~status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (((~![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(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28))) | (~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!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!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~((~status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((~![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(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28))) | (~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 ((~![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))))))) | (~((~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~((~status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (~((~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~((~status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[70, 64])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (((~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~((~((~status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_3(S2!28, S1!29), tptp_fun_C_2(S2!28, S1!29), S2!28))) | isa(S1!29, S2!28)))) | ((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (^[Ax: $i, C: $i] : refl((~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))))) <=> (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))))) <=> ![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (^[Ax: $i, C: $i] : rewrite((~((~status(Ax, C, S1!29)) | (~(isa(S1!29, S2!28) & (xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) <=> (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~(isa(S1!29, S2!28) & (xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) <=> ![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~![S1: $i, S2: $i] : ?[Ax: $i, C: $i] : ((~status(Ax, C, S1)) | (~(isa(S1, S2) & (xora(S1, S2) | nevera(S1, S2) | nota(S1, S2)))))) <=> (~![S1: $i, S2: $i] : ?[Ax: $i, C: $i] : ((~status(Ax, C, S1)) | (~(isa(S1, S2) & (xora(S1, S2) | nevera(S1, S2) | nota(S1, S2))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 ((~![S1: $i, S2: $i] : ?[Ax: $i, C: $i] : (status(Ax, C, S1) => (~(isa(S1, S2) & ((nota(S1, S2) | nevera(S1, S2)) | xora(S1, S2)))))) <=> (~![S1: $i, S2: $i] : ?[Ax: $i, C: $i] : ((~status(Ax, C, S1)) | (~(isa(S1, S2) & (xora(S1, S2) | nevera(S1, S2) | nota(S1, S2))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(80,axiom,(~![S1: $i, S2: $i] : ?[Ax: $i, C: $i] : (status(Ax, C, S1) => (~(isa(S1, S2) & ((nota(S1, S2) | nevera(S1, S2)) | xora(S1, S2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isa_exclusive')).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (~![S1: $i, S2: $i] : ?[Ax: $i, C: $i] : ((~status(Ax, C, S1)) | (~(isa(S1, S2) & (xora(S1, S2) | nevera(S1, S2) | nota(S1, S2)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (~![S1: $i, S2: $i] : ?[Ax: $i, C: $i] : ((~status(Ax, C, S1)) | (~(isa(S1, S2) & (xora(S1, S2) | nevera(S1, S2) | nota(S1, S2)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (~![S1: $i, S2: $i] : ?[Ax: $i, C: $i] : ((~status(Ax, C, S1)) | (~(isa(S1, S2) & (xora(S1, S2) | nevera(S1, S2) | nota(S1, S2)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (~![S1: $i, S2: $i] : ?[Ax: $i, C: $i] : ((~status(Ax, C, S1)) | (~(isa(S1, S2) & (xora(S1, S2) | nevera(S1, S2) | nota(S1, S2)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 78])).
% 0.19/0.41 tff(85,plain,(
% 0.19/0.41 $oeq((~?[Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~(isa(S1!29, S2!28) & (xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))), ![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~(isa(S1!29, S2!28) & (xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))))),
% 0.19/0.41 inference(transitivity,[status(sab)],[84])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[85, 77])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[86, 75])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) | (~((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29))))) <=> ((~![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) | (~((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~((~status(I1!12, I1!12, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))))) <=> (~((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (((~![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) | (~((~status(I1!12, I1!12, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) <=> ((~![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) | (~((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (((~![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) | (~((~status(I1!12, I1!12, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) <=> ((~![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) | (~((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ((~![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) | (~((~status(I1!12, I1!12, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.42 ((~![Ax: $i, C: $i] : (~((~status(Ax, C, S1!29)) | (~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)))))) | (~((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (~((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 87])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29))) | isa(S1!29, S2!28)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (isa(S1!29, S2!28)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 ((~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | (~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ((~((~isa(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[98, 73])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29))) | status(I1!12, I1!12, S1!29)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (status(I1!12, I1!12, S1!29)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[100, 94])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))) | ((~status(I1!12, I1!12, S1!29)) | status(I1!12, I1!12, S2!28))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))) | (~status(I1!12, I1!12, S1!29)) | status(I1!12, I1!12, S2!28))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))) | ((~status(I1!12, I1!12, S1!29)) | status(I1!12, I1!12, S2!28))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))) | (~status(I1!12, I1!12, S1!29)) | status(I1!12, I1!12, S2!28)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (status(I1!12, I1!12, S2!28)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[104, 101, 99])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 ((status(I1!12, I1!12, S1!29) <=> status(I1!12, I1!12, S2!28)) | (~status(I1!12, I1!12, S1!29)) | (~status(I1!12, I1!12, S2!28))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (status(I1!12, I1!12, S1!29) <=> status(I1!12, I1!12, S2!28)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[106, 101, 105])).
% 0.19/0.42 tff(108,assumption,(![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28)))), introduced(assumption)).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((~![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28)))) | (~(status(I1!12, I1!12, S1!29) <=> status(I1!12, I1!12, S2!28)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[109, 108, 107])).
% 0.19/0.42 tff(111,plain,(~![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 ((~((~xora(S1!29, S2!28)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28))))) | (~xora(S1!29, S2!28)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 ((~((~xora(S1!29, S2!28)) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1!29) <=> status(Ax, C, S2!28))))) | (~xora(S1!29, S2!28))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (~xora(S1!29, S2!28)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[113, 45])).
% 0.19/0.42 tff(115,assumption,((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)))) | nevera(S1!29, S2!28)))), introduced(assumption)).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (^[S1: $i, S2: $i] : refl((~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[120])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[121, 119])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))), ((((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))), rewrite((((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))), ((((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (^[S1: $i, S2: $i] : rewrite((![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.42 tff(128,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','nevera')).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.19/0.42 tff(131,plain,(
% 0.19/0.42 ![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[130])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[132, 122])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[133, 117])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)))) | nevera(S1!29, S2!28)))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)))) | nevera(S1!29, S2!28))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((~((~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)))) | nevera(S1!29, S2!28))) | (~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!28)) | (~status(Ax, C, S1!29))))))) <=> (~((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)))) | nevera(S1!29, S2!28)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)))) | nevera(S1!29, S2!28))) | (~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!28)) | (~status(Ax, C, S1!29)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)))) | nevera(S1!29, S2!28))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)))) | nevera(S1!29, S2!28))) | (~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!28)) | (~status(Ax, C, S1!29)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)))) | nevera(S1!29, S2!28))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[137, 135])).
% 0.19/0.43 tff(139,plain,
% 0.19/0.43 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)))) | nevera(S1!29, S2!28))) | (~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2!28)) | (~status(Ax, C, S1!29)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S2)) | (~status(tptp_fun_Ax_7(S2, S1), tptp_fun_C_6(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)))) | nevera(S1!29, S2!28)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[140, 134, 115])).
% 0.19/0.43 tff(142,plain,(~((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)))) | nevera(S1!29, S2!28))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 (((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~((~((~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S1!29)) | (~status(tptp_fun_Ax_7(S2!28, S1!29), tptp_fun_C_6(S2!28, S1!29), S2!28)))) | nevera(S1!29, S2!28)))) | ((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 ((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.19/0.43 tff(145,assumption,(![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28)))), introduced(assumption)).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28)))) | ((~status(I1!12, I1!12, S1!29)) | (~status(I1!12, I1!12, S2!28)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28)))) | (~status(I1!12, I1!12, S1!29)) | (~status(I1!12, I1!12, S2!28)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28)))) | ((~status(I1!12, I1!12, S1!29)) | (~status(I1!12, I1!12, S2!28)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28)))) | (~status(I1!12, I1!12, S1!29)) | (~status(I1!12, I1!12, S2!28))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[148, 101, 105, 145])).
% 0.19/0.43 tff(150,plain,(~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 ((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 ((~((~nevera(S1!29, S2!28)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | (~status(Ax, C, S2!28))))) | (~nevera(S1!29, S2!28))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 (~nevera(S1!29, S2!28)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[152, 144])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (((~isa(S1!29, S2!28)) | (~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | (~status(I1!12, I1!12, S1!29))) | (xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[154, 94])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 ((~(xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28))) | xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (xora(S1!29, S2!28) | nevera(S1!29, S2!28) | nota(S1!29, S2!28)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (xora(S1!29, S2!28) | nota(S1!29, S2!28)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[157, 153])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (nota(S1!29, S2!28)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[158, 114])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 ((~((~nota(S1!29, S2!28)) | (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28))))) | (~nota(S1!29, S2!28)) | (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 ((~((~nota(S1!29, S2!28)) | (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28))))) | (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 (~((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[161, 20])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 (((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28)) | (~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 (~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 (((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 (status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[165, 162])).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 (((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))) | ((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))) | (~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))) | ((~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 ((~![Ax: $i, C: $i] : ((~status(Ax, C, S1!29)) | status(Ax, C, S2!28))) | (~status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S1!29)) | status(tptp_fun_Ax_5(S2!28, S1!29), tptp_fun_C_4(S2!28, S1!29), S2!28)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[169, 99, 166, 164])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------