%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS203+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:13:34 AM UTC 2025
% Result : Theorem 1.30s 1.46s
% Output : Proof 1.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS203+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:12:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.30/1.46 % SZS status Theorem
% 1.30/1.46 % SZS output start Proof
% 1.30/1.46 tff(model_type, type, (
% 1.30/1.46 model: ( $i * $i ) > $o)).
% 1.30/1.46 tff(tptp_fun_Ax_38_type, type, (
% 1.30/1.46 tptp_fun_Ax_38: $i)).
% 1.30/1.46 tff(tptp_fun_C_37_type, type, (
% 1.30/1.46 tptp_fun_C_37: $i)).
% 1.30/1.46 tff(status_type, type, (
% 1.30/1.46 status: ( $i * $i * $i ) > $o)).
% 1.30/1.46 tff(thm_type, type, (
% 1.30/1.46 thm: $i)).
% 1.30/1.46 tff(tptp_fun_I1_3_type, type, (
% 1.30/1.46 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 1.30/1.46 tff(sat_type, type, (
% 1.30/1.46 sat: $i)).
% 1.30/1.46 tff(tptp_fun_I1_39_type, type, (
% 1.30/1.46 tptp_fun_I1_39: $i)).
% 1.30/1.46 tff(tptp_fun_I4_41_type, type, (
% 1.30/1.46 tptp_fun_I4_41: $i)).
% 1.30/1.46 tff(tptp_fun_I3_40_type, type, (
% 1.30/1.46 tptp_fun_I3_40: $i)).
% 1.30/1.46 tff(tptp_fun_I1_2_type, type, (
% 1.30/1.46 tptp_fun_I1_2: ( $i * $i ) > $i)).
% 1.30/1.46 tff(nota_type, type, (
% 1.30/1.46 nota: ( $i * $i ) > $o)).
% 1.30/1.46 tff(tptp_fun_C_22_type, type, (
% 1.30/1.46 tptp_fun_C_22: ( $i * $i ) > $i)).
% 1.30/1.46 tff(tptp_fun_Ax_23_type, type, (
% 1.30/1.46 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 1.30/1.46 tff(1,plain,
% 1.30/1.46 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C)))))))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(2,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[1])).
% 1.30/1.46 tff(3,plain,
% 1.30/1.46 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(4,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[3])).
% 1.30/1.46 tff(5,plain,
% 1.30/1.46 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(6,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[5])).
% 1.30/1.46 tff(7,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.30/1.46 inference(transitivity,[status(thm)],[6, 4])).
% 1.30/1.46 tff(8,plain,
% 1.30/1.46 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))), rewrite((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(9,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[8])).
% 1.30/1.46 tff(10,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(11,plain,
% 1.30/1.46 (^[Ax: $i, C: $i] : rewrite((![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(12,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[11])).
% 1.30/1.46 tff(13,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','thm')).
% 1.30/1.46 tff(14,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.30/1.46 tff(15,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[14, 10])).
% 1.30/1.46 tff(16,plain,(
% 1.30/1.46 ![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))),
% 1.30/1.46 inference(skolemize,[status(sab)],[15])).
% 1.30/1.46 tff(17,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[16, 9])).
% 1.30/1.46 tff(18,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[17, 7])).
% 1.30/1.46 tff(19,plain,
% 1.30/1.46 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[18, 2])).
% 1.30/1.46 tff(20,plain,
% 1.30/1.46 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm))))))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(21,plain,
% 1.30/1.46 ((~((~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm))) | (~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))))) <=> (~((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm)))))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(22,plain,
% 1.30/1.46 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm))) | (~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm))))))),
% 1.30/1.46 inference(monotonicity,[status(thm)],[21])).
% 1.30/1.46 tff(23,plain,
% 1.30/1.46 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm))) | (~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm))))))),
% 1.30/1.46 inference(transitivity,[status(thm)],[22, 20])).
% 1.30/1.46 tff(24,plain,
% 1.30/1.46 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm))) | (~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))))))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(25,plain,
% 1.30/1.46 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm)))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.30/1.47 tff(26,plain,
% 1.30/1.47 (~((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm))))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[25, 19])).
% 1.30/1.47 tff(27,plain,
% 1.30/1.47 (((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, C!37), C!37)) | model(tptp_fun_I1_3(Ax!38, C!37), Ax!38))) | status(C!37, Ax!38, thm)))) | ((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))),
% 1.30/1.47 inference(tautology,[status(thm)],[])).
% 1.30/1.47 tff(28,plain,
% 1.30/1.47 ((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[27, 26])).
% 1.30/1.47 tff(29,assumption,(![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))), introduced(assumption)).
% 1.30/1.47 tff(30,plain,
% 1.30/1.47 (^[I2: $i] : refl(((~model(I2, Ax!38)) | model(I2, C!37)) <=> ((~model(I2, Ax!38)) | model(I2, C!37)))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(31,plain,
% 1.30/1.47 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) <=> ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[30])).
% 1.30/1.47 tff(32,plain,
% 1.30/1.47 ((model(I1!39, Ax!38) & ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) & ((~model(I3!40, Ax!38)) & model(I3!40, C!37)) & (~model(I4!41, C!37))) <=> (model(I1!39, Ax!38) & ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) & (~model(I3!40, Ax!38)) & model(I3!40, C!37) & (~model(I4!41, C!37)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(33,plain,
% 1.30/1.47 (?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C))) <=> ?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(34,plain,
% 1.30/1.47 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))), (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) <=> ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))))), rewrite(((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)))), (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))))), ((((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))) <=> ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))))), rewrite(((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))), ((((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(35,plain,
% 1.30/1.47 (?[Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))) <=> ?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[34])).
% 1.30/1.47 tff(36,axiom,(?[Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','mixed_pair')).
% 1.30/1.47 tff(37,plain,
% 1.30/1.47 (?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.30/1.47 tff(38,plain,
% 1.30/1.47 (?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[37, 33])).
% 1.30/1.47 tff(39,plain,
% 1.30/1.47 (model(I1!39, Ax!38) & ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) & (~model(I3!40, Ax!38)) & model(I3!40, C!37) & (~model(I4!41, C!37))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[38, 32])).
% 1.30/1.47 tff(40,plain,
% 1.30/1.47 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 1.30/1.47 inference(and_elim,[status(thm)],[39])).
% 1.30/1.47 tff(41,plain,
% 1.30/1.47 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[40, 31])).
% 1.30/1.47 tff(42,plain,
% 1.30/1.47 (model(I1!39, Ax!38)),
% 1.30/1.47 inference(and_elim,[status(thm)],[39])).
% 1.30/1.47 tff(43,plain,
% 1.30/1.47 (((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(I1!39, Ax!38)) | model(I1!39, C!37))) <=> ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(I1!39, Ax!38)) | model(I1!39, C!37))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(44,plain,
% 1.30/1.47 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(I1!39, Ax!38)) | model(I1!39, C!37))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(45,plain,
% 1.30/1.47 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(I1!39, Ax!38)) | model(I1!39, C!37)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.30/1.47 tff(46,plain,
% 1.30/1.47 (model(I1!39, C!37)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[45, 42, 41])).
% 1.30/1.47 tff(47,plain,
% 1.30/1.47 (((~![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))) | ((~model(I1!39, Ax!38)) | (~model(I1!39, C!37)))) <=> ((~![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))) | (~model(I1!39, Ax!38)) | (~model(I1!39, C!37)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(48,plain,
% 1.30/1.47 (((~model(I1!39, C!37)) | (~model(I1!39, Ax!38))) <=> ((~model(I1!39, Ax!38)) | (~model(I1!39, C!37)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(49,plain,
% 1.30/1.47 (((~![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))) | ((~model(I1!39, C!37)) | (~model(I1!39, Ax!38)))) <=> ((~![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))) | ((~model(I1!39, Ax!38)) | (~model(I1!39, C!37))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[48])).
% 1.30/1.47 tff(50,plain,
% 1.30/1.47 (((~![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))) | ((~model(I1!39, C!37)) | (~model(I1!39, Ax!38)))) <=> ((~![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))) | (~model(I1!39, Ax!38)) | (~model(I1!39, C!37)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[49, 47])).
% 1.30/1.47 tff(51,plain,
% 1.30/1.47 ((~![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))) | ((~model(I1!39, C!37)) | (~model(I1!39, Ax!38)))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(52,plain,
% 1.30/1.47 ((~![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))) | (~model(I1!39, Ax!38)) | (~model(I1!39, C!37))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.30/1.47 tff(53,plain,
% 1.30/1.47 ($false),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[52, 42, 46, 29])).
% 1.30/1.47 tff(54,plain,(~![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))), inference(lemma,lemma(discharge,[]))).
% 1.30/1.47 tff(55,plain,
% 1.30/1.47 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(56,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[55])).
% 1.30/1.47 tff(57,plain,
% 1.30/1.47 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(58,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[57])).
% 1.30/1.47 tff(59,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 1.30/1.47 inference(transitivity,[status(thm)],[58, 56])).
% 1.30/1.47 tff(60,plain,
% 1.30/1.47 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) <=> (status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))), trans(monotonicity(rewrite((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) <=> (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))), (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))) <=> ((~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))) | (~status(Ax, C, sat))))), rewrite(((~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))) | (~status(Ax, C, sat))) <=> ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))), (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))) <=> ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))), (((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ((status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C)))) & ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))), rewrite(((status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C)))) & ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))), (((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(61,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[60])).
% 1.30/1.47 tff(62,plain,
% 1.30/1.47 (^[Ax: $i, C: $i] : rewrite(((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(63,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[62])).
% 1.30/1.47 tff(64,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat)) <=> ![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(65,axiom,(![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','sat')).
% 1.30/1.47 tff(66,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.30/1.47 tff(67,plain,(
% 1.30/1.47 ![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 1.30/1.47 inference(skolemize,[status(sab)],[66])).
% 1.30/1.47 tff(68,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[67, 63])).
% 1.30/1.47 tff(69,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[68, 61])).
% 1.30/1.47 tff(70,plain,
% 1.30/1.47 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[69, 59])).
% 1.30/1.47 tff(71,plain,
% 1.30/1.47 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(C!37, Ax!38, sat) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38))))) | (~((~status(C!37, Ax!38, sat)) | (~((~model(tptp_fun_I1_2(Ax!38, C!37), C!37)) | (~model(tptp_fun_I1_2(Ax!38, C!37), Ax!38))))))))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(72,plain,
% 1.30/1.47 (~((~(status(C!37, Ax!38, sat) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38))))) | (~((~status(C!37, Ax!38, sat)) | (~((~model(tptp_fun_I1_2(Ax!38, C!37), C!37)) | (~model(tptp_fun_I1_2(Ax!38, C!37), Ax!38)))))))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[71, 70])).
% 1.33/1.47 tff(73,plain,
% 1.33/1.47 (((~(status(C!37, Ax!38, sat) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38))))) | (~((~status(C!37, Ax!38, sat)) | (~((~model(tptp_fun_I1_2(Ax!38, C!37), C!37)) | (~model(tptp_fun_I1_2(Ax!38, C!37), Ax!38))))))) | (status(C!37, Ax!38, sat) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38))))),
% 1.33/1.47 inference(tautology,[status(thm)],[])).
% 1.33/1.47 tff(74,plain,
% 1.33/1.47 (status(C!37, Ax!38, sat) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[73, 72])).
% 1.33/1.47 tff(75,plain,
% 1.33/1.47 ((~(status(C!37, Ax!38, sat) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38))))) | status(C!37, Ax!38, sat) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))),
% 1.33/1.47 inference(tautology,[status(thm)],[])).
% 1.33/1.47 tff(76,plain,
% 1.33/1.47 (status(C!37, Ax!38, sat) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, Ax!38)))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[75, 74])).
% 1.33/1.47 tff(77,plain,
% 1.33/1.47 (status(C!37, Ax!38, sat)),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[76, 54])).
% 1.33/1.47 tff(78,plain,
% 1.33/1.47 (^[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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 1.33/1.47 inference(bind,[status(th)],[])).
% 1.33/1.47 tff(79,plain,
% 1.33/1.47 (![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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.33/1.47 inference(quant_intro,[status(thm)],[78])).
% 1.33/1.47 tff(80,plain,
% 1.33/1.47 (^[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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 1.33/1.47 inference(bind,[status(th)],[])).
% 1.33/1.47 tff(81,plain,
% 1.33/1.47 (![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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.33/1.47 inference(quant_intro,[status(thm)],[80])).
% 1.33/1.47 tff(82,plain,
% 1.33/1.47 (![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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.33/1.47 inference(transitivity,[status(thm)],[81, 79])).
% 1.33/1.47 tff(83,plain,
% 1.33/1.47 (^[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_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) <=> (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))))),
% 1.33/1.47 inference(bind,[status(th)],[])).
% 1.33/1.47 tff(84,plain,
% 1.33/1.47 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.33/1.47 inference(quant_intro,[status(thm)],[83])).
% 1.33/1.47 tff(85,plain,
% 1.33/1.47 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))))),
% 1.33/1.47 inference(bind,[status(th)],[])).
% 1.33/1.47 tff(86,plain,
% 1.33/1.47 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(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_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 1.33/1.47 inference(quant_intro,[status(thm)],[85])).
% 1.33/1.47 tff(87,plain,
% 1.33/1.47 (![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))),
% 1.33/1.47 inference(rewrite,[status(thm)],[])).
% 1.33/1.47 tff(88,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')).
% 1.33/1.47 tff(89,plain,
% 1.33/1.47 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.33/1.47 tff(90,plain,(
% 1.33/1.47 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 1.33/1.47 inference(skolemize,[status(sab)],[89])).
% 1.33/1.47 tff(91,plain,
% 1.33/1.47 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[90, 86])).
% 1.33/1.47 tff(92,plain,
% 1.33/1.47 (![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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[91, 84])).
% 1.33/1.47 tff(93,plain,
% 1.33/1.47 (![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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[92, 82])).
% 1.33/1.47 tff(94,plain,
% 1.33/1.47 ((~![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_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))) | (~((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | (~((~nota(sat, thm)) | (~((~status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), sat)) | status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), thm)))))))),
% 1.33/1.47 inference(quant_inst,[status(thm)],[])).
% 1.33/1.47 tff(95,plain,
% 1.33/1.47 (~((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | (~((~nota(sat, thm)) | (~((~status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), sat)) | status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), thm))))))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[94, 93])).
% 1.33/1.47 tff(96,plain,
% 1.33/1.47 (((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | (~((~nota(sat, thm)) | (~((~status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), sat)) | status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), thm)))))) | (nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))),
% 1.33/1.47 inference(tautology,[status(thm)],[])).
% 1.33/1.47 tff(97,plain,
% 1.33/1.47 (nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[96, 95])).
% 1.33/1.47 tff(98,plain,
% 1.33/1.47 ((~nota(sat, thm)) <=> (~nota(sat, thm))),
% 1.33/1.47 inference(rewrite,[status(thm)],[])).
% 1.33/1.47 tff(99,axiom,(~nota(sat, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nota_sat_thm')).
% 1.33/1.47 tff(100,plain,
% 1.33/1.47 (~nota(sat, thm)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.33/1.47 tff(101,plain,
% 1.33/1.47 ((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))),
% 1.33/1.47 inference(tautology,[status(thm)],[])).
% 1.33/1.47 tff(102,plain,
% 1.33/1.47 ((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[101, 100])).
% 1.33/1.47 tff(103,plain,
% 1.33/1.47 (![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[102, 97])).
% 1.33/1.47 tff(104,plain,
% 1.33/1.47 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))) | ((~status(C!37, Ax!38, sat)) | status(C!37, Ax!38, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))) | (~status(C!37, Ax!38, sat)) | status(C!37, Ax!38, thm))),
% 1.33/1.47 inference(rewrite,[status(thm)],[])).
% 1.33/1.47 tff(105,plain,
% 1.33/1.47 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))) | ((~status(C!37, Ax!38, sat)) | status(C!37, Ax!38, thm))),
% 1.33/1.47 inference(quant_inst,[status(thm)],[])).
% 1.33/1.47 tff(106,plain,
% 1.33/1.47 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))) | (~status(C!37, Ax!38, sat)) | status(C!37, Ax!38, thm)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.33/1.47 tff(107,plain,
% 1.33/1.47 (status(C!37, Ax!38, thm)),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[106, 103, 77])).
% 1.33/1.47 tff(108,plain,
% 1.33/1.47 ((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | (~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))),
% 1.33/1.47 inference(tautology,[status(thm)],[])).
% 1.33/1.47 tff(109,plain,
% 1.33/1.47 ((~((~status(C!37, Ax!38, thm)) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38)))) | ![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[108, 107])).
% 1.33/1.47 tff(110,plain,
% 1.33/1.47 (![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[109, 28])).
% 1.33/1.47 tff(111,plain,
% 1.33/1.47 (model(I3!40, C!37)),
% 1.33/1.47 inference(and_elim,[status(thm)],[39])).
% 1.33/1.47 tff(112,plain,
% 1.33/1.47 (~model(I3!40, Ax!38)),
% 1.33/1.47 inference(and_elim,[status(thm)],[39])).
% 1.33/1.47 tff(113,plain,
% 1.33/1.47 (((~![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))) | ((~model(I3!40, C!37)) | model(I3!40, Ax!38))) <=> ((~![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))) | (~model(I3!40, C!37)) | model(I3!40, Ax!38))),
% 1.33/1.47 inference(rewrite,[status(thm)],[])).
% 1.33/1.47 tff(114,plain,
% 1.33/1.47 ((~![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))) | ((~model(I3!40, C!37)) | model(I3!40, Ax!38))),
% 1.33/1.47 inference(quant_inst,[status(thm)],[])).
% 1.33/1.47 tff(115,plain,
% 1.33/1.47 ((~![I1: $i] : ((~model(I1, C!37)) | model(I1, Ax!38))) | (~model(I3!40, C!37)) | model(I3!40, Ax!38)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.33/1.47 tff(116,plain,
% 1.33/1.47 ($false),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[115, 112, 111, 110])).
% 1.33/1.47 % SZS output end Proof
% 1.33/1.48 % E exiting
%------------------------------------------------------------------------------