%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS261+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:13:39 AM UTC 2025
% Result : Theorem 0.60s 0.77s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KRS261+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:21:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.60/0.77 % SZS status Theorem
% 0.60/0.77 % SZS output start Proof
% 0.60/0.77 tff(model_type, type, (
% 0.60/0.77 model: ( $i * $i ) > $o)).
% 0.60/0.77 tff(tptp_fun_C_42_type, type, (
% 0.60/0.77 tptp_fun_C_42: $i)).
% 0.60/0.77 tff(status_type, type, (
% 0.60/0.77 status: ( $i * $i * $i ) > $o)).
% 0.60/0.77 tff(eth_type, type, (
% 0.60/0.77 eth: $i)).
% 0.60/0.77 tff(tptp_fun_I2_8_type, type, (
% 0.60/0.77 tptp_fun_I2_8: $i > $i)).
% 0.60/0.77 tff(tptp_fun_I1_0_type, type, (
% 0.60/0.77 tptp_fun_I1_0: $i > $i)).
% 0.60/0.77 tff(tptp_fun_I3_9_type, type, (
% 0.60/0.77 tptp_fun_I3_9: ( $i * $i ) > $i)).
% 0.60/0.77 tff(thm_type, type, (
% 0.60/0.77 thm: $i)).
% 0.60/0.77 tff(tptp_fun_I1_3_type, type, (
% 0.60/0.77 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 0.60/0.77 tff(mighta_type, type, (
% 0.60/0.77 mighta: ( $i * $i ) > $o)).
% 0.60/0.77 tff(tptp_fun_C_18_type, type, (
% 0.60/0.77 tptp_fun_C_18: ( $i * $i ) > $i)).
% 0.60/0.77 tff(tptp_fun_Ax_19_type, type, (
% 0.60/0.77 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 0.60/0.77 tff(tptp_fun_I2_45_type, type, (
% 0.60/0.77 tptp_fun_I2_45: $i)).
% 0.60/0.77 tff(tptp_fun_I1_44_type, type, (
% 0.60/0.77 tptp_fun_I1_44: $i)).
% 0.60/0.77 tff(tptp_fun_Ax_43_type, type, (
% 0.60/0.77 tptp_fun_Ax_43: $i)).
% 0.60/0.77 tff(1,plain,
% 0.60/0.77 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(2,plain,
% 0.60/0.77 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1])).
% 0.60/0.77 tff(3,plain,
% 0.60/0.77 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(4,plain,
% 0.60/0.77 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[3])).
% 0.60/0.77 tff(5,plain,
% 0.60/0.77 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(6,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[5])).
% 0.60/0.78 tff(7,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 0.60/0.78 inference(transitivity,[status(thm)],[6, 4])).
% 0.60/0.78 tff(8,plain,
% 0.60/0.78 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) <=> (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))), ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) <=> (status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))))), rewrite((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) <=> (status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))), ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) <=> (status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))) <=> ((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, eth))))), rewrite(((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, eth))) <=> ((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))) <=> ((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))), (((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))), rewrite(((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))) <=> (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))), (((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(9,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[8])).
% 0.60/0.78 tff(10,plain,
% 0.60/0.78 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) | status(Ax, C, eth)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(11,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) | status(Ax, C, eth)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[10])).
% 0.60/0.78 tff(12,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(13,plain,
% 0.60/0.78 (^[Ax: $i, C: $i] : rewrite((((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth)) <=> ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth)))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(14,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[13])).
% 0.60/0.78 tff(15,axiom,(![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','eth')).
% 0.60/0.78 tff(16,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.60/0.78 tff(17,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.60/0.78 tff(18,plain,(
% 0.60/0.78 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) | status(Ax, C, eth)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))))),
% 0.60/0.78 inference(skolemize,[status(sab)],[17])).
% 0.60/0.78 tff(19,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.60/0.78 tff(20,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.60/0.78 tff(21,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.60/0.78 tff(22,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.60/0.78 tff(23,plain,
% 0.60/0.78 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))) | (~((~status(C!42, C!42, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42)))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))) | (~((~status(C!42, C!42, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42))))))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(24,plain,
% 0.60/0.78 ((~((~(status(C!42, C!42, eth) | (~(model(tptp_fun_I3_9(C!42, C!42), C!42) <=> model(tptp_fun_I3_9(C!42, C!42), C!42))) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, C!42, eth)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, C!42))))))))) <=> (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))) | (~((~status(C!42, C!42, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42)))))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(25,plain,
% 0.60/0.78 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(status(C!42, C!42, eth) | (~(model(tptp_fun_I3_9(C!42, C!42), C!42) <=> model(tptp_fun_I3_9(C!42, C!42), C!42))) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, C!42, eth)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, C!42)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))) | (~((~status(C!42, C!42, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42))))))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[24])).
% 0.60/0.78 tff(26,plain,
% 0.60/0.78 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(status(C!42, C!42, eth) | (~(model(tptp_fun_I3_9(C!42, C!42), C!42) <=> model(tptp_fun_I3_9(C!42, C!42), C!42))) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, C!42, eth)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, C!42)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))) | (~((~status(C!42, C!42, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42))))))))),
% 0.60/0.78 inference(transitivity,[status(thm)],[25, 23])).
% 0.60/0.78 tff(27,plain,
% 0.60/0.78 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(status(C!42, C!42, eth) | (~(model(tptp_fun_I3_9(C!42, C!42), C!42) <=> model(tptp_fun_I3_9(C!42, C!42), C!42))) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, C!42, eth)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, C!42)))))))))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(28,plain,
% 0.60/0.78 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))) | (~((~status(C!42, C!42, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42)))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.60/0.78 tff(29,plain,
% 0.60/0.78 (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))) | (~((~status(C!42, C!42, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42))))))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.60/0.78 tff(30,plain,
% 0.60/0.78 (((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))) | (~((~status(C!42, C!42, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42)))))) | (![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(31,plain,
% 0.60/0.78 (![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.60/0.78 tff(32,assumption,(~status(C!42, C!42, thm)), introduced(assumption)).
% 0.60/0.78 tff(33,plain,
% 0.60/0.78 (^[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)))))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(34,plain,
% 0.60/0.78 (![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))))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[33])).
% 0.60/0.78 tff(35,plain,
% 0.60/0.78 (^[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)))))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(36,plain,
% 0.60/0.78 (![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))))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[35])).
% 0.60/0.78 tff(37,plain,
% 0.60/0.78 (^[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)))))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(38,plain,
% 0.60/0.78 (![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))))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[37])).
% 0.60/0.78 tff(39,plain,
% 0.60/0.78 (![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))))))),
% 0.60/0.78 inference(transitivity,[status(thm)],[38, 36])).
% 0.60/0.78 tff(40,plain,
% 0.60/0.78 (^[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))))))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(41,plain,
% 0.60/0.78 (![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))))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[40])).
% 0.60/0.78 tff(42,plain,
% 0.60/0.78 (![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))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(43,plain,
% 0.60/0.78 (^[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)))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(44,plain,
% 0.60/0.78 (![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))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[43])).
% 0.60/0.78 tff(45,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','thm')).
% 0.60/0.78 tff(46,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.60/0.78 tff(47,plain,
% 0.60/0.78 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.60/0.78 tff(48,plain,(
% 0.60/0.78 ![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))))),
% 0.60/0.78 inference(skolemize,[status(sab)],[47])).
% 0.60/0.78 tff(49,plain,
% 0.60/0.78 (![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))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.60/0.78 tff(50,plain,
% 0.60/0.78 (![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))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.60/0.78 tff(51,plain,
% 0.60/0.78 (![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))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[50, 34])).
% 0.60/0.78 tff(52,plain,
% 0.60/0.78 (((~![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!42, C!42, 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!42, C!42, thm))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(53,plain,
% 0.60/0.78 ((~(~status(C!42, C!42, thm))) <=> status(C!42, C!42, thm)),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(54,plain,
% 0.60/0.78 (((~status(C!42, C!42, thm)) | $false) <=> (~status(C!42, C!42, thm))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(55,plain,
% 0.60/0.78 ((~$true) <=> $false),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(56,plain,
% 0.60/0.78 (((~status(C!42, C!42, thm)) | $true) <=> $true),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(57,plain,
% 0.60/0.78 (![I1: $i] : $true <=> $true),
% 0.60/0.78 inference(elim_unused_vars,[status(thm)],[])).
% 0.60/0.78 tff(58,plain,
% 0.60/0.78 (![I1: $i] : $true <=> ![I1: $i] : $true),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(59,plain,
% 0.60/0.78 (![I1: $i] : $true <=> $true),
% 0.60/0.78 inference(transitivity,[status(thm)],[58, 57])).
% 0.60/0.78 tff(60,plain,
% 0.60/0.78 (^[I1: $i] : rewrite(((~model(I1, C!42)) | model(I1, C!42)) <=> $true)),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(61,plain,
% 0.60/0.78 (![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42)) <=> ![I1: $i] : $true),
% 0.60/0.78 inference(quant_intro,[status(thm)],[60])).
% 0.60/0.78 tff(62,plain,
% 0.60/0.78 (![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42)) <=> $true),
% 0.60/0.78 inference(transitivity,[status(thm)],[61, 59])).
% 0.60/0.78 tff(63,plain,
% 0.60/0.78 (((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42))) <=> ((~status(C!42, C!42, thm)) | $true)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[62])).
% 0.60/0.78 tff(64,plain,
% 0.60/0.78 (((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42))) <=> $true),
% 0.60/0.78 inference(transitivity,[status(thm)],[63, 56])).
% 0.60/0.78 tff(65,plain,
% 0.60/0.78 ((~((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42)))) <=> (~$true)),
% 0.60/0.78 inference(monotonicity,[status(thm)],[64])).
% 0.60/0.78 tff(66,plain,
% 0.60/0.78 ((~((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42)))) <=> $false),
% 0.60/0.78 inference(transitivity,[status(thm)],[65, 55])).
% 0.60/0.78 tff(67,plain,
% 0.60/0.78 ((~((~((~model(tptp_fun_I1_3(C!42, C!42), C!42)) | model(tptp_fun_I1_3(C!42, C!42), C!42))) | status(C!42, C!42, thm))) <=> (~status(C!42, C!42, thm))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(68,plain,
% 0.60/0.78 (((~((~((~model(tptp_fun_I1_3(C!42, C!42), C!42)) | model(tptp_fun_I1_3(C!42, C!42), C!42))) | status(C!42, C!42, thm))) | (~((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42))))) <=> ((~status(C!42, C!42, thm)) | $false)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[67, 66])).
% 0.60/0.79 tff(69,plain,
% 0.60/0.79 (((~((~((~model(tptp_fun_I1_3(C!42, C!42), C!42)) | model(tptp_fun_I1_3(C!42, C!42), C!42))) | status(C!42, C!42, thm))) | (~((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42))))) <=> (~status(C!42, C!42, thm))),
% 0.60/0.79 inference(transitivity,[status(thm)],[68, 54])).
% 0.60/0.79 tff(70,plain,
% 0.60/0.79 ((~((~((~((~model(tptp_fun_I1_3(C!42, C!42), C!42)) | model(tptp_fun_I1_3(C!42, C!42), C!42))) | status(C!42, C!42, thm))) | (~((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42)))))) <=> (~(~status(C!42, C!42, thm)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[69])).
% 0.60/0.79 tff(71,plain,
% 0.60/0.79 ((~((~((~((~model(tptp_fun_I1_3(C!42, C!42), C!42)) | model(tptp_fun_I1_3(C!42, C!42), C!42))) | status(C!42, C!42, thm))) | (~((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42)))))) <=> status(C!42, C!42, thm)),
% 0.60/0.79 inference(transitivity,[status(thm)],[70, 53])).
% 0.60/0.79 tff(72,plain,
% 0.60/0.79 (((~![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(C!42, C!42), C!42)) | model(tptp_fun_I1_3(C!42, C!42), C!42))) | status(C!42, C!42, thm))) | (~((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42))))))) <=> ((~![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!42, C!42, thm))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[71])).
% 0.60/0.79 tff(73,plain,
% 0.60/0.79 (((~![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(C!42, C!42), C!42)) | model(tptp_fun_I1_3(C!42, C!42), C!42))) | status(C!42, C!42, thm))) | (~((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42))))))) <=> ((~![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!42, C!42, thm))),
% 0.60/0.79 inference(transitivity,[status(thm)],[72, 52])).
% 0.60/0.79 tff(74,plain,
% 0.60/0.79 ((~![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(C!42, C!42), C!42)) | model(tptp_fun_I1_3(C!42, C!42), C!42))) | status(C!42, C!42, thm))) | (~((~status(C!42, C!42, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, C!42))))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(75,plain,
% 0.60/0.79 ((~![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: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(C!42, C!42, thm)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.60/0.79 tff(76,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[75, 51, 32])).
% 0.60/0.79 tff(77,plain,(status(C!42, C!42, thm)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(78,plain,
% 0.60/0.79 (^[S1: $i, S2: $i] : refl((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(79,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[78])).
% 0.60/0.79 tff(80,plain,
% 0.60/0.79 (^[S1: $i, S2: $i] : rewrite((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(81,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[80])).
% 0.60/0.79 tff(82,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.60/0.79 inference(transitivity,[status(thm)],[81, 79])).
% 0.60/0.79 tff(83,plain,
% 0.60/0.79 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) <=> (mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))), trans(monotonicity(rewrite((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) <=> (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))), rewrite(((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(84,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[83])).
% 0.60/0.79 tff(85,plain,
% 0.60/0.79 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(86,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[85])).
% 0.60/0.79 tff(87,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(88,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','mighta')).
% 0.60/0.79 tff(89,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.60/0.79 tff(90,plain,(
% 0.60/0.79 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.60/0.79 inference(skolemize,[status(sab)],[89])).
% 0.60/0.79 tff(91,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.60/0.79 tff(92,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.60/0.79 tff(93,plain,
% 0.60/0.79 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.60/0.79 tff(94,plain,
% 0.60/0.79 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, thm)) | (~((~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), eth)) | (~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), thm))))))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(95,plain,
% 0.60/0.79 (~((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, thm)) | (~((~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), eth)) | (~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), thm)))))))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.60/0.79 tff(96,plain,
% 0.60/0.79 (((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, thm)) | (~((~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), eth)) | (~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), thm))))))) | (mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))),
% 0.60/0.79 inference(tautology,[status(thm)],[])).
% 0.60/0.79 tff(97,plain,
% 0.60/0.79 (mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.60/0.79 tff(98,plain,
% 0.60/0.79 ((~mighta(eth, thm)) <=> (~mighta(eth, thm))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(99,axiom,(~mighta(eth, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_eth_thm')).
% 0.60/0.79 tff(100,plain,
% 0.60/0.79 (~mighta(eth, thm)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.60/0.79 tff(101,plain,
% 0.60/0.79 ((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))),
% 0.60/0.79 inference(tautology,[status(thm)],[])).
% 0.60/0.79 tff(102,plain,
% 0.60/0.79 ((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.60/0.79 tff(103,plain,
% 0.60/0.79 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[102, 97])).
% 0.60/0.79 tff(104,plain,
% 0.60/0.79 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | ((~status(C!42, C!42, eth)) | (~status(C!42, C!42, thm)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | (~status(C!42, C!42, eth)) | (~status(C!42, C!42, thm)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(105,plain,
% 0.60/0.79 (((~status(C!42, C!42, thm)) | (~status(C!42, C!42, eth))) <=> ((~status(C!42, C!42, eth)) | (~status(C!42, C!42, thm)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(106,plain,
% 0.60/0.79 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | ((~status(C!42, C!42, thm)) | (~status(C!42, C!42, eth)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | ((~status(C!42, C!42, eth)) | (~status(C!42, C!42, thm))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[105])).
% 0.60/0.79 tff(107,plain,
% 0.60/0.79 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | ((~status(C!42, C!42, thm)) | (~status(C!42, C!42, eth)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | (~status(C!42, C!42, eth)) | (~status(C!42, C!42, thm)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[106, 104])).
% 0.60/0.79 tff(108,plain,
% 0.60/0.79 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | ((~status(C!42, C!42, thm)) | (~status(C!42, C!42, eth)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(109,plain,
% 0.60/0.79 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | (~status(C!42, C!42, eth)) | (~status(C!42, C!42, thm))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.60/0.79 tff(110,plain,
% 0.60/0.79 (~status(C!42, C!42, eth)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[109, 103, 77])).
% 0.60/0.79 tff(111,assumption,(![I1: $i] : (~model(I1, C!42))), introduced(assumption)).
% 0.60/0.79 tff(112,plain,
% 0.60/0.79 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C)) <=> ?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(113,plain,
% 0.60/0.79 (^[I1: $i, Ax: $i, C: $i] : rewrite(((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C)) <=> (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C)))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(114,plain,
% 0.60/0.79 (?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C)) <=> ?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[113])).
% 0.60/0.79 tff(115,axiom,(?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','non_thm_spt')).
% 0.60/0.79 tff(116,plain,
% 0.60/0.79 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.60/0.79 tff(117,plain,
% 0.60/0.79 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.60/0.79 tff(118,plain,
% 0.60/0.79 (model(I2!45, C!42)),
% 0.60/0.79 inference(and_elim,[status(thm)],[117])).
% 0.60/0.79 tff(119,plain,
% 0.60/0.79 ((~![I1: $i] : (~model(I1, C!42))) | (~model(I2!45, C!42))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(120,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[119, 118, 111])).
% 0.60/0.79 tff(121,plain,(~![I1: $i] : (~model(I1, C!42))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(122,plain,
% 0.60/0.79 ((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth))) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, C!42, eth)),
% 0.60/0.79 inference(tautology,[status(thm)],[])).
% 0.60/0.79 tff(123,plain,
% 0.60/0.79 (![I2: $i] : model(I2, C!42)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[122, 121, 110, 31])).
% 0.60/0.79 tff(124,plain,
% 0.60/0.79 (~model(I1!44, C!42)),
% 0.60/0.79 inference(and_elim,[status(thm)],[117])).
% 0.60/0.79 tff(125,plain,
% 0.60/0.79 ((~![I2: $i] : model(I2, C!42)) | model(I1!44, C!42)),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(126,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[125, 124, 123])).
% 0.60/0.79 % SZS output end Proof
% 0.60/0.80 % E exiting
%------------------------------------------------------------------------------