TSTP Solution File: KRS268+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS268+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 Sep 17 17:45:22 EDT 2022
% Result : Theorem 156.82s 98.08s
% Output : Proof 156.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KRS268+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Sep 1 10:16:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 156.82/98.08 % SZS status Theorem
% 156.82/98.08 % SZS output start Proof
% 156.82/98.08 tff(status_type, type, (
% 156.82/98.08 status: ( $i * $i * $i ) > $o)).
% 156.82/98.08 tff(wca_type, type, (
% 156.82/98.08 wca: $i)).
% 156.82/98.08 tff(tptp_fun_C_18_type, type, (
% 156.82/98.08 tptp_fun_C_18: ( $i * $i ) > $i)).
% 156.82/98.08 tff(eth_type, type, (
% 156.82/98.08 eth: $i)).
% 156.82/98.08 tff(sap_type, type, (
% 156.82/98.08 sap: $i)).
% 156.82/98.08 tff(tptp_fun_F_32_type, type, (
% 156.82/98.08 tptp_fun_F_32: $i)).
% 156.82/98.08 tff(model_type, type, (
% 156.82/98.08 model: ( $i * $i ) > $o)).
% 156.82/98.08 tff(tptp_fun_I1_0_type, type, (
% 156.82/98.08 tptp_fun_I1_0: $i > $i)).
% 156.82/98.08 tff(tptp_fun_I2_8_type, type, (
% 156.82/98.08 tptp_fun_I2_8: $i > $i)).
% 156.82/98.08 tff(tptp_fun_Ax_19_type, type, (
% 156.82/98.08 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 156.82/98.08 tff(tptp_fun_I3_9_type, type, (
% 156.82/98.08 tptp_fun_I3_9: ( $i * $i ) > $i)).
% 156.82/98.08 tff(mighta_type, type, (
% 156.82/98.08 mighta: ( $i * $i ) > $o)).
% 156.82/98.08 tff(tptp_fun_F_29_type, type, (
% 156.82/98.08 tptp_fun_F_29: $i)).
% 156.82/98.08 tff(tptp_fun_I2_31_type, type, (
% 156.82/98.08 tptp_fun_I2_31: $i)).
% 156.82/98.08 tff(tptp_fun_I1_30_type, type, (
% 156.82/98.08 tptp_fun_I1_30: $i)).
% 156.82/98.08 tff(tptp_fun_I2_1_type, type, (
% 156.82/98.08 tptp_fun_I2_1: $i > $i)).
% 156.82/98.08 tff(tptp_fun_I3_13_type, type, (
% 156.82/98.08 tptp_fun_I3_13: $i > $i)).
% 156.82/98.08 tff(nevera_type, type, (
% 156.82/98.08 nevera: ( $i * $i ) > $o)).
% 156.82/98.08 tff(tptp_fun_C_24_type, type, (
% 156.82/98.08 tptp_fun_C_24: ( $i * $i ) > $i)).
% 156.82/98.08 tff(tptp_fun_Ax_25_type, type, (
% 156.82/98.08 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 156.82/98.08 tff(tptp_fun_I1_3_type, type, (
% 156.82/98.08 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 156.82/98.08 tff(thm_type, type, (
% 156.82/98.08 thm: $i)).
% 156.82/98.08 tff(1,assumption,(model(tptp_fun_I1_0(F!32), F!32)), introduced(assumption)).
% 156.82/98.08 tff(2,plain,
% 156.82/98.08 (^[I: $i] : refl((~model(I, F!32)) <=> (~model(I, F!32)))),
% 156.82/98.08 inference(bind,[status(th)],[])).
% 156.82/98.08 tff(3,plain,
% 156.82/98.08 (![I: $i] : (~model(I, F!32)) <=> ![I: $i] : (~model(I, F!32))),
% 156.82/98.08 inference(quant_intro,[status(thm)],[2])).
% 156.82/98.08 tff(4,plain,
% 156.82/98.08 (?[F: $i] : ![I: $i] : (~model(I, F)) <=> ?[F: $i] : ![I: $i] : (~model(I, F))),
% 156.82/98.08 inference(rewrite,[status(thm)],[])).
% 156.82/98.08 tff(5,axiom,(?[F: $i] : ![I: $i] : (~model(I, F))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','contradiction')).
% 156.82/98.08 tff(6,plain,
% 156.82/98.08 (?[F: $i] : ![I: $i] : (~model(I, F))),
% 156.82/98.08 inference(modus_ponens,[status(thm)],[5, 4])).
% 156.82/98.08 tff(7,plain,(
% 156.82/98.08 $oeq(![I: $i] : (~model(I, F!32)), ![I: $i] : (~model(I, F!32)))),
% 156.82/98.08 inference(transitivity,[status(sab)],[6])).
% 156.82/98.08 tff(8,plain,
% 156.82/98.08 (![I: $i] : (~model(I, F!32))),
% 156.82/98.08 inference(modus_ponens,[status(thm)],[7, 3])).
% 156.82/98.08 tff(9,plain,
% 156.82/98.08 ((~![I: $i] : (~model(I, F!32))) | (~model(tptp_fun_I1_0(F!32), F!32))),
% 156.82/98.08 inference(quant_inst,[status(thm)],[])).
% 156.82/98.08 tff(10,plain,
% 156.82/98.08 ($false),
% 156.82/98.08 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 156.82/98.08 tff(11,plain,(~model(tptp_fun_I1_0(F!32), F!32)), inference(lemma,lemma(discharge,[]))).
% 156.82/98.08 tff(12,assumption,(![I3: $i] : model(I3, tptp_fun_C_18(sap, eth))), introduced(assumption)).
% 156.82/98.08 tff(13,plain,
% 156.82/98.08 (^[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))))))))))),
% 156.82/98.08 inference(bind,[status(th)],[])).
% 156.82/98.08 tff(14,plain,
% 156.82/98.08 (![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)))))))))),
% 156.82/98.08 inference(quant_intro,[status(thm)],[13])).
% 156.82/98.08 tff(15,plain,
% 156.82/98.08 (^[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)))))))))),
% 156.82/98.08 inference(bind,[status(th)],[])).
% 156.82/98.08 tff(16,plain,
% 156.82/98.08 (![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))))))))),
% 156.82/98.08 inference(quant_intro,[status(thm)],[15])).
% 156.82/98.08 tff(17,plain,
% 156.82/98.08 (^[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)))))))))),
% 156.82/98.08 inference(bind,[status(th)],[])).
% 156.82/98.08 tff(18,plain,
% 156.82/98.08 (![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))))))))),
% 156.82/98.08 inference(quant_intro,[status(thm)],[17])).
% 156.82/98.08 tff(19,plain,
% 156.82/98.08 (![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))))))))),
% 156.82/98.08 inference(transitivity,[status(thm)],[18, 16])).
% 156.82/98.08 tff(20,plain,
% 156.82/98.08 (^[Ax: $i, C: $i] : trans(monotonicity(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)))), 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))))))))))),
% 156.82/98.08 inference(bind,[status(th)],[])).
% 156.82/98.08 tff(21,plain,
% 156.82/98.08 (![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))))))))),
% 156.82/98.08 inference(quant_intro,[status(thm)],[20])).
% 156.82/98.08 tff(22,plain,
% 156.82/98.08 (^[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)))))),
% 156.82/98.09 inference(bind,[status(th)],[])).
% 156.82/98.09 tff(23,plain,
% 156.82/98.09 (![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))))),
% 156.82/98.09 inference(quant_intro,[status(thm)],[22])).
% 156.82/98.09 tff(24,plain,
% 156.82/98.09 (![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))),
% 156.82/98.09 inference(rewrite,[status(thm)],[])).
% 156.82/98.09 tff(25,plain,
% 156.82/98.09 (^[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)))),
% 156.82/98.09 inference(bind,[status(th)],[])).
% 156.82/98.09 tff(26,plain,
% 156.82/98.09 (![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))),
% 156.82/98.09 inference(quant_intro,[status(thm)],[25])).
% 156.82/98.09 tff(27,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')).
% 156.82/98.09 tff(28,plain,
% 156.82/98.09 (![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))),
% 156.82/98.09 inference(modus_ponens,[status(thm)],[27, 26])).
% 156.82/98.09 tff(29,plain,
% 156.82/98.09 (![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))),
% 156.82/98.09 inference(modus_ponens,[status(thm)],[28, 24])).
% 156.82/98.09 tff(30,plain,(
% 156.82/98.09 ![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))))),
% 156.82/98.09 inference(skolemize,[status(sab)],[29])).
% 156.82/98.09 tff(31,plain,
% 156.82/98.09 (![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))))),
% 156.82/98.09 inference(modus_ponens,[status(thm)],[30, 23])).
% 156.82/98.09 tff(32,plain,
% 156.82/98.09 (![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))))))))),
% 156.82/98.09 inference(modus_ponens,[status(thm)],[31, 21])).
% 156.82/98.09 tff(33,plain,
% 156.82/98.09 (![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))))))))),
% 156.82/98.09 inference(modus_ponens,[status(thm)],[32, 19])).
% 156.82/98.09 tff(34,plain,
% 156.82/98.09 (![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)))))))))),
% 156.82/98.09 inference(modus_ponens,[status(thm)],[33, 14])).
% 156.82/98.09 tff(35,plain,
% 156.82/98.09 (((~![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(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))))))) <=> ((~![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(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))))))))))),
% 156.82/98.09 inference(rewrite,[status(thm)],[])).
% 156.82/98.09 tff(36,plain,
% 156.82/98.09 ((~((~(status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))))))))) <=> (~((~(status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))))))),
% 156.82/98.09 inference(rewrite,[status(thm)],[])).
% 156.82/98.09 tff(37,plain,
% 156.82/98.09 (((~![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(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))))))) <=> ((~![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(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))))))))))),
% 156.82/98.09 inference(monotonicity,[status(thm)],[36])).
% 156.82/98.09 tff(38,plain,
% 156.82/98.09 (((~![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(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))))))) <=> ((~![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(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))))))))))),
% 156.82/98.09 inference(transitivity,[status(thm)],[37, 35])).
% 156.82/98.09 tff(39,plain,
% 156.82/98.09 ((~![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(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))))))),
% 156.82/98.09 inference(quant_inst,[status(thm)],[])).
% 156.82/98.09 tff(40,plain,
% 156.82/98.09 ((~![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(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))))))),
% 156.82/98.09 inference(modus_ponens,[status(thm)],[39, 38])).
% 156.82/98.09 tff(41,plain,
% 156.82/98.09 (~((~(status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))))))))),
% 156.82/98.09 inference(unit_resolution,[status(thm)],[40, 34])).
% 156.82/98.09 tff(42,plain,
% 156.82/98.09 (((~(status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth) | ![I2: $i] : model(I2, tptp_fun_Ax_19(sap, eth)) | ((~model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) <=> model(tptp_fun_I3_9(tptp_fun_C_18(sap, eth), tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))))) | ((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))))))),
% 156.82/98.09 inference(tautology,[status(thm)],[])).
% 156.82/98.09 tff(43,plain,
% 156.82/98.09 ((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))),
% 156.82/98.09 inference(unit_resolution,[status(thm)],[42, 41])).
% 156.82/98.09 tff(44,assumption,(![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth)))), introduced(assumption)).
% 156.82/98.09 tff(45,assumption,(![I2: $i] : model(I2, F!29)), introduced(assumption)).
% 156.82/98.09 tff(46,plain,
% 156.82/98.09 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 156.82/98.09 inference(rewrite,[status(thm)],[])).
% 156.82/98.09 tff(47,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 156.82/98.09 tff(48,plain,
% 156.82/98.09 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 156.82/98.09 inference(modus_ponens,[status(thm)],[47, 46])).
% 156.82/98.09 tff(49,plain,
% 156.82/98.09 (~model(I2!31, F!29)),
% 156.82/98.09 inference(and_elim,[status(thm)],[48])).
% 156.82/98.09 tff(50,plain,
% 156.82/98.09 ((~![I2: $i] : model(I2, F!29)) | model(I2!31, F!29)),
% 156.82/98.09 inference(quant_inst,[status(thm)],[])).
% 156.82/98.09 tff(51,plain,
% 156.82/98.09 ($false),
% 156.82/98.09 inference(unit_resolution,[status(thm)],[50, 49, 45])).
% 156.82/98.09 tff(52,plain,(~![I2: $i] : model(I2, F!29)), inference(lemma,lemma(discharge,[]))).
% 156.82/98.09 tff(53,plain,
% 156.82/98.09 (((~![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, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | model(tptp_fun_I2_8(F!29), F!29)))))))) <=> ((~![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, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | model(tptp_fun_I2_8(F!29), F!29))))))))),
% 156.82/98.09 inference(rewrite,[status(thm)],[])).
% 156.82/98.09 tff(54,plain,
% 156.82/98.09 ((~((~(status(F!29, F!29, eth) | ((~model(tptp_fun_I3_9(F!29, F!29), F!29)) <=> model(tptp_fun_I3_9(F!29, F!29), F!29)) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : (model(I3, F!29) <=> model(I3, F!29))))))))) <=> (~((~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | model(tptp_fun_I2_8(F!29), F!29)))))))),
% 156.82/98.09 inference(rewrite,[status(thm)],[])).
% 156.82/98.09 tff(55,plain,
% 156.82/98.09 (((~![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(F!29, F!29, eth) | ((~model(tptp_fun_I3_9(F!29, F!29), F!29)) <=> model(tptp_fun_I3_9(F!29, F!29), F!29)) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : (model(I3, F!29) <=> model(I3, F!29)))))))))) <=> ((~![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, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | model(tptp_fun_I2_8(F!29), F!29))))))))),
% 156.82/98.09 inference(monotonicity,[status(thm)],[54])).
% 156.82/98.09 tff(56,plain,
% 156.82/98.09 (((~![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(F!29, F!29, eth) | ((~model(tptp_fun_I3_9(F!29, F!29), F!29)) <=> model(tptp_fun_I3_9(F!29, F!29), F!29)) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : (model(I3, F!29) <=> model(I3, F!29)))))))))) <=> ((~![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, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | model(tptp_fun_I2_8(F!29), F!29))))))))),
% 156.82/98.09 inference(transitivity,[status(thm)],[55, 53])).
% 156.82/98.09 tff(57,plain,
% 156.82/98.09 ((~![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(F!29, F!29, eth) | ((~model(tptp_fun_I3_9(F!29, F!29), F!29)) <=> model(tptp_fun_I3_9(F!29, F!29), F!29)) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : (model(I3, F!29) <=> model(I3, F!29)))))))))),
% 156.82/98.09 inference(quant_inst,[status(thm)],[])).
% 156.82/98.09 tff(58,plain,
% 156.82/98.09 ((~![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, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | model(tptp_fun_I2_8(F!29), F!29)))))))),
% 156.82/98.09 inference(modus_ponens,[status(thm)],[57, 56])).
% 156.82/98.09 tff(59,plain,
% 156.82/98.09 (~((~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | model(tptp_fun_I2_8(F!29), F!29))))))),
% 156.82/98.09 inference(unit_resolution,[status(thm)],[58, 34])).
% 156.82/98.09 tff(60,plain,
% 156.82/98.09 (((~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | model(tptp_fun_I2_8(F!29), F!29)))))) | (![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(61,plain,
% 156.82/98.10 (![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth)),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[60, 59])).
% 156.82/98.10 tff(62,assumption,(![I1: $i] : (~model(I1, F!29))), introduced(assumption)).
% 156.82/98.10 tff(63,plain,
% 156.82/98.10 (model(I1!30, F!29)),
% 156.82/98.10 inference(and_elim,[status(thm)],[48])).
% 156.82/98.10 tff(64,plain,
% 156.82/98.10 ((~![I1: $i] : (~model(I1, F!29))) | (~model(I1!30, F!29))),
% 156.82/98.10 inference(quant_inst,[status(thm)],[])).
% 156.82/98.10 tff(65,plain,
% 156.82/98.10 ($false),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[64, 63, 62])).
% 156.82/98.10 tff(66,plain,(~![I1: $i] : (~model(I1, F!29))), inference(lemma,lemma(discharge,[]))).
% 156.82/98.10 tff(67,plain,
% 156.82/98.10 ((~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth)),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(68,plain,
% 156.82/98.10 ((~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth))) | ![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth)),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[67, 66])).
% 156.82/98.10 tff(69,plain,
% 156.82/98.10 (![I2: $i] : model(I2, F!29) | status(F!29, F!29, eth)),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[68, 61])).
% 156.82/98.10 tff(70,plain,
% 156.82/98.10 (status(F!29, F!29, eth)),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[69, 52])).
% 156.82/98.10 tff(71,assumption,(![I2: $i] : (~model(I2, F!29))), introduced(assumption)).
% 156.82/98.10 tff(72,plain,
% 156.82/98.10 ((~![I2: $i] : (~model(I2, F!29))) | (~model(I1!30, F!29))),
% 156.82/98.10 inference(quant_inst,[status(thm)],[])).
% 156.82/98.10 tff(73,plain,
% 156.82/98.10 ($false),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[72, 63, 71])).
% 156.82/98.10 tff(74,plain,(~![I2: $i] : (~model(I2, F!29))), inference(lemma,lemma(discharge,[]))).
% 156.82/98.10 tff(75,plain,
% 156.82/98.10 (((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29)))) | ![I2: $i] : (~model(I2, F!29))),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(76,plain,
% 156.82/98.10 ((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29)))),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[75, 74])).
% 156.82/98.10 tff(77,plain,
% 156.82/98.10 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax)))))))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(78,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[77])).
% 156.82/98.10 tff(79,plain,
% 156.82/98.10 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(80,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[79])).
% 156.82/98.10 tff(81,plain,
% 156.82/98.10 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(82,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[81])).
% 156.82/98.10 tff(83,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 156.82/98.10 inference(transitivity,[status(thm)],[82, 80])).
% 156.82/98.10 tff(84,plain,
% 156.82/98.10 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite(((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) <=> ((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))), rewrite((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))) <=> (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))), ((((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> (((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))), rewrite((((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))), ((((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(85,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[84])).
% 156.82/98.10 tff(86,plain,
% 156.82/98.10 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & ((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sap)))) <=> (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(87,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & ((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sap)))) <=> ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[86])).
% 156.82/98.10 tff(88,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 156.82/98.10 inference(rewrite,[status(thm)],[])).
% 156.82/98.10 tff(89,plain,
% 156.82/98.10 (^[Ax: $i, C: $i] : rewrite(((?[I1: $i] : model(I1, Ax) => ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)) <=> (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(90,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) => ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[89])).
% 156.82/98.10 tff(91,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) => ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','sap')).
% 156.82/98.10 tff(92,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[91, 90])).
% 156.82/98.10 tff(93,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[92, 88])).
% 156.82/98.10 tff(94,plain,(
% 156.82/98.10 ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & ((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sap))))),
% 156.82/98.10 inference(skolemize,[status(sab)],[93])).
% 156.82/98.10 tff(95,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[94, 87])).
% 156.82/98.10 tff(96,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[95, 85])).
% 156.82/98.10 tff(97,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[96, 83])).
% 156.82/98.10 tff(98,plain,
% 156.82/98.10 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[97, 78])).
% 156.82/98.10 tff(99,plain,
% 156.82/98.10 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!29)) | (~status(F!29, F!29, sap))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!29)) | (~status(F!29, F!29, sap)))))))),
% 156.82/98.10 inference(rewrite,[status(thm)],[])).
% 156.82/98.10 tff(100,plain,
% 156.82/98.10 ((~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)) | ![I1: $i] : (~model(I1, F!29)))))) <=> (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!29)) | (~status(F!29, F!29, sap))))))),
% 156.82/98.10 inference(rewrite,[status(thm)],[])).
% 156.82/98.10 tff(101,plain,
% 156.82/98.10 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)) | ![I1: $i] : (~model(I1, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!29)) | (~status(F!29, F!29, sap)))))))),
% 156.82/98.10 inference(monotonicity,[status(thm)],[100])).
% 156.82/98.10 tff(102,plain,
% 156.82/98.10 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)) | ![I1: $i] : (~model(I1, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!29)) | (~status(F!29, F!29, sap)))))))),
% 156.82/98.10 inference(transitivity,[status(thm)],[101, 99])).
% 156.82/98.10 tff(103,plain,
% 156.82/98.10 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)) | ![I1: $i] : (~model(I1, F!29))))))),
% 156.82/98.10 inference(quant_inst,[status(thm)],[])).
% 156.82/98.10 tff(104,plain,
% 156.82/98.10 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!29)) | (~status(F!29, F!29, sap))))))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[103, 102])).
% 156.82/98.10 tff(105,plain,
% 156.82/98.10 (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!29)) | (~status(F!29, F!29, sap)))))),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[104, 98])).
% 156.82/98.10 tff(106,plain,
% 156.82/98.10 (((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!29)) | (~status(F!29, F!29, sap))))) | ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(107,plain,
% 156.82/98.10 ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap)),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[106, 105])).
% 156.82/98.10 tff(108,plain,
% 156.82/98.10 ((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap)),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(109,plain,
% 156.82/98.10 ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap)),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[108, 107])).
% 156.82/98.10 tff(110,plain,
% 156.82/98.10 (status(F!29, F!29, sap)),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[109, 76])).
% 156.82/98.10 tff(111,plain,
% 156.82/98.10 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth)))) | ((~status(F!29, F!29, sap)) | (~status(F!29, F!29, eth)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth)))) | (~status(F!29, F!29, sap)) | (~status(F!29, F!29, eth)))),
% 156.82/98.10 inference(rewrite,[status(thm)],[])).
% 156.82/98.10 tff(112,plain,
% 156.82/98.10 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth)))) | ((~status(F!29, F!29, sap)) | (~status(F!29, F!29, eth)))),
% 156.82/98.10 inference(quant_inst,[status(thm)],[])).
% 156.82/98.10 tff(113,plain,
% 156.82/98.10 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth)))) | (~status(F!29, F!29, sap)) | (~status(F!29, F!29, eth))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[112, 111])).
% 156.82/98.10 tff(114,plain,
% 156.82/98.10 ($false),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[113, 110, 70, 44])).
% 156.82/98.10 tff(115,plain,(~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth)))), inference(lemma,lemma(discharge,[]))).
% 156.82/98.10 tff(116,plain,
% 156.82/98.10 (^[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)))))))))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(117,plain,
% 156.82/98.10 (![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))))))))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[116])).
% 156.82/98.10 tff(118,plain,
% 156.82/98.10 (^[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)))))))))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(119,plain,
% 156.82/98.10 (![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))))))))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[118])).
% 156.82/98.10 tff(120,plain,
% 156.82/98.10 (![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))))))))),
% 156.82/98.10 inference(transitivity,[status(thm)],[119, 117])).
% 156.82/98.10 tff(121,plain,
% 156.82/98.10 (^[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))))))))))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(122,plain,
% 156.82/98.10 (![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))))))))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[121])).
% 156.82/98.10 tff(123,plain,
% 156.82/98.10 (^[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)))))),
% 156.82/98.10 inference(bind,[status(th)],[])).
% 156.82/98.10 tff(124,plain,
% 156.82/98.10 (![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))))),
% 156.82/98.10 inference(quant_intro,[status(thm)],[123])).
% 156.82/98.10 tff(125,plain,
% 156.82/98.10 (![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))),
% 156.82/98.10 inference(rewrite,[status(thm)],[])).
% 156.82/98.10 tff(126,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')).
% 156.82/98.10 tff(127,plain,
% 156.82/98.10 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[126, 125])).
% 156.82/98.10 tff(128,plain,(
% 156.82/98.10 ![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))))),
% 156.82/98.10 inference(skolemize,[status(sab)],[127])).
% 156.82/98.10 tff(129,plain,
% 156.82/98.10 (![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))))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[128, 124])).
% 156.82/98.10 tff(130,plain,
% 156.82/98.10 (![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))))))))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[129, 122])).
% 156.82/98.10 tff(131,plain,
% 156.82/98.10 (![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))))))))),
% 156.82/98.10 inference(modus_ponens,[status(thm)],[130, 120])).
% 156.82/98.10 tff(132,plain,
% 156.82/98.10 ((~![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, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, sap)) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))))))))),
% 156.82/98.10 inference(quant_inst,[status(thm)],[])).
% 156.82/98.10 tff(133,plain,
% 156.82/98.10 (~((~(mighta(eth, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, sap)) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)))))))),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[132, 131])).
% 156.82/98.10 tff(134,plain,
% 156.82/98.10 (((~(mighta(eth, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, sap)) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))))))) | (mighta(eth, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth))))),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(135,plain,
% 156.82/98.10 (mighta(eth, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth)))),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[134, 133])).
% 156.82/98.10 tff(136,plain,
% 156.82/98.10 ((~(mighta(eth, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth))))) | mighta(eth, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth)))),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(137,plain,
% 156.82/98.10 (mighta(eth, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth)))),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[136, 135])).
% 156.82/98.10 tff(138,plain,
% 156.82/98.10 (mighta(eth, sap)),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[137, 115])).
% 156.82/98.10 tff(139,plain,
% 156.82/98.10 (((~(mighta(eth, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, sap)) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))))))) | ((~mighta(eth, sap)) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)))))),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(140,plain,
% 156.82/98.10 ((~mighta(eth, sap)) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))))),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[139, 133])).
% 156.82/98.10 tff(141,plain,
% 156.82/98.10 ((~((~mighta(eth, sap)) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)))))) | (~mighta(eth, sap)) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))))),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(142,plain,
% 156.82/98.10 ((~mighta(eth, sap)) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))))),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[141, 140])).
% 156.82/98.10 tff(143,plain,
% 156.82/98.10 (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)))),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[142, 138])).
% 156.82/98.10 tff(144,plain,
% 156.82/98.10 (((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(145,plain,
% 156.82/98.10 (status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)),
% 156.82/98.10 inference(unit_resolution,[status(thm)],[144, 143])).
% 156.82/98.10 tff(146,plain,
% 156.82/98.10 ((~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))))))) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))),
% 156.82/98.10 inference(tautology,[status(thm)],[])).
% 156.82/98.10 tff(147,plain,
% 156.82/98.10 ((~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))))))) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[146, 145])).
% 156.82/98.11 tff(148,plain,
% 156.82/98.11 (~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[147, 43])).
% 156.82/98.11 tff(149,plain,
% 156.82/98.11 ((model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))) | ![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))),
% 156.82/98.11 inference(tautology,[status(thm)],[])).
% 156.82/98.11 tff(150,plain,
% 156.82/98.11 (![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[149, 148])).
% 156.82/98.11 tff(151,plain,
% 156.82/98.11 ((~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth)))) | (model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) <=> model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth)))),
% 156.82/98.11 inference(quant_inst,[status(thm)],[])).
% 156.82/98.11 tff(152,plain,
% 156.82/98.11 (model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) <=> model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[151, 150])).
% 156.82/98.11 tff(153,plain,
% 156.82/98.11 ((model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))) | (~model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)))),
% 156.82/98.11 inference(tautology,[status(thm)],[])).
% 156.82/98.11 tff(154,plain,
% 156.82/98.11 (~model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[153, 148])).
% 156.82/98.11 tff(155,plain,
% 156.82/98.11 ((~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) <=> model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth)))) | model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth)))),
% 156.82/98.11 inference(tautology,[status(thm)],[])).
% 156.82/98.11 tff(156,plain,
% 156.82/98.11 ((~(model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) <=> model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth)))) | (~model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth)))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[155, 154])).
% 156.82/98.11 tff(157,plain,
% 156.82/98.11 (~model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[156, 152])).
% 156.82/98.11 tff(158,plain,
% 156.82/98.11 ((~![I3: $i] : model(I3, tptp_fun_C_18(sap, eth))) | model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_C_18(sap, eth))),
% 156.82/98.11 inference(quant_inst,[status(thm)],[])).
% 156.82/98.11 tff(159,plain,
% 156.82/98.11 ($false),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[158, 157, 12])).
% 156.82/98.11 tff(160,plain,(~![I3: $i] : model(I3, tptp_fun_C_18(sap, eth))), inference(lemma,lemma(discharge,[]))).
% 156.82/98.11 tff(161,assumption,(![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))), introduced(assumption)).
% 156.82/98.11 tff(162,plain,
% 156.82/98.11 ((model(tptp_fun_I2_8(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I3: $i] : (model(I3, tptp_fun_Ax_19(sap, eth)) <=> model(I3, tptp_fun_C_18(sap, eth))))) | model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))),
% 156.82/98.11 inference(tautology,[status(thm)],[])).
% 156.82/98.11 tff(163,plain,
% 156.82/98.11 (model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[162, 148])).
% 156.82/98.11 tff(164,plain,
% 156.82/98.11 ((~![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth)))),
% 156.82/98.11 inference(quant_inst,[status(thm)],[])).
% 156.82/98.11 tff(165,plain,
% 156.82/98.11 ($false),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[164, 163, 161])).
% 156.82/98.11 tff(166,plain,(~![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))), inference(lemma,lemma(discharge,[]))).
% 156.82/98.11 tff(167,plain,
% 156.82/98.11 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))))))),
% 156.82/98.11 inference(rewrite,[status(thm)],[])).
% 156.82/98.11 tff(168,plain,
% 156.82/98.11 ((~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))))) <=> (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))))))),
% 156.82/98.11 inference(rewrite,[status(thm)],[])).
% 156.82/98.11 tff(169,plain,
% 156.82/98.11 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))))))),
% 156.82/98.11 inference(monotonicity,[status(thm)],[168])).
% 156.82/98.11 tff(170,plain,
% 156.82/98.11 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))))))),
% 156.82/98.11 inference(transitivity,[status(thm)],[169, 167])).
% 156.82/98.11 tff(171,plain,
% 156.82/98.11 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))))))),
% 156.82/98.11 inference(quant_inst,[status(thm)],[])).
% 156.82/98.11 tff(172,plain,
% 156.82/98.11 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))))))),
% 156.82/98.11 inference(modus_ponens,[status(thm)],[171, 170])).
% 156.82/98.11 tff(173,plain,
% 156.82/98.11 (~((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[172, 98])).
% 156.82/98.11 tff(174,plain,
% 156.82/98.11 (((~((~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(sap, eth)), tptp_fun_Ax_19(sap, eth))) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | (~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))))) | ((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))),
% 156.82/98.11 inference(tautology,[status(thm)],[])).
% 156.82/98.11 tff(175,plain,
% 156.82/98.11 ((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[174, 173])).
% 156.82/98.11 tff(176,plain,
% 156.82/98.11 (((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), eth)) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap))) | status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)),
% 156.82/98.11 inference(tautology,[status(thm)],[])).
% 156.82/98.11 tff(177,plain,
% 156.82/98.11 (status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[176, 143])).
% 156.82/98.11 tff(178,plain,
% 156.82/98.11 ((~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | (~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))),
% 156.82/98.11 inference(tautology,[status(thm)],[])).
% 156.82/98.11 tff(179,plain,
% 156.82/98.11 ((~((~status(tptp_fun_Ax_19(sap, eth), tptp_fun_C_18(sap, eth), sap)) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth))))) | model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[178, 177])).
% 156.82/98.11 tff(180,plain,
% 156.82/98.11 (model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(sap, eth)))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[179, 175])).
% 156.82/98.11 tff(181,plain,
% 156.82/98.11 (model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth))),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[180, 166])).
% 156.82/98.11 tff(182,assumption,(![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))), introduced(assumption)).
% 156.82/98.11 tff(183,plain,
% 156.82/98.11 ((~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)))),
% 156.82/98.11 inference(quant_inst,[status(thm)],[])).
% 156.82/98.11 tff(184,plain,
% 156.82/98.11 ($false),
% 156.82/98.11 inference(unit_resolution,[status(thm)],[183, 182, 181])).
% 156.82/98.11 tff(185,plain,(~![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth)))), inference(lemma,lemma(discharge,[]))).
% 156.82/98.11 tff(186,plain,
% 156.82/98.11 (^[Ax: $i, C: $i] : rewrite((~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 156.82/98.11 inference(bind,[status(th)],[])).
% 156.82/98.11 tff(187,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 156.82/98.11 inference(quant_intro,[status(thm)],[186])).
% 156.82/98.11 tff(188,plain,
% 156.82/98.11 (^[Ax: $i, C: $i] : refl((~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 156.82/98.11 inference(bind,[status(th)],[])).
% 156.82/98.11 tff(189,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 156.82/98.11 inference(quant_intro,[status(thm)],[188])).
% 156.82/98.11 tff(190,plain,
% 156.82/98.11 (^[Ax: $i, C: $i] : rewrite((~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 156.82/98.11 inference(bind,[status(th)],[])).
% 156.82/98.11 tff(191,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 156.82/98.11 inference(quant_intro,[status(thm)],[190])).
% 156.82/98.11 tff(192,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 156.82/98.11 inference(transitivity,[status(thm)],[191, 189])).
% 156.82/98.11 tff(193,plain,
% 156.82/98.11 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) <=> (![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))), trans(monotonicity(rewrite((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) <=> (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))) <=> ((~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, wca))))), rewrite(((~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, wca))) <=> ((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))) <=> ((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))), (((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))), rewrite(((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))) <=> (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))), (((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))))),
% 156.82/98.11 inference(bind,[status(th)],[])).
% 156.82/98.11 tff(194,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> ![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 156.82/98.11 inference(quant_intro,[status(thm)],[193])).
% 156.82/98.11 tff(195,plain,
% 156.82/98.11 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : (~(~model(I3, C)))) | status(Ax, C, wca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))))),
% 156.82/98.11 inference(bind,[status(th)],[])).
% 156.82/98.11 tff(196,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : (~(~model(I3, C)))) | status(Ax, C, wca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> ![Ax: $i, C: $i] : ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))))),
% 156.82/98.11 inference(quant_intro,[status(thm)],[195])).
% 156.82/98.11 tff(197,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))),
% 156.82/98.11 inference(rewrite,[status(thm)],[])).
% 156.82/98.11 tff(198,plain,
% 156.82/98.11 (^[Ax: $i, C: $i] : rewrite(((((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca)) <=> (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca)))),
% 156.82/98.11 inference(bind,[status(th)],[])).
% 156.82/98.11 tff(199,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : ((((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))),
% 156.82/98.11 inference(quant_intro,[status(thm)],[198])).
% 156.82/98.11 tff(200,axiom,(![Ax: $i, C: $i] : ((((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','wca')).
% 156.82/98.11 tff(201,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))),
% 156.82/98.11 inference(modus_ponens,[status(thm)],[200, 199])).
% 156.82/98.11 tff(202,plain,
% 156.82/98.11 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))),
% 156.82/98.11 inference(modus_ponens,[status(thm)],[201, 197])).
% 156.82/98.11 tff(203,plain,(
% 156.82/98.11 ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : (~(~model(I3, C)))) | status(Ax, C, wca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))))),
% 156.82/98.12 inference(skolemize,[status(sab)],[202])).
% 156.82/98.12 tff(204,plain,
% 156.82/98.12 (![Ax: $i, C: $i] : ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[203, 196])).
% 156.82/98.12 tff(205,plain,
% 156.82/98.12 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[204, 194])).
% 156.82/98.12 tff(206,plain,
% 156.82/98.12 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[205, 192])).
% 156.82/98.12 tff(207,plain,
% 156.82/98.12 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[206, 187])).
% 156.82/98.12 tff(208,plain,
% 156.82/98.12 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~![I1: $i] : (~model(I1, F!32))) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~![I1: $i] : (~model(I1, F!32))) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth))))))))))),
% 156.82/98.12 inference(rewrite,[status(thm)],[])).
% 156.82/98.12 tff(209,plain,
% 156.82/98.12 ((~((~(status(F!32, tptp_fun_C_18(sap, eth), wca) | model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth))) | (~![I1: $i] : (~model(I1, F!32))))))))) <=> (~((~(model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~![I1: $i] : (~model(I1, F!32))) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)))))))))),
% 156.82/98.12 inference(rewrite,[status(thm)],[])).
% 156.82/98.12 tff(210,plain,
% 156.82/98.12 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(F!32, tptp_fun_C_18(sap, eth), wca) | model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth))) | (~![I1: $i] : (~model(I1, F!32)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~![I1: $i] : (~model(I1, F!32))) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth))))))))))),
% 156.82/98.12 inference(monotonicity,[status(thm)],[209])).
% 156.82/98.12 tff(211,plain,
% 156.82/98.12 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(F!32, tptp_fun_C_18(sap, eth), wca) | model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth))) | (~![I1: $i] : (~model(I1, F!32)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~![I1: $i] : (~model(I1, F!32))) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth))))))))))),
% 156.82/98.12 inference(transitivity,[status(thm)],[210, 208])).
% 156.82/98.12 tff(212,plain,
% 156.82/98.12 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(F!32, tptp_fun_C_18(sap, eth), wca) | model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth))) | (~![I1: $i] : (~model(I1, F!32)))))))))),
% 156.82/98.12 inference(quant_inst,[status(thm)],[])).
% 156.82/98.12 tff(213,plain,
% 156.82/98.12 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~![I1: $i] : (~model(I1, F!32))) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)))))))))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[212, 211])).
% 156.82/98.12 tff(214,plain,
% 156.82/98.12 (~((~(model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~![I1: $i] : (~model(I1, F!32))) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth))))))))),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[213, 207])).
% 156.82/98.12 tff(215,plain,
% 156.82/98.12 (((~(model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))) | (~((~status(F!32, tptp_fun_C_18(sap, eth), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)) | (~![I1: $i] : (~model(I1, F!32))) | (~model(tptp_fun_I2_1(tptp_fun_C_18(sap, eth)), tptp_fun_C_18(sap, eth)))))))) | (model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))),
% 156.82/98.12 inference(tautology,[status(thm)],[])).
% 156.82/98.12 tff(216,plain,
% 156.82/98.12 (model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca)),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[215, 214])).
% 156.82/98.12 tff(217,plain,
% 156.82/98.12 ((~(model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca))) | model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca)),
% 156.82/98.12 inference(tautology,[status(thm)],[])).
% 156.82/98.12 tff(218,plain,
% 156.82/98.12 (model(tptp_fun_I1_0(F!32), F!32) | ![I2: $i] : (~model(I2, tptp_fun_C_18(sap, eth))) | ![I3: $i] : model(I3, tptp_fun_C_18(sap, eth)) | status(F!32, tptp_fun_C_18(sap, eth), wca)),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[217, 216])).
% 156.82/98.12 tff(219,plain,
% 156.82/98.12 (model(tptp_fun_I1_0(F!32), F!32) | status(F!32, tptp_fun_C_18(sap, eth), wca)),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[218, 185, 160])).
% 156.82/98.12 tff(220,plain,
% 156.82/98.12 (status(F!32, tptp_fun_C_18(sap, eth), wca)),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[219, 11])).
% 156.82/98.12 tff(221,plain,
% 156.82/98.12 (^[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)))))))),
% 156.82/98.12 inference(bind,[status(th)],[])).
% 156.82/98.12 tff(222,plain,
% 156.82/98.12 (![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))))))),
% 156.82/98.12 inference(quant_intro,[status(thm)],[221])).
% 156.82/98.12 tff(223,plain,
% 156.82/98.12 (^[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)))))))),
% 156.82/98.12 inference(bind,[status(th)],[])).
% 156.82/98.12 tff(224,plain,
% 156.82/98.12 (![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))))))),
% 156.82/98.12 inference(quant_intro,[status(thm)],[223])).
% 156.82/98.12 tff(225,plain,
% 156.82/98.12 (^[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)))))))),
% 156.82/98.12 inference(bind,[status(th)],[])).
% 156.82/98.12 tff(226,plain,
% 156.82/98.12 (![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))))))),
% 156.82/98.12 inference(quant_intro,[status(thm)],[225])).
% 156.82/98.12 tff(227,plain,
% 156.82/98.12 (![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))))))),
% 156.82/98.12 inference(transitivity,[status(thm)],[226, 224])).
% 156.82/98.12 tff(228,plain,
% 156.82/98.12 (^[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))))))))),
% 156.82/98.12 inference(bind,[status(th)],[])).
% 156.82/98.12 tff(229,plain,
% 156.82/98.12 (![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))))))),
% 156.82/98.12 inference(quant_intro,[status(thm)],[228])).
% 156.82/98.12 tff(230,plain,
% 156.82/98.12 (![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))),
% 156.82/98.12 inference(rewrite,[status(thm)],[])).
% 156.82/98.12 tff(231,plain,
% 156.82/98.12 (^[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)))),
% 156.82/98.12 inference(bind,[status(th)],[])).
% 156.82/98.12 tff(232,plain,
% 156.82/98.12 (![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))),
% 156.82/98.12 inference(quant_intro,[status(thm)],[231])).
% 156.82/98.12 tff(233,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')).
% 156.82/98.12 tff(234,plain,
% 156.82/98.12 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[233, 232])).
% 156.82/98.12 tff(235,plain,
% 156.82/98.12 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[234, 230])).
% 156.82/98.12 tff(236,plain,(
% 156.82/98.12 ![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))))),
% 156.82/98.12 inference(skolemize,[status(sab)],[235])).
% 156.82/98.12 tff(237,plain,
% 156.82/98.12 (![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))))))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[236, 229])).
% 156.82/98.12 tff(238,plain,
% 156.82/98.12 (![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))))))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[237, 227])).
% 156.82/98.12 tff(239,plain,
% 156.82/98.12 (![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))))))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[238, 222])).
% 156.82/98.12 tff(240,plain,
% 156.82/98.12 ((~![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(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca)))) | status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm))) | (~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(wca, wca))) | model(I1, tptp_fun_C_24(wca, wca)))))))),
% 156.82/98.12 inference(quant_inst,[status(thm)],[])).
% 156.82/98.12 tff(241,plain,
% 156.82/98.12 (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca)))) | status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm))) | (~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(wca, wca))) | model(I1, tptp_fun_C_24(wca, wca))))))),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[240, 239])).
% 156.82/98.12 tff(242,plain,
% 156.82/98.12 (((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca)))) | status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm))) | (~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(wca, wca))) | model(I1, tptp_fun_C_24(wca, wca)))))) | ((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca)))) | status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm))),
% 156.82/98.12 inference(tautology,[status(thm)],[])).
% 156.82/98.12 tff(243,plain,
% 156.82/98.12 ((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca)))) | status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[242, 241])).
% 156.82/98.12 tff(244,assumption,(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)), introduced(assumption)).
% 156.82/98.12 tff(245,plain,
% 156.82/98.12 ((~![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(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm))))))))),
% 156.82/98.12 inference(quant_inst,[status(thm)],[])).
% 156.82/98.12 tff(246,plain,
% 156.82/98.12 (~((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)))))))),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[245, 131])).
% 156.82/98.12 tff(247,plain,
% 156.82/98.12 (((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm))))))) | (mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))),
% 156.82/98.12 inference(tautology,[status(thm)],[])).
% 156.82/98.12 tff(248,plain,
% 156.82/98.12 (mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[247, 246])).
% 156.82/98.12 tff(249,plain,
% 156.82/98.12 ((~mighta(wca, thm)) <=> (~mighta(wca, thm))),
% 156.82/98.12 inference(rewrite,[status(thm)],[])).
% 156.82/98.12 tff(250,axiom,(~mighta(wca, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_wca_thm')).
% 156.82/98.12 tff(251,plain,
% 156.82/98.12 (~mighta(wca, thm)),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[250, 249])).
% 156.82/98.12 tff(252,plain,
% 156.82/98.12 ((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))),
% 156.82/98.12 inference(tautology,[status(thm)],[])).
% 156.82/98.12 tff(253,plain,
% 156.82/98.12 ((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[252, 251])).
% 156.82/98.12 tff(254,plain,
% 156.82/98.12 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[253, 248])).
% 156.82/98.12 tff(255,plain,
% 156.82/98.12 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))) | ((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)))),
% 156.82/98.12 inference(rewrite,[status(thm)],[])).
% 156.82/98.12 tff(256,plain,
% 156.82/98.12 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))) | ((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)))),
% 156.82/98.12 inference(quant_inst,[status(thm)],[])).
% 156.82/98.12 tff(257,plain,
% 156.82/98.12 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca))),
% 156.82/98.12 inference(modus_ponens,[status(thm)],[256, 255])).
% 156.82/98.12 tff(258,plain,
% 156.82/98.12 (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)),
% 156.82/98.12 inference(unit_resolution,[status(thm)],[257, 254, 244])).
% 156.82/98.12 tff(259,plain,
% 156.82/98.13 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca)))) | status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca)))) | status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm)),
% 156.82/98.13 inference(tautology,[status(thm)],[])).
% 156.82/98.13 tff(260,plain,
% 156.82/98.13 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca)))) | status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca))))),
% 156.82/98.13 inference(unit_resolution,[status(thm)],[259, 258])).
% 156.82/98.13 tff(261,plain,
% 156.82/98.13 (~((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca)))),
% 156.82/98.13 inference(unit_resolution,[status(thm)],[260, 243])).
% 156.82/98.13 tff(262,plain,
% 156.82/98.13 (((~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_C_24(wca, wca))) | model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))),
% 156.82/98.13 inference(tautology,[status(thm)],[])).
% 156.82/98.13 tff(263,plain,
% 156.82/98.13 (model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca))),
% 156.82/98.13 inference(unit_resolution,[status(thm)],[262, 261])).
% 156.82/98.13 tff(264,plain,
% 156.82/98.13 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | model(tptp_fun_I1_0(tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca)) | ![I2: $i] : (~model(I2, tptp_fun_C_24(wca, wca))) | ![I3: $i] : model(I3, tptp_fun_C_24(wca, wca)))) | (~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca))))))))))),
% 156.82/98.13 inference(quant_inst,[status(thm)],[])).
% 156.82/98.13 tff(265,plain,
% 156.82/98.13 (~((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | model(tptp_fun_I1_0(tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca)) | ![I2: $i] : (~model(I2, tptp_fun_C_24(wca, wca))) | ![I3: $i] : model(I3, tptp_fun_C_24(wca, wca)))) | (~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca)))))))))),
% 156.82/98.13 inference(unit_resolution,[status(thm)],[264, 207])).
% 156.82/98.13 tff(266,plain,
% 156.82/98.13 (((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | model(tptp_fun_I1_0(tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca)) | ![I2: $i] : (~model(I2, tptp_fun_C_24(wca, wca))) | ![I3: $i] : model(I3, tptp_fun_C_24(wca, wca)))) | (~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca))))))))) | ((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca)))))))),
% 156.82/98.13 inference(tautology,[status(thm)],[])).
% 156.82/98.13 tff(267,plain,
% 156.82/98.13 ((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca))))))),
% 156.82/98.13 inference(unit_resolution,[status(thm)],[266, 265])).
% 156.82/98.13 tff(268,plain,
% 156.82/98.13 ((~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca)))))))) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca))))))),
% 156.82/98.13 inference(tautology,[status(thm)],[])).
% 156.82/98.13 tff(269,plain,
% 156.82/98.13 ((~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca)))))))) | (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca))))))),
% 156.82/98.13 inference(unit_resolution,[status(thm)],[268, 244])).
% 156.82/98.13 tff(270,plain,
% 156.82/98.13 (~(model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca)))))),
% 156.82/98.13 inference(unit_resolution,[status(thm)],[269, 267])).
% 156.82/98.13 tff(271,plain,
% 156.82/98.13 ((model(tptp_fun_I3_13(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca)) | (~model(tptp_fun_I2_1(tptp_fun_C_24(wca, wca)), tptp_fun_C_24(wca, wca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca))))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca)))),
% 156.82/98.13 inference(tautology,[status(thm)],[])).
% 156.82/98.13 tff(272,plain,
% 156.82/98.13 (![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca)))),
% 156.82/98.13 inference(unit_resolution,[status(thm)],[271, 270])).
% 156.82/98.13 tff(273,plain,
% 156.82/98.13 ((~![I1: $i] : (~model(I1, tptp_fun_Ax_25(wca, wca)))) | (~model(tptp_fun_I1_3(tptp_fun_C_24(wca, wca), tptp_fun_Ax_25(wca, wca)), tptp_fun_Ax_25(wca, wca)))),
% 156.82/98.13 inference(quant_inst,[status(thm)],[])).
% 156.82/98.13 tff(274,plain,
% 156.82/98.13 ($false),
% 156.82/98.13 inference(unit_resolution,[status(thm)],[273, 272, 263])).
% 156.82/98.13 tff(275,plain,(~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)), inference(lemma,lemma(discharge,[]))).
% 156.82/98.13 tff(276,plain,
% 156.82/98.13 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))))))),
% 156.82/98.13 inference(bind,[status(th)],[])).
% 156.82/98.13 tff(277,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 156.82/98.13 inference(quant_intro,[status(thm)],[276])).
% 156.82/98.13 tff(278,plain,
% 156.82/98.13 (^[S1: $i, S2: $i] : refl((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 156.82/98.13 inference(bind,[status(th)],[])).
% 156.82/98.13 tff(279,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 156.82/98.13 inference(quant_intro,[status(thm)],[278])).
% 156.82/98.13 tff(280,plain,
% 156.82/98.13 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 156.82/98.13 inference(bind,[status(th)],[])).
% 156.82/98.13 tff(281,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 156.82/98.13 inference(quant_intro,[status(thm)],[280])).
% 156.82/98.13 tff(282,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 156.82/98.13 inference(transitivity,[status(thm)],[281, 279])).
% 156.82/98.13 tff(283,plain,
% 156.82/98.13 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))), rewrite((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))))),
% 156.82/98.13 inference(bind,[status(th)],[])).
% 156.82/98.13 tff(284,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 156.82/98.13 inference(quant_intro,[status(thm)],[283])).
% 156.82/98.13 tff(285,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 156.82/98.13 inference(rewrite,[status(thm)],[])).
% 156.82/98.13 tff(286,plain,
% 156.82/98.13 (^[S1: $i, S2: $i] : rewrite((![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)))),
% 156.82/98.13 inference(bind,[status(th)],[])).
% 156.82/98.13 tff(287,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 156.82/98.13 inference(quant_intro,[status(thm)],[286])).
% 156.82/98.13 tff(288,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','nevera')).
% 156.82/98.13 tff(289,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 156.82/98.13 inference(modus_ponens,[status(thm)],[288, 287])).
% 156.82/98.13 tff(290,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 156.82/98.13 inference(modus_ponens,[status(thm)],[289, 285])).
% 156.82/98.13 tff(291,plain,(
% 156.82/98.13 ![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))),
% 156.82/98.13 inference(skolemize,[status(sab)],[290])).
% 156.82/98.13 tff(292,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 156.82/98.13 inference(modus_ponens,[status(thm)],[291, 284])).
% 156.82/98.13 tff(293,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 156.82/98.13 inference(modus_ponens,[status(thm)],[292, 282])).
% 156.82/98.13 tff(294,plain,
% 156.82/98.13 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 156.82/98.13 inference(modus_ponens,[status(thm)],[293, 277])).
% 156.82/98.13 tff(295,plain,
% 156.82/98.13 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca)))))))),
% 156.82/98.13 inference(rewrite,[status(thm)],[])).
% 156.82/98.13 tff(296,plain,
% 156.82/98.13 ((~((~((~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)))) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wca)) | (~status(Ax, C, wca))))))) <=> (~((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca))))))),
% 156.82/98.13 inference(rewrite,[status(thm)],[])).
% 156.82/98.13 tff(297,plain,
% 156.82/98.13 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)))) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wca)) | (~status(Ax, C, wca)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca)))))))),
% 156.82/98.13 inference(monotonicity,[status(thm)],[296])).
% 156.82/98.13 tff(298,plain,
% 156.82/98.13 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)))) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wca)) | (~status(Ax, C, wca)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca)))))))),
% 156.82/98.13 inference(transitivity,[status(thm)],[297, 295])).
% 156.82/98.13 tff(299,plain,
% 156.82/98.13 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)) | (~status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca)))) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wca)) | (~status(Ax, C, wca)))))))),
% 156.82/98.14 inference(quant_inst,[status(thm)],[])).
% 156.82/98.14 tff(300,plain,
% 156.82/98.14 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca))))))),
% 156.82/98.14 inference(modus_ponens,[status(thm)],[299, 298])).
% 156.82/98.14 tff(301,plain,
% 156.82/98.14 (~((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca)))))),
% 156.82/98.14 inference(unit_resolution,[status(thm)],[300, 294])).
% 156.82/98.14 tff(302,plain,
% 156.82/98.14 (((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca))))) | (status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))),
% 156.82/98.14 inference(tautology,[status(thm)],[])).
% 156.82/98.14 tff(303,plain,
% 156.82/98.14 (status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca)),
% 156.82/98.14 inference(unit_resolution,[status(thm)],[302, 301])).
% 156.82/98.14 tff(304,plain,
% 156.82/98.14 ((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca)),
% 156.82/98.14 inference(tautology,[status(thm)],[])).
% 156.82/98.14 tff(305,plain,
% 156.82/98.14 (status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca)),
% 156.82/98.14 inference(unit_resolution,[status(thm)],[304, 303])).
% 156.82/98.14 tff(306,plain,
% 156.82/98.14 (nevera(wca, wca)),
% 156.82/98.14 inference(unit_resolution,[status(thm)],[305, 275])).
% 156.82/98.14 tff(307,plain,
% 156.82/98.14 (((~(status(tptp_fun_Ax_25(wca, wca), tptp_fun_C_24(wca, wca), wca) | nevera(wca, wca))) | (~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca))))) | ((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca)))),
% 156.82/98.14 inference(tautology,[status(thm)],[])).
% 156.82/98.14 tff(308,plain,
% 156.82/98.14 ((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca))),
% 156.82/98.14 inference(unit_resolution,[status(thm)],[307, 301])).
% 156.82/98.14 tff(309,plain,
% 156.82/98.14 ((~((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca)))) | (~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca))),
% 156.82/98.14 inference(tautology,[status(thm)],[])).
% 156.82/98.14 tff(310,plain,
% 156.82/98.14 ((~nevera(wca, wca)) | ![Ax: $i, C: $i] : (~status(Ax, C, wca))),
% 156.82/98.14 inference(unit_resolution,[status(thm)],[309, 308])).
% 156.82/98.14 tff(311,plain,
% 156.82/98.14 (![Ax: $i, C: $i] : (~status(Ax, C, wca))),
% 156.82/98.14 inference(unit_resolution,[status(thm)],[310, 306])).
% 156.82/98.14 tff(312,plain,
% 156.82/98.14 ((~![Ax: $i, C: $i] : (~status(Ax, C, wca))) | (~status(F!32, tptp_fun_C_18(sap, eth), wca))),
% 156.82/98.14 inference(quant_inst,[status(thm)],[])).
% 156.82/98.14 tff(313,plain,
% 156.82/98.14 ($false),
% 156.82/98.14 inference(unit_resolution,[status(thm)],[312, 311, 220])).
% 156.82/98.14 % SZS output end Proof
%------------------------------------------------------------------------------