TSTP Solution File: KRS261+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS261+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 17:45:21 EDT 2022
% Result : Theorem 4.58s 3.19s
% Output : Proof 4.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KRS261+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 10:16:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 4.58/3.19 % SZS status Theorem
% 4.58/3.19 % SZS output start Proof
% 4.58/3.19 tff(model_type, type, (
% 4.58/3.19 model: ( $i * $i ) > $o)).
% 4.58/3.19 tff(tptp_fun_F_29_type, type, (
% 4.58/3.19 tptp_fun_F_29: $i)).
% 4.58/3.19 tff(tptp_fun_I1_0_type, type, (
% 4.58/3.19 tptp_fun_I1_0: $i > $i)).
% 4.58/3.19 tff(tptp_fun_I2_8_type, type, (
% 4.58/3.19 tptp_fun_I2_8: $i > $i)).
% 4.58/3.19 tff(status_type, type, (
% 4.58/3.19 status: ( $i * $i * $i ) > $o)).
% 4.58/3.19 tff(eth_type, type, (
% 4.58/3.19 eth: $i)).
% 4.58/3.19 tff(thm_type, type, (
% 4.58/3.19 thm: $i)).
% 4.58/3.19 tff(tptp_fun_I1_3_type, type, (
% 4.58/3.19 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 4.58/3.19 tff(mighta_type, type, (
% 4.58/3.19 mighta: ( $i * $i ) > $o)).
% 4.58/3.19 tff(tptp_fun_C_18_type, type, (
% 4.58/3.19 tptp_fun_C_18: ( $i * $i ) > $i)).
% 4.58/3.19 tff(tptp_fun_Ax_19_type, type, (
% 4.58/3.19 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 4.58/3.19 tff(tptp_fun_I2_31_type, type, (
% 4.58/3.19 tptp_fun_I2_31: $i)).
% 4.58/3.19 tff(tptp_fun_I1_30_type, type, (
% 4.58/3.19 tptp_fun_I1_30: $i)).
% 4.58/3.19 tff(tptp_fun_I3_9_type, type, (
% 4.58/3.19 tptp_fun_I3_9: ( $i * $i ) > $i)).
% 4.58/3.19 tff(1,plain,
% 4.58/3.19 (^[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)))))))),
% 4.58/3.19 inference(bind,[status(th)],[])).
% 4.58/3.19 tff(2,plain,
% 4.58/3.19 (![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))))))),
% 4.58/3.19 inference(quant_intro,[status(thm)],[1])).
% 4.58/3.19 tff(3,plain,
% 4.58/3.19 (^[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)))))))),
% 4.58/3.19 inference(bind,[status(th)],[])).
% 4.58/3.19 tff(4,plain,
% 4.58/3.19 (![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))))))),
% 4.58/3.19 inference(quant_intro,[status(thm)],[3])).
% 4.58/3.19 tff(5,plain,
% 4.58/3.19 (^[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)))))))),
% 4.58/3.19 inference(bind,[status(th)],[])).
% 4.58/3.19 tff(6,plain,
% 4.58/3.19 (![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))))))),
% 4.58/3.19 inference(quant_intro,[status(thm)],[5])).
% 4.58/3.19 tff(7,plain,
% 4.58/3.19 (![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))))))),
% 4.58/3.19 inference(transitivity,[status(thm)],[6, 4])).
% 4.58/3.19 tff(8,plain,
% 4.58/3.19 (^[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))))))))),
% 4.58/3.19 inference(bind,[status(th)],[])).
% 4.58/3.19 tff(9,plain,
% 4.58/3.19 (![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))))))),
% 4.58/3.19 inference(quant_intro,[status(thm)],[8])).
% 4.58/3.19 tff(10,plain,
% 4.58/3.19 (![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))),
% 4.58/3.19 inference(rewrite,[status(thm)],[])).
% 4.58/3.19 tff(11,plain,
% 4.58/3.19 (^[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)))),
% 4.58/3.19 inference(bind,[status(th)],[])).
% 4.58/3.19 tff(12,plain,
% 4.58/3.19 (![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))),
% 4.58/3.19 inference(quant_intro,[status(thm)],[11])).
% 4.58/3.19 tff(13,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','thm')).
% 4.58/3.19 tff(14,plain,
% 4.58/3.19 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 4.58/3.19 inference(modus_ponens,[status(thm)],[13, 12])).
% 4.58/3.19 tff(15,plain,
% 4.58/3.19 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 4.58/3.19 inference(modus_ponens,[status(thm)],[14, 10])).
% 4.58/3.19 tff(16,plain,(
% 4.58/3.19 ![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))))),
% 4.58/3.19 inference(skolemize,[status(sab)],[15])).
% 4.58/3.19 tff(17,plain,
% 4.58/3.19 (![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))))))),
% 4.58/3.19 inference(modus_ponens,[status(thm)],[16, 9])).
% 4.58/3.19 tff(18,plain,
% 4.58/3.19 (![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))))))),
% 4.58/3.19 inference(modus_ponens,[status(thm)],[17, 7])).
% 4.58/3.19 tff(19,plain,
% 4.58/3.19 (![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))))))),
% 4.58/3.19 inference(modus_ponens,[status(thm)],[18, 2])).
% 4.58/3.19 tff(20,plain,
% 4.58/3.19 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(F!29, F!29, thm)) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(F!29, F!29, thm))),
% 4.58/3.19 inference(rewrite,[status(thm)],[])).
% 4.58/3.19 tff(21,plain,
% 4.58/3.19 ((~(~status(F!29, F!29, thm))) <=> status(F!29, F!29, thm)),
% 4.58/3.19 inference(rewrite,[status(thm)],[])).
% 4.58/3.19 tff(22,plain,
% 4.58/3.19 (((~status(F!29, F!29, thm)) | $false) <=> (~status(F!29, F!29, thm))),
% 4.58/3.19 inference(rewrite,[status(thm)],[])).
% 4.58/3.19 tff(23,plain,
% 4.58/3.19 ((~$true) <=> $false),
% 4.58/3.19 inference(rewrite,[status(thm)],[])).
% 4.58/3.19 tff(24,plain,
% 4.58/3.19 (((~status(F!29, F!29, thm)) | $true) <=> $true),
% 4.58/3.19 inference(rewrite,[status(thm)],[])).
% 4.58/3.19 tff(25,plain,
% 4.58/3.19 (![I1: $i] : $true <=> $true),
% 4.58/3.19 inference(elim_unused_vars,[status(thm)],[])).
% 4.58/3.19 tff(26,plain,
% 4.58/3.19 (![I1: $i] : $true <=> ![I1: $i] : $true),
% 4.58/3.19 inference(rewrite,[status(thm)],[])).
% 4.58/3.19 tff(27,plain,
% 4.58/3.19 (![I1: $i] : $true <=> $true),
% 4.58/3.19 inference(transitivity,[status(thm)],[26, 25])).
% 4.58/3.19 tff(28,plain,
% 4.58/3.19 (^[I1: $i] : rewrite(((~model(I1, F!29)) | model(I1, F!29)) <=> $true)),
% 4.58/3.19 inference(bind,[status(th)],[])).
% 4.58/3.19 tff(29,plain,
% 4.58/3.19 (![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)) <=> ![I1: $i] : $true),
% 4.58/3.19 inference(quant_intro,[status(thm)],[28])).
% 4.58/3.19 tff(30,plain,
% 4.58/3.19 (![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)) <=> $true),
% 4.58/3.19 inference(transitivity,[status(thm)],[29, 27])).
% 4.58/3.19 tff(31,plain,
% 4.58/3.19 (((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))) <=> ((~status(F!29, F!29, thm)) | $true)),
% 4.58/3.19 inference(monotonicity,[status(thm)],[30])).
% 4.58/3.19 tff(32,plain,
% 4.58/3.19 (((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))) <=> $true),
% 4.58/3.19 inference(transitivity,[status(thm)],[31, 24])).
% 4.58/3.19 tff(33,plain,
% 4.58/3.19 ((~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)))) <=> (~$true)),
% 4.58/3.19 inference(monotonicity,[status(thm)],[32])).
% 4.58/3.19 tff(34,plain,
% 4.58/3.19 ((~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)))) <=> $false),
% 4.58/3.19 inference(transitivity,[status(thm)],[33, 23])).
% 4.58/3.19 tff(35,plain,
% 4.58/3.19 ((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) <=> (~status(F!29, F!29, thm))),
% 4.58/3.19 inference(rewrite,[status(thm)],[])).
% 4.58/3.19 tff(36,plain,
% 4.58/3.19 (((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))) <=> ((~status(F!29, F!29, thm)) | $false)),
% 4.58/3.19 inference(monotonicity,[status(thm)],[35, 34])).
% 4.58/3.19 tff(37,plain,
% 4.58/3.19 (((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))) <=> (~status(F!29, F!29, thm))),
% 4.58/3.19 inference(transitivity,[status(thm)],[36, 22])).
% 4.58/3.19 tff(38,plain,
% 4.58/3.19 ((~((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)))))) <=> (~(~status(F!29, F!29, thm)))),
% 4.58/3.19 inference(monotonicity,[status(thm)],[37])).
% 4.58/3.19 tff(39,plain,
% 4.58/3.19 ((~((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)))))) <=> status(F!29, F!29, thm)),
% 4.58/3.19 inference(transitivity,[status(thm)],[38, 21])).
% 4.58/3.19 tff(40,plain,
% 4.58/3.19 (((~![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(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(F!29, F!29, thm))),
% 4.58/3.19 inference(monotonicity,[status(thm)],[39])).
% 4.58/3.19 tff(41,plain,
% 4.58/3.19 (((~![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(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(F!29, F!29, thm))),
% 4.58/3.19 inference(transitivity,[status(thm)],[40, 20])).
% 4.58/3.19 tff(42,plain,
% 4.58/3.19 ((~![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(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))))),
% 4.58/3.19 inference(quant_inst,[status(thm)],[])).
% 4.58/3.19 tff(43,plain,
% 4.58/3.19 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(F!29, F!29, thm)),
% 4.58/3.19 inference(modus_ponens,[status(thm)],[42, 41])).
% 4.58/3.19 tff(44,plain,
% 4.58/3.19 (status(F!29, F!29, thm)),
% 4.58/3.19 inference(unit_resolution,[status(thm)],[43, 19])).
% 4.58/3.19 tff(45,plain,
% 4.58/3.19 (^[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)))))))))),
% 4.58/3.19 inference(bind,[status(th)],[])).
% 4.58/3.19 tff(46,plain,
% 4.58/3.19 (![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))))))))),
% 4.58/3.19 inference(quant_intro,[status(thm)],[45])).
% 4.58/3.19 tff(47,plain,
% 4.58/3.19 (^[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)))))))))),
% 4.58/3.19 inference(bind,[status(th)],[])).
% 4.58/3.19 tff(48,plain,
% 4.58/3.19 (![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))))))))),
% 4.58/3.20 inference(quant_intro,[status(thm)],[47])).
% 4.58/3.20 tff(49,plain,
% 4.58/3.20 (![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))))))))),
% 4.58/3.20 inference(transitivity,[status(thm)],[48, 46])).
% 4.58/3.20 tff(50,plain,
% 4.58/3.20 (^[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))))))))))),
% 4.58/3.20 inference(bind,[status(th)],[])).
% 4.58/3.20 tff(51,plain,
% 4.58/3.20 (![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))))))))),
% 4.67/3.20 inference(quant_intro,[status(thm)],[50])).
% 4.67/3.20 tff(52,plain,
% 4.67/3.20 (^[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)))))),
% 4.67/3.20 inference(bind,[status(th)],[])).
% 4.67/3.20 tff(53,plain,
% 4.67/3.20 (![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))))),
% 4.67/3.20 inference(quant_intro,[status(thm)],[52])).
% 4.67/3.20 tff(54,plain,
% 4.67/3.20 (![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))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(55,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','mighta')).
% 4.67/3.20 tff(56,plain,
% 4.67/3.20 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[55, 54])).
% 4.67/3.20 tff(57,plain,(
% 4.67/3.20 ![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))))),
% 4.67/3.20 inference(skolemize,[status(sab)],[56])).
% 4.67/3.20 tff(58,plain,
% 4.67/3.20 (![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))))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[57, 53])).
% 4.67/3.20 tff(59,plain,
% 4.67/3.20 (![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))))))))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[58, 51])).
% 4.67/3.20 tff(60,plain,
% 4.67/3.20 (![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))))))))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[59, 49])).
% 4.67/3.20 tff(61,plain,
% 4.67/3.20 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, thm)) | (~((~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), eth)) | (~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), thm))))))))),
% 4.67/3.20 inference(quant_inst,[status(thm)],[])).
% 4.67/3.20 tff(62,plain,
% 4.67/3.20 (~((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, thm)) | (~((~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), eth)) | (~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), thm)))))))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[61, 60])).
% 4.67/3.20 tff(63,plain,
% 4.67/3.20 (((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | (~((~mighta(eth, thm)) | (~((~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), eth)) | (~status(tptp_fun_Ax_19(thm, eth), tptp_fun_C_18(thm, eth), thm))))))) | (mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))),
% 4.67/3.20 inference(tautology,[status(thm)],[])).
% 4.67/3.20 tff(64,plain,
% 4.67/3.20 (mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[63, 62])).
% 4.67/3.20 tff(65,plain,
% 4.67/3.20 ((~mighta(eth, thm)) <=> (~mighta(eth, thm))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(66,axiom,(~mighta(eth, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mighta_eth_thm')).
% 4.67/3.20 tff(67,plain,
% 4.67/3.20 (~mighta(eth, thm)),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[66, 65])).
% 4.67/3.20 tff(68,plain,
% 4.67/3.20 ((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))),
% 4.67/3.20 inference(tautology,[status(thm)],[])).
% 4.67/3.20 tff(69,plain,
% 4.67/3.20 ((~(mighta(eth, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[68, 67])).
% 4.67/3.20 tff(70,plain,
% 4.67/3.20 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[69, 64])).
% 4.67/3.20 tff(71,plain,
% 4.67/3.20 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | ((~status(F!29, F!29, thm)) | (~status(F!29, F!29, eth)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | (~status(F!29, F!29, thm)) | (~status(F!29, F!29, eth)))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(72,plain,
% 4.67/3.20 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | ((~status(F!29, F!29, thm)) | (~status(F!29, F!29, eth)))),
% 4.67/3.20 inference(quant_inst,[status(thm)],[])).
% 4.67/3.20 tff(73,plain,
% 4.67/3.20 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eth)))) | (~status(F!29, F!29, thm)) | (~status(F!29, F!29, eth))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[72, 71])).
% 4.67/3.20 tff(74,plain,
% 4.67/3.20 (~status(F!29, F!29, eth)),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[73, 70, 44])).
% 4.67/3.20 tff(75,assumption,(![I2: $i] : model(I2, F!29)), introduced(assumption)).
% 4.67/3.20 tff(76,plain,
% 4.67/3.20 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(77,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 4.67/3.20 tff(78,plain,
% 4.67/3.20 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[77, 76])).
% 4.67/3.20 tff(79,plain,
% 4.67/3.20 (~model(I2!31, F!29)),
% 4.67/3.20 inference(and_elim,[status(thm)],[78])).
% 4.67/3.20 tff(80,plain,
% 4.67/3.20 ((~![I2: $i] : model(I2, F!29)) | model(I2!31, F!29)),
% 4.67/3.20 inference(quant_inst,[status(thm)],[])).
% 4.67/3.20 tff(81,plain,
% 4.67/3.20 ($false),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[80, 79, 75])).
% 4.67/3.20 tff(82,plain,(~![I2: $i] : model(I2, F!29)), inference(lemma,lemma(discharge,[]))).
% 4.67/3.20 tff(83,assumption,(![I1: $i] : (~model(I1, F!29))), introduced(assumption)).
% 4.67/3.20 tff(84,plain,
% 4.67/3.20 (model(I1!30, F!29)),
% 4.67/3.20 inference(and_elim,[status(thm)],[78])).
% 4.67/3.20 tff(85,plain,
% 4.67/3.20 ((~![I1: $i] : (~model(I1, F!29))) | (~model(I1!30, F!29))),
% 4.67/3.20 inference(quant_inst,[status(thm)],[])).
% 4.67/3.20 tff(86,plain,
% 4.67/3.20 ($false),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[85, 84, 83])).
% 4.67/3.20 tff(87,plain,(~![I1: $i] : (~model(I1, F!29))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.20 tff(88,plain,
% 4.67/3.20 ((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))) | ![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth)),
% 4.67/3.20 inference(tautology,[status(thm)],[])).
% 4.67/3.20 tff(89,plain,
% 4.67/3.20 (~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[88, 87, 82, 74])).
% 4.67/3.20 tff(90,plain,
% 4.67/3.20 (((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29))))))) | (![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))),
% 4.67/3.20 inference(tautology,[status(thm)],[])).
% 4.67/3.20 tff(91,plain,
% 4.67/3.20 ((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29))))))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[90, 89])).
% 4.67/3.20 tff(92,plain,
% 4.67/3.20 (^[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))))))))))),
% 4.67/3.20 inference(bind,[status(th)],[])).
% 4.67/3.20 tff(93,plain,
% 4.67/3.20 (![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)))))))))),
% 4.67/3.20 inference(quant_intro,[status(thm)],[92])).
% 4.67/3.20 tff(94,plain,
% 4.67/3.20 (^[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)))))))))),
% 4.67/3.20 inference(bind,[status(th)],[])).
% 4.67/3.20 tff(95,plain,
% 4.67/3.20 (![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))))))))),
% 4.67/3.20 inference(quant_intro,[status(thm)],[94])).
% 4.67/3.20 tff(96,plain,
% 4.67/3.20 (^[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)))))))))),
% 4.67/3.20 inference(bind,[status(th)],[])).
% 4.67/3.20 tff(97,plain,
% 4.67/3.20 (![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))))))))),
% 4.67/3.20 inference(quant_intro,[status(thm)],[96])).
% 4.67/3.20 tff(98,plain,
% 4.67/3.20 (![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))))))))),
% 4.67/3.20 inference(transitivity,[status(thm)],[97, 95])).
% 4.67/3.20 tff(99,plain,
% 4.67/3.20 (^[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))))))))))),
% 4.67/3.20 inference(bind,[status(th)],[])).
% 4.67/3.20 tff(100,plain,
% 4.67/3.20 (![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))))))))),
% 4.67/3.20 inference(quant_intro,[status(thm)],[99])).
% 4.67/3.20 tff(101,plain,
% 4.67/3.20 (^[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)))))),
% 4.67/3.20 inference(bind,[status(th)],[])).
% 4.67/3.20 tff(102,plain,
% 4.67/3.20 (![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))))),
% 4.67/3.20 inference(quant_intro,[status(thm)],[101])).
% 4.67/3.20 tff(103,plain,
% 4.67/3.20 (![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))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(104,plain,
% 4.67/3.20 (^[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)))),
% 4.67/3.20 inference(bind,[status(th)],[])).
% 4.67/3.20 tff(105,plain,
% 4.67/3.20 (![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))),
% 4.67/3.20 inference(quant_intro,[status(thm)],[104])).
% 4.67/3.20 tff(106,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/sandbox/benchmark/Axioms/KRS001+0.ax','eth')).
% 4.67/3.20 tff(107,plain,
% 4.67/3.20 (![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))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[106, 105])).
% 4.67/3.20 tff(108,plain,
% 4.67/3.20 (![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))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[107, 103])).
% 4.67/3.20 tff(109,plain,(
% 4.67/3.20 ![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))))),
% 4.67/3.20 inference(skolemize,[status(sab)],[108])).
% 4.67/3.20 tff(110,plain,
% 4.67/3.20 (![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))))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[109, 102])).
% 4.67/3.20 tff(111,plain,
% 4.67/3.20 (![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))))))))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[110, 100])).
% 4.67/3.20 tff(112,plain,
% 4.67/3.20 (![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))))))))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[111, 98])).
% 4.67/3.20 tff(113,plain,
% 4.67/3.20 (![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)))))))))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[112, 93])).
% 4.67/3.20 tff(114,plain,
% 4.67/3.20 (((~![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)))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(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)))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)))))))))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(115,plain,
% 4.67/3.20 ((~((~(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))))))))) <=> (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29))))))))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(116,plain,
% 4.67/3.20 (((~![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)))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)))))))))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[115])).
% 4.67/3.20 tff(117,plain,
% 4.67/3.20 (((~![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)))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)))))))))),
% 4.67/3.20 inference(transitivity,[status(thm)],[116, 114])).
% 4.67/3.20 tff(118,plain,
% 4.67/3.20 ((~![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)))))))))),
% 4.67/3.21 inference(quant_inst,[status(thm)],[])).
% 4.67/3.21 tff(119,plain,
% 4.67/3.21 ((~![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)))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | status(F!29, F!29, eth))) | (~((~status(F!29, F!29, eth)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29))))))))),
% 4.67/3.21 inference(modus_ponens,[status(thm)],[118, 117])).
% 4.67/3.21 tff(120,plain,
% 4.67/3.21 ($false),
% 4.67/3.21 inference(unit_resolution,[status(thm)],[119, 113, 91])).
% 4.67/3.21 % SZS output end Proof
%------------------------------------------------------------------------------