TSTP Solution File: KRS251+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS251+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 17:45:19 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS251+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n019.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 10:13:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(model_type, type, (
% 0.19/0.40 model: ( $i * $i ) > $o)).
% 0.19/0.40 tff(not_type, type, (
% 0.19/0.40 not: $i > $i)).
% 0.19/0.40 tff(tptp_fun_C_26_type, type, (
% 0.19/0.40 tptp_fun_C_26: ( $i * $i ) > $i)).
% 0.19/0.40 tff(csa_type, type, (
% 0.19/0.40 csa: $i)).
% 0.19/0.40 tff(thm_type, type, (
% 0.19/0.40 thm: $i)).
% 0.19/0.40 tff(tptp_fun_I1_14_type, type, (
% 0.19/0.40 tptp_fun_I1_14: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Ax_27_type, type, (
% 0.19/0.40 tptp_fun_Ax_27: ( $i * $i ) > $i)).
% 0.19/0.40 tff(status_type, type, (
% 0.19/0.40 status: ( $i * $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_I1_3_type, type, (
% 0.19/0.40 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 0.19/0.40 tff(xora_type, type, (
% 0.19/0.40 xora: ( $i * $i ) > $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[I: $i, F: $i] : refl(((~model(I, F)) <=> model(I, not(F))) <=> ((~model(I, F)) <=> model(I, not(F))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (^[I: $i, F: $i] : rewrite((~(model(I, F) <=> model(I, not(F)))) <=> ((~model(I, F)) <=> model(I, not(F))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.40 tff(6,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','completeness')).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.40 tff(9,plain,(
% 0.19/0.40 ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[8])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 ((~![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))) | ((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 ((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.40 tff(13,assumption,(~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) <=> model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))), introduced(assumption)).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 ((~![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))) | ((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) <=> model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[14, 10, 13])).
% 0.19/0.40 tff(16,plain,((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) <=> model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(17,assumption,(~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)), introduced(assumption)).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (^[S1: $i, S2: $i] : rewrite((~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~((~xora(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~((~xora(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (^[S1: $i, S2: $i] : refl((~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (^[S1: $i, S2: $i] : rewrite((~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[23, 21])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))), (((xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))) <=> ((xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))), rewrite(((xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))))), (((xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))) <=> (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : ((xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (^[S1: $i, S2: $i] : rewrite((((~((~status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1)) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) | xora(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))) <=> ((xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1)) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) | xora(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2)))) <=> ![S1: $i, S2: $i] : ((xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) <=> xora(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) <=> xora(S1, S2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (^[S1: $i, S2: $i] : rewrite((![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) <=> xora(S1, S2)) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) <=> xora(S1, S2)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) <=> xora(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) <=> xora(S1, S2))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.41 tff(32,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (~(status(Ax, C, S1) <=> status(Ax, C, S2))) <=> xora(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','xora')).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) <=> xora(S1, S2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) <=> xora(S1, S2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.41 tff(35,plain,(
% 0.19/0.41 ![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1)) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) | xora(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[34])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : ((xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2))) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2)) | (~xora(S1, S2))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 24])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~((~xora(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 19])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![S1: $i, S2: $i] : (~((~(xora(S1, S2) | (status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S1) <=> status(tptp_fun_Ax_27(S2, S1), tptp_fun_C_26(S2, S1), S2)))) | (~((~xora(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) <=> status(Ax, C, S2))))))) | (~((~(xora(csa, thm) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)))) | (~((~xora(csa, thm)) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) <=> status(Ax, C, thm))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (~((~(xora(csa, thm) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)))) | (~((~xora(csa, thm)) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) <=> status(Ax, C, thm)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (((~(xora(csa, thm) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)))) | (~((~xora(csa, thm)) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) <=> status(Ax, C, thm))))) | (xora(csa, thm) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (xora(csa, thm) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~xora(csa, thm)) <=> (~xora(csa, thm))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(45,axiom,(~xora(csa, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','xora_csa_thm')).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (~xora(csa, thm)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~(xora(csa, thm) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)))) | xora(csa, thm) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 ((~(xora(csa, thm) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)))) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[48, 43])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((~(status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | (~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | (~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[51, 17])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[58, 56])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))), rewrite((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (^[Ax: $i, C: $i] : rewrite((![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.41 tff(65,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')).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.41 tff(68,plain,(
% 0.19/0.41 ![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 54])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))) | (~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))) | (~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (((~((~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))) | (~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))))) | ((~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ((~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[77, 52])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) | (~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ((~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) <=> model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[81, 80, 16])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) <=> (status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))), trans(monotonicity(rewrite((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) <=> (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))), (((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))) <=> ((~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))) | (~status(Ax, C, csa))))), rewrite(((~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))) | (~status(Ax, C, csa))) <=> ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))), (((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))) <=> ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))), (((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ((status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))) & ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))), rewrite(((status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))) & ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))), (((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (^[Ax: $i, C: $i] : rewrite(((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa)) <=> ![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(95,axiom,(![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','csa')).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.43 tff(97,plain,(
% 0.19/0.43 ![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[96])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[100, 84])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))))) | (~(status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (~((~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))))) | (~(status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (((~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))))) | (~(status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))))) | (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa))))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 ((~(status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa))))))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[107, 17])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[109, 78])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (((~![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))) | ((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))) <=> ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))) | (~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))) | ((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))) | (~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[113, 110, 108, 82])).
% 0.19/0.43 tff(115,plain,(status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (((~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))))) | (~(status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | (~model(I1, not(tptp_fun_C_26(thm, csa)))))))) | ((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 ((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[116, 103])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 ((~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))))) | (~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 ((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[119, 115])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))) | model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 ((~(status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa) <=> status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))) | (~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 ((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), csa)) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[123, 49])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[124, 115])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (((~((~((~model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_3(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) | status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm))) | (~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))))) | ((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 ((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[126, 73])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 ((~((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa))))) | (~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 ((~status(tptp_fun_Ax_27(thm, csa), tptp_fun_C_26(thm, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 (![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[129, 125])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 (((~![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))) | ((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))) <=> ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))) | ((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_27(thm, csa))) | model(I1, tptp_fun_C_26(thm, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[133, 130, 122])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_Ax_27(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))) | model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 (model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[135, 120])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 ((~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 ((~((~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), not(tptp_fun_C_26(thm, csa))))) | (~model(tptp_fun_I1_14(tptp_fun_C_26(thm, csa), tptp_fun_Ax_27(thm, csa)), tptp_fun_C_26(thm, csa)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[138, 134, 12])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------