TSTP Solution File: SCT064-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SCT064-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 03:41:29 EDT 2022
% Result : Unsatisfiable 0.19s 0.58s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT064-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 23:46:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.58 % SZS status Unsatisfiable
% 0.19/0.58 % SZS output start Proof
% 0.19/0.58 tff(c_in_type, type, (
% 0.19/0.58 c_in: ( $i * $i * $i ) > $o)).
% 0.19/0.58 tff(tc_prod_type, type, (
% 0.19/0.58 tc_prod: ( $i * $i ) > $i)).
% 0.19/0.58 tff(tc_Arrow__Order__Mirabelle_Oalt_type, type, (
% 0.19/0.58 tc_Arrow__Order__Mirabelle_Oalt: $i)).
% 0.19/0.58 tff(v_F_type, type, (
% 0.19/0.58 v_F: $i > $i)).
% 0.19/0.58 tff(c_Fun_Ocomp_type, type, (
% 0.19/0.58 c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.58 tff(tc_Arrow__Order__Mirabelle_Oindi_type, type, (
% 0.19/0.58 tc_Arrow__Order__Mirabelle_Oindi: $i)).
% 0.19/0.58 tff(tc_fun_type, type, (
% 0.19/0.58 tc_fun: ( $i * $i ) > $i)).
% 0.19/0.58 tff(tc_bool_type, type, (
% 0.19/0.58 tc_bool: $i)).
% 0.19/0.58 tff(v_P_____type, type, (
% 0.19/0.58 v_P____: $i)).
% 0.19/0.58 tff(c_Relation_Oconverse_type, type, (
% 0.19/0.58 c_Relation_Oconverse: ( $i * $i ) > $i)).
% 0.19/0.58 tff(c_Pair_type, type, (
% 0.19/0.58 c_Pair: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.58 tff(v_a_____type, type, (
% 0.19/0.58 v_a____: $i)).
% 0.19/0.58 tff(v_b_____type, type, (
% 0.19/0.58 v_b____: $i)).
% 0.19/0.58 tff(v_P_H_____type, type, (
% 0.19/0.58 v_P_H____: $i)).
% 0.19/0.58 tff(v_c_____type, type, (
% 0.19/0.58 v_c____: $i)).
% 0.19/0.58 tff(1,assumption,(~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))), introduced(assumption)).
% 0.19/0.58 tff(2,plain,
% 0.19/0.58 (((~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) <=> ((~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(3,plain,
% 0.19/0.58 ((c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))) <=> ((~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(4,axiom,(c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_CHAINED_0_02')).
% 0.19/0.59 tff(5,plain,
% 0.19/0.59 ((~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.59 tff(6,plain,
% 0.19/0.59 ((~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.59 tff(7,plain,
% 0.19/0.59 (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.19/0.59 tff(8,plain,
% 0.19/0.59 ((c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) <=> (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(9,axiom,(c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.19/0.59 tff(10,plain,
% 0.19/0.59 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.59 tff(11,plain,
% 0.19/0.59 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[10, 1])).
% 0.19/0.59 tff(12,plain,
% 0.19/0.59 ((c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))) <=> (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(13,axiom,(c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_CHAINED_0')).
% 0.19/0.59 tff(14,plain,
% 0.19/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.59 tff(15,plain,
% 0.19/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.19/0.59 tff(16,plain,
% 0.19/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.59 tff(17,plain,
% 0.19/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.59 tff(18,plain,
% 0.19/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.19/0.59 tff(19,plain,
% 0.19/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.19/0.59 tff(20,plain,
% 0.19/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.49/0.59 tff(21,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.49/0.59 tff(22,plain,
% 0.49/0.59 ($false),
% 0.49/0.59 inference(unit_resolution,[status(thm)],[21, 11, 7])).
% 0.49/0.59 tff(23,plain,(c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.59 tff(24,plain,
% 0.49/0.59 ((c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))) <=> (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))))),
% 0.49/0.59 inference(rewrite,[status(thm)],[])).
% 0.49/0.59 tff(25,axiom,(c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_CHAINED_1_01')).
% 0.49/0.59 tff(26,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.49/0.59 tff(27,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[26, 24])).
% 0.49/0.59 tff(28,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.49/0.59 tff(29,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.49/0.59 tff(30,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.49/0.59 tff(31,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.49/0.59 tff(32,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.49/0.59 tff(33,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.49/0.59 tff(34,plain,
% 0.49/0.59 (c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))),
% 0.49/0.59 inference(unit_resolution,[status(thm)],[33, 23])).
% 0.49/0.59 tff(35,plain,
% 0.49/0.59 (((~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))) <=> ((~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))))),
% 0.49/0.59 inference(rewrite,[status(thm)],[])).
% 0.49/0.59 tff(36,plain,
% 0.49/0.59 (((~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))) <=> ((~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))))),
% 0.49/0.59 inference(rewrite,[status(thm)],[])).
% 0.49/0.59 tff(37,axiom,((~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.49/0.59 tff(38,plain,
% 0.49/0.59 ((~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.49/0.59 tff(39,plain,
% 0.49/0.59 ((~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))) | (~c_in(c_Pair(v_b____, v_c____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P_H____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.49/0.59 tff(40,plain,
% 0.49/0.59 (~c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))),
% 0.49/0.59 inference(unit_resolution,[status(thm)],[39, 23])).
% 0.49/0.59 tff(41,plain,
% 0.49/0.59 ((c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))) <=> (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))))),
% 0.49/0.59 inference(rewrite,[status(thm)],[])).
% 0.49/0.59 tff(42,axiom,(c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_CHAINED_1')).
% 0.49/0.59 tff(43,plain,
% 0.49/0.59 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.49/0.60 tff(44,plain,
% 0.49/0.60 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[43, 41])).
% 0.49/0.60 tff(45,plain,
% 0.49/0.60 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.49/0.60 tff(46,plain,
% 0.49/0.60 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.49/0.60 tff(47,plain,
% 0.49/0.60 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.49/0.60 tff(48,plain,
% 0.49/0.60 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[47, 41])).
% 0.51/0.62 tff(49,plain,
% 0.51/0.62 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.51/0.62 tff(50,plain,
% 0.51/0.62 (c_in(c_Pair(v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | (~c_in(c_Pair(v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_F(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_Arrow__Order__Mirabelle_Oindi)), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[49, 41])).
% 0.51/0.62 tff(51,plain,
% 0.51/0.62 ($false),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[50, 40, 34])).
% 0.51/0.62 % SZS output end Proof
%------------------------------------------------------------------------------