TSTP Solution File: LCL442-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL442-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Sun Sep 18 04:56:18 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL442-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.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 : Thu Sep 1 21:25:12 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.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(c_in_type, type, (
% 0.19/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tc_PropLog_Opl_type, type, (
% 0.19/0.39 tc_PropLog_Opl: $i > $i)).
% 0.19/0.39 tff(t_a_type, type, (
% 0.19/0.39 t_a: $i)).
% 0.19/0.39 tff(c_PropLog_Othms_type, type, (
% 0.19/0.39 c_PropLog_Othms: ( $i * $i ) > $i)).
% 0.19/0.39 tff(c_union_type, type, (
% 0.19/0.39 c_union: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(c_PropLog_Ohyps_type, type, (
% 0.19/0.39 c_PropLog_Ohyps: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(v_tt_type, type, (
% 0.19/0.39 v_tt: $i)).
% 0.19/0.39 tff(v_pl2_type, type, (
% 0.19/0.39 v_pl2: $i)).
% 0.19/0.39 tff(v_pl1_type, type, (
% 0.19/0.39 v_pl1: $i)).
% 0.19/0.39 tff(c_PropLog_Opl_Oop_A_N_62_type, type, (
% 0.19/0.39 c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(c_PropLog_Oeval_type, type, (
% 0.19/0.39 c_PropLog_Oeval: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(c_PropLog_Opl_Ofalse_type, type, (
% 0.19/0.39 c_PropLog_Opl_Ofalse: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[V_q: $i, V_H: $i, T_a: $i, V_p: $i] : refl(((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_PropLog_Oweaken__right_0')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,assumption,(~c_PropLog_Oeval(v_tt, v_pl2, t_a)), introduced(assumption)).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ((c_PropLog_Oeval(v_tt, v_pl2, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) <=> (c_PropLog_Oeval(v_tt, v_pl2, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 ((c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a)) <=> (c_PropLog_Oeval(v_tt, v_pl2, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(11,axiom,(c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (c_PropLog_Oeval(v_tt, v_pl2, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (c_PropLog_Oeval(v_tt, v_pl2, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[13, 8])).
% 0.19/0.39 tff(15,assumption,(~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (^[T_a: $i, V_p: $i, V_A: $i, V_G: $i] : refl(((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))) <=> ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))) <=> ![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))) <=> ![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(19,axiom,(![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_PropLog_Oweaken__left__Un2_0')).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.39 tff(21,plain,(
% 0.19/0.39 ![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.39 tff(23,assumption,(c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (((~![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 ((~![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 ((~![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[26, 23, 22, 15])).
% 0.19/0.40 tff(28,plain,(c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[28, 14])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (^[V_q: $i, V_H: $i, T_a: $i, V_p: $i] : refl(((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(33,axiom,(![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_PropLog_Ofalse__imp_0')).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.40 tff(35,plain,(
% 0.19/0.40 ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.40 tff(37,assumption,(~c_PropLog_Oeval(v_tt, v_pl1, t_a)), introduced(assumption)).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> (c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(39,axiom,(c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 38])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[47, 37])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[51, 48, 36])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[T_a: $i, V_p: $i, V_B: $i, V_G: $i] : refl(((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))) <=> ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))) <=> ![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))) <=> ![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(56,axiom,(![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_PropLog_Oweaken__left__Un1_0')).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,(
% 0.19/0.41 ![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[57])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 ((c_PropLog_Oeval(v_tt, v_pl1, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) <=> (c_PropLog_Oeval(v_tt, v_pl1, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | c_PropLog_Oeval(v_tt, v_pl1, t_a)) <=> (c_PropLog_Oeval(v_tt, v_pl1, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,axiom,(c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | c_PropLog_Oeval(v_tt, v_pl1, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (c_PropLog_Oeval(v_tt, v_pl1, t_a) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[64, 37])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (((~![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 ((~![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((~![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 65, 59, 52])).
% 0.19/0.41 tff(70,plain,(c_PropLog_Oeval(v_tt, v_pl1, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 ((c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))) <=> (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(72,axiom,(c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[73, 71])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[74, 71])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 71])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 71])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[79, 71])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[80, 70])).
% 0.19/0.41 tff(82,assumption,(~c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 0.19/0.41 tff(83,assumption,(c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (((~![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((~![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[86, 83, 59, 82])).
% 0.19/0.42 tff(88,plain,(c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[88, 81])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (^[V_q: $i, V_H: $i, T_a: $i, V_p: $i] : refl((c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) <=> (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) <=> ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) <=> ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (^[V_q: $i, V_H: $i, T_a: $i, V_p: $i] : trans(monotonicity(rewrite(((~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) <=> ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))), ((((~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> (((~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))), rewrite((((~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))), ((((~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (((~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.42 tff(95,axiom,(![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (((~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_PropLog_Oimp__false_0')).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.42 tff(98,plain,(
% 0.19/0.42 ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[97])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 ((((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_PropLog_Oeval(v_tt, v_pl2, t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))) <=> ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(102,axiom,(((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_PropLog_Oeval(v_tt, v_pl2, t_a)) | (~c_PropLog_Oeval(v_tt, v_pl1, t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_9')).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 100])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[105, 100])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[106, 100])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[108, 100])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~c_PropLog_Oeval(v_tt, v_pl1, t_a)) | c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[109, 100])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (c_PropLog_Oeval(v_tt, v_pl2, t_a) | (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 70])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[111, 8])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))) <=> ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[115, 112, 99, 89, 29])).
% 0.19/0.43 tff(117,plain,(c_PropLog_Oeval(v_tt, v_pl2, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (((~c_PropLog_Oeval(v_tt, v_pl2, t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~c_PropLog_Oeval(v_tt, v_pl2, t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(119,axiom,((~c_PropLog_Oeval(v_tt, v_pl2, t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 ((~c_PropLog_Oeval(v_tt, v_pl2, t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(v_pl2, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_pl2, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(v_pl2, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_pl2, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (~c_in(v_pl2, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[124, 121, 7])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 ((c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))) <=> (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(127,axiom,(c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[128, 126])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[129, 126])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[131, 126])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[132, 126])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Oeval(v_tt, v_pl2, t_a))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[134, 126])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[135, 117])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 (((~![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(v_pl2, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(v_pl2, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 ((~![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | ((~c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(v_pl2, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 ((~![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(v_pl2, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[139, 136, 22, 125])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------