%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL442-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:03 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL442-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 20:37:07 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(c_in_type, type, (
% 0.13/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(tc_PropLog_Opl_type, type, (
% 0.13/0.39 tc_PropLog_Opl: $i > $i)).
% 0.13/0.39 tff(t_a_type, type, (
% 0.13/0.39 t_a: $i)).
% 0.13/0.39 tff(c_PropLog_Othms_type, type, (
% 0.13/0.39 c_PropLog_Othms: ( $i * $i ) > $i)).
% 0.13/0.39 tff(c_PropLog_Ohyps_type, type, (
% 0.13/0.39 c_PropLog_Ohyps: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(v_tt_type, type, (
% 0.13/0.39 v_tt: $i)).
% 0.13/0.39 tff(v_pl2_type, type, (
% 0.13/0.39 v_pl2: $i)).
% 0.13/0.39 tff(c_PropLog_Opl_Oop_A_N_62_type, type, (
% 0.13/0.39 c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(v_pl1_type, type, (
% 0.13/0.39 v_pl1: $i)).
% 0.13/0.39 tff(c_union_type, type, (
% 0.13/0.39 c_union: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(c_PropLog_Oeval_type, type, (
% 0.13/0.39 c_PropLog_Oeval: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(c_PropLog_Opl_Ofalse_type, type, (
% 0.13/0.39 c_PropLog_Opl_Ofalse: $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,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/sandbox/benchmark/theBenchmark.p','cls_PropLog_Oweaken__left__Un2_0')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,(
% 0.13/0.39 ![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)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,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)).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(12,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/sandbox/benchmark/theBenchmark.p','cls_PropLog_Oweaken__left__Un1_0')).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.13/0.39 tff(14,plain,(
% 0.13/0.39 ![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)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.13/0.39 tff(16,assumption,(~c_PropLog_Oeval(v_tt, v_pl1, t_a)), introduced(assumption)).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 ((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))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(18,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (~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))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[23, 16])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (((~![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, v_pl2, 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, 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)))) <=> ((~![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, v_pl2, 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, 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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~![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, v_pl2, 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, 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)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 ((~![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, v_pl2, 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, 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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[27, 24, 15])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(32,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/sandbox/benchmark/theBenchmark.p','cls_PropLog_Ofalse__imp_0')).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.13/0.39 tff(34,plain,(
% 0.13/0.39 ![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)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[33])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ((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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(38,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[40, 16])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (((~![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_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, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, 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_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, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((~![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_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, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[44, 41, 35, 28])).
% 0.13/0.39 tff(46,plain,(c_PropLog_Oeval(v_tt, v_pl1, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ((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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(48,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[49, 47])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[52, 47])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 (c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[53, 46])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (((~![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 ((~![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)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 ((~![T_a: $i, V_p: $i, V_B: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_G, V_B, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_pl1, c_PropLog_Othms(c_PropLog_Ohyps(v_pl1, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[57, 54, 15, 8])).
% 0.13/0.39 tff(59,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))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(60,assumption,(~c_PropLog_Oeval(v_tt, v_pl2, t_a)), introduced(assumption)).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 ((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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 ((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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(63,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[64, 61])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[65, 60])).
% 0.13/0.39 tff(67,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)).
% 0.13/0.39 tff(68,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)).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (((~![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 ((~![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)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 ((~![T_a: $i, V_p: $i, V_A: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_union(V_A, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[71, 68, 7, 67])).
% 0.13/0.39 tff(73,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,[]))).
% 0.13/0.39 tff(74,plain,
% 0.13/0.39 (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))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[73, 66])).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 (^[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)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(76,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.13/0.39 tff(77,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 (^[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))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(79,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[78])).
% 0.13/0.39 tff(80,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/sandbox/benchmark/theBenchmark.p','cls_PropLog_Oimp__false_0')).
% 0.13/0.39 tff(81,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.13/0.39 tff(82,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.13/0.39 tff(83,plain,(
% 0.13/0.39 ![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))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[82])).
% 0.13/0.39 tff(84,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.13/0.39 tff(85,plain,
% 0.13/0.39 (((~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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 ((((~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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(87,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_9')).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 ((~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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 ((~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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 ((~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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 ((~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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[90, 85])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 ((~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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[91, 85])).
% 0.13/0.40 tff(93,plain,
% 0.13/0.40 (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)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[92, 46])).
% 0.13/0.40 tff(94,plain,
% 0.13/0.40 (~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))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[93, 60])).
% 0.13/0.40 tff(95,plain,
% 0.13/0.40 (((~![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(96,plain,
% 0.13/0.40 ((~![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))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(97,plain,
% 0.13/0.40 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_q, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_pl1, c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1, v_tt, t_a), c_PropLog_Ohyps(v_pl2, v_tt, t_a), tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.13/0.40 tff(98,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[97, 94, 84, 74, 59])).
% 0.13/0.40 tff(99,plain,(c_PropLog_Oeval(v_tt, v_pl2, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(100,plain,
% 0.13/0.40 (((~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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(101,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.13/0.40 tff(102,plain,
% 0.13/0.40 ((~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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.13/0.40 tff(103,plain,
% 0.13/0.40 (~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))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.13/0.40 tff(104,plain,
% 0.13/0.40 (((~![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_pl1, v_pl2, 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_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)))) <=> ((~![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_pl1, v_pl2, 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_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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(105,plain,
% 0.13/0.40 ((~![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_pl1, v_pl2, 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_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)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(106,plain,
% 0.13/0.40 ((~![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_pl1, v_pl2, 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_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))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.13/0.40 tff(107,plain,
% 0.13/0.40 (~c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[106, 103, 7])).
% 0.13/0.40 tff(108,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(109,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[108])).
% 0.13/0.40 tff(110,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(111,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/sandbox/benchmark/theBenchmark.p','cls_PropLog_Oweaken__right_0')).
% 0.13/0.40 tff(112,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.13/0.40 tff(113,plain,(
% 0.13/0.40 ![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)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[112])).
% 0.13/0.40 tff(114,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.13/0.40 tff(115,plain,
% 0.13/0.40 ((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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(116,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.13/0.40 tff(117,plain,
% 0.13/0.40 (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))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.13/0.40 tff(118,plain,
% 0.13/0.40 (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))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[117, 115])).
% 0.13/0.40 tff(119,plain,
% 0.13/0.40 (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))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[118, 115])).
% 0.13/0.40 tff(120,plain,
% 0.13/0.40 (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))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.13/0.40 tff(121,plain,
% 0.13/0.40 (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))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[120, 115])).
% 0.13/0.40 tff(122,plain,
% 0.13/0.40 (c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[121, 99])).
% 0.13/0.40 tff(123,plain,
% 0.13/0.40 (((~![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_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_pl1, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, 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_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_pl1, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(124,plain,
% 0.13/0.40 ((~![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_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_pl1, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(125,plain,
% 0.13/0.40 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_pl2, c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1, v_pl2, t_a), c_PropLog_Othms(c_PropLog_Ohyps(v_pl2, v_tt, t_a), t_a), tc_PropLog_Opl(t_a))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.13/0.40 tff(126,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[125, 122, 114, 107])).
% 0.13/0.40 % SZS output end Proof
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------