TSTP Solution File: LCL443-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL443-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 2.05s 1.55s
% Output : Proof 2.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : LCL443-2 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n002.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 21:40:30 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 2.05/1.55 % SZS status Unsatisfiable
% 2.05/1.55 % SZS output start Proof
% 2.05/1.55 tff(c_in_type, type, (
% 2.05/1.55 c_in: ( $i * $i * $i ) > $o)).
% 2.05/1.55 tff(tc_PropLog_Opl_type, type, (
% 2.05/1.55 tc_PropLog_Opl: $i > $i)).
% 2.05/1.55 tff(t_a_type, type, (
% 2.05/1.55 t_a: $i)).
% 2.05/1.55 tff(c_PropLog_Othms_type, type, (
% 2.05/1.55 c_PropLog_Othms: ( $i * $i ) > $i)).
% 2.05/1.55 tff(c_insert_type, type, (
% 2.05/1.55 c_insert: ( $i * $i * $i ) > $i)).
% 2.05/1.55 tff(v_H_type, type, (
% 2.05/1.55 v_H: $i)).
% 2.05/1.55 tff(c_PropLog_Opl_Oop_A_N_62_type, type, (
% 2.05/1.55 c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i)).
% 2.05/1.55 tff(v_q_type, type, (
% 2.05/1.55 v_q: $i)).
% 2.05/1.55 tff(v_p_type, type, (
% 2.05/1.55 v_p: $i)).
% 2.05/1.55 tff(c_PropLog_Opl_Ofalse_type, type, (
% 2.05/1.55 c_PropLog_Opl_Ofalse: $i)).
% 2.05/1.55 tff(1,assumption,(~c_in(c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 2.05/1.55 tff(2,plain,
% 2.05/1.55 (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))),
% 2.05/1.55 inference(rewrite,[status(thm)],[])).
% 2.05/1.55 tff(3,axiom,(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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 2.05/1.55 tff(4,plain,
% 2.05/1.55 (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))),
% 2.05/1.55 inference(modus_ponens,[status(thm)],[3, 2])).
% 2.05/1.55 tff(5,plain,
% 2.05/1.55 (^[V_a: $i, T_a: $i, V_p: $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_insert(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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))))),
% 2.05/1.55 inference(bind,[status(th)],[])).
% 2.05/1.55 tff(6,plain,
% 2.05/1.55 (![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))) <=> ![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.55 inference(quant_intro,[status(thm)],[5])).
% 2.05/1.55 tff(7,plain,
% 2.05/1.55 (![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a))) <=> ![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.55 inference(rewrite,[status(thm)],[])).
% 2.05/1.55 tff(8,axiom,(![V_a: $i, T_a: $i, V_p: $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_insert(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__insert_0')).
% 2.05/1.55 tff(9,plain,
% 2.05/1.55 (![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.55 inference(modus_ponens,[status(thm)],[8, 7])).
% 2.05/1.55 tff(10,plain,(
% 2.05/1.55 ![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.55 inference(skolemize,[status(sab)],[9])).
% 2.05/1.55 tff(11,plain,
% 2.05/1.55 (![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.55 inference(modus_ponens,[status(thm)],[10, 6])).
% 2.05/1.55 tff(12,plain,
% 2.05/1.55 (((~![V_a: $i, T_a: $i, V_p: $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_insert(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_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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~![V_a: $i, T_a: $i, V_p: $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_insert(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_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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(13,plain,
% 2.05/1.56 ((~![V_a: $i, T_a: $i, V_p: $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_insert(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_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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.56 inference(quant_inst,[status(thm)],[])).
% 2.05/1.56 tff(14,plain,
% 2.05/1.56 ((~![V_a: $i, T_a: $i, V_p: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[13, 12])).
% 2.05/1.56 tff(15,plain,
% 2.05/1.56 ($false),
% 2.05/1.56 inference(unit_resolution,[status(thm)],[14, 11, 4, 1])).
% 2.05/1.56 tff(16,plain,(c_in(c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), inference(lemma,lemma(discharge,[]))).
% 2.05/1.56 tff(17,assumption,(~c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 2.05/1.56 tff(18,plain,
% 2.05/1.56 (^[V_x: $i, T_a: $i, V_B: $i] : refl(c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> c_in(V_x, c_insert(V_x, V_B, T_a), T_a))),
% 2.05/1.56 inference(bind,[status(th)],[])).
% 2.05/1.56 tff(19,plain,
% 2.05/1.56 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 2.05/1.56 inference(quant_intro,[status(thm)],[18])).
% 2.05/1.56 tff(20,plain,
% 2.05/1.56 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(21,axiom,(![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OinsertCI_1')).
% 2.05/1.56 tff(22,plain,
% 2.05/1.56 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[21, 20])).
% 2.05/1.56 tff(23,plain,(
% 2.05/1.56 ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 2.05/1.56 inference(skolemize,[status(sab)],[22])).
% 2.05/1.56 tff(24,plain,
% 2.05/1.56 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[23, 19])).
% 2.05/1.56 tff(25,plain,
% 2.05/1.56 ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 2.05/1.56 inference(quant_inst,[status(thm)],[])).
% 2.05/1.56 tff(26,plain,
% 2.05/1.56 (c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 2.05/1.56 inference(unit_resolution,[status(thm)],[25, 24])).
% 2.05/1.56 tff(27,plain,
% 2.05/1.56 (^[V_H: $i, T_a: $i, V_p: $i] : refl(((~c_in(V_p, V_H, 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, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 2.05/1.56 inference(bind,[status(th)],[])).
% 2.05/1.56 tff(28,plain,
% 2.05/1.56 (![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> ![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.56 inference(quant_intro,[status(thm)],[27])).
% 2.05/1.56 tff(29,plain,
% 2.05/1.56 (![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) <=> ![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(30,axiom,(![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_PropLog_Othms_OH_0')).
% 2.05/1.56 tff(31,plain,
% 2.05/1.56 (![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[30, 29])).
% 2.05/1.56 tff(32,plain,(
% 2.05/1.56 ![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.56 inference(skolemize,[status(sab)],[31])).
% 2.05/1.56 tff(33,plain,
% 2.05/1.56 (![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[32, 28])).
% 2.05/1.56 tff(34,plain,
% 2.05/1.56 (((~![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, 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_p, v_q, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, 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_p, v_q, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(35,plain,
% 2.05/1.56 ((~![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, 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_p, v_q, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.56 inference(quant_inst,[status(thm)],[])).
% 2.05/1.56 tff(36,plain,
% 2.05/1.56 ((~![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[35, 34])).
% 2.05/1.56 tff(37,plain,
% 2.05/1.56 ($false),
% 2.05/1.56 inference(unit_resolution,[status(thm)],[36, 33, 26, 17])).
% 2.05/1.56 tff(38,plain,(c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), inference(lemma,lemma(discharge,[]))).
% 2.05/1.56 tff(39,assumption,(~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 2.05/1.56 tff(40,plain,
% 2.05/1.56 (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))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(41,axiom,(c_in(v_p, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 2.05/1.56 tff(42,plain,
% 2.05/1.56 (c_in(v_p, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[41, 40])).
% 2.05/1.56 tff(43,plain,
% 2.05/1.56 (((~![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(44,plain,
% 2.05/1.56 ((~![V_a: $i, T_a: $i, V_p: $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_insert(V_a, V_G, tc_PropLog_Opl(T_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.56 inference(quant_inst,[status(thm)],[])).
% 2.05/1.56 tff(45,plain,
% 2.05/1.56 ((~![V_a: $i, T_a: $i, V_p: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_p, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))) | c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[44, 43])).
% 2.05/1.56 tff(46,plain,
% 2.05/1.56 ($false),
% 2.05/1.56 inference(unit_resolution,[status(thm)],[45, 11, 42, 39])).
% 2.05/1.56 tff(47,plain,(c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), inference(lemma,lemma(discharge,[]))).
% 2.05/1.56 tff(48,plain,
% 2.05/1.56 (^[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_p, 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))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))))),
% 2.05/1.56 inference(bind,[status(th)],[])).
% 2.05/1.56 tff(49,plain,
% 2.05/1.56 (![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_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(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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 2.05/1.56 inference(quant_intro,[status(thm)],[48])).
% 2.05/1.56 tff(50,plain,
% 2.05/1.56 (![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_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(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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(51,plain,
% 2.05/1.56 (^[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_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, V_q, 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_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))) | (~c_in(V_p, 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))))), rewrite((((~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_p, 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(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_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_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(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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))))),
% 2.05/1.56 inference(bind,[status(th)],[])).
% 2.05/1.56 tff(52,plain,
% 2.05/1.56 (![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_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))) <=> ![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 2.05/1.56 inference(quant_intro,[status(thm)],[51])).
% 2.05/1.56 tff(53,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_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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_PropLog_Othms_OMP_0')).
% 2.05/1.56 tff(54,plain,
% 2.05/1.56 (![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[53, 52])).
% 2.05/1.56 tff(55,plain,
% 2.05/1.56 (![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[54, 50])).
% 2.05/1.56 tff(56,plain,(
% 2.05/1.56 ![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 2.05/1.56 inference(skolemize,[status(sab)],[55])).
% 2.05/1.56 tff(57,plain,
% 2.05/1.56 (![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[56, 49])).
% 2.05/1.56 tff(58,plain,
% 2.05/1.56 (((~![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | ((~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, 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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(59,plain,
% 2.05/1.56 ((c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(60,plain,
% 2.05/1.56 (((~![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, 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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | ((~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 2.05/1.56 inference(monotonicity,[status(thm)],[59])).
% 2.05/1.56 tff(61,plain,
% 2.05/1.56 (((~![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, 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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.56 inference(transitivity,[status(thm)],[60, 58])).
% 2.05/1.56 tff(62,plain,
% 2.05/1.56 ((~![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 2.05/1.56 inference(quant_inst,[status(thm)],[])).
% 2.05/1.56 tff(63,plain,
% 2.05/1.56 ((~![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (~c_in(v_p, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[62, 61])).
% 2.05/1.56 tff(64,plain,
% 2.05/1.56 (c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 2.05/1.56 inference(unit_resolution,[status(thm)],[63, 57, 47, 38])).
% 2.05/1.56 tff(65,plain,
% 2.05/1.56 ((~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)))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(66,axiom,(~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_conjecture_2')).
% 2.05/1.56 tff(67,plain,
% 2.05/1.56 (~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))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[66, 65])).
% 2.05/1.56 tff(68,plain,
% 2.05/1.56 (^[V_q: $i, V_H: $i, T_a: $i, V_p: $i] : refl(((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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))))),
% 2.05/1.56 inference(bind,[status(th)],[])).
% 2.05/1.56 tff(69,plain,
% 2.05/1.56 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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)))),
% 2.05/1.56 inference(quant_intro,[status(thm)],[68])).
% 2.05/1.56 tff(70,plain,
% 2.05/1.56 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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)))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(71,axiom,(![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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_Odeduction_0')).
% 2.05/1.56 tff(72,plain,
% 2.05/1.56 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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)))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[71, 70])).
% 2.05/1.56 tff(73,plain,(
% 2.05/1.56 ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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)))),
% 2.05/1.56 inference(skolemize,[status(sab)],[72])).
% 2.05/1.56 tff(74,plain,
% 2.05/1.56 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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)))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[73, 69])).
% 2.05/1.56 tff(75,plain,
% 2.05/1.56 (((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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)))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(76,plain,
% 2.05/1.56 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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)))),
% 2.05/1.56 inference(quant_inst,[status(thm)],[])).
% 2.05/1.56 tff(77,plain,
% 2.05/1.56 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_q, c_PropLog_Othms(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), 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_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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))),
% 2.05/1.56 inference(modus_ponens,[status(thm)],[76, 75])).
% 2.05/1.56 tff(78,plain,
% 2.05/1.56 (~c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 2.05/1.56 inference(unit_resolution,[status(thm)],[77, 74, 67])).
% 2.05/1.56 tff(79,plain,
% 2.05/1.56 (((~![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, 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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 2.05/1.56 inference(rewrite,[status(thm)],[])).
% 2.05/1.56 tff(80,plain,
% 2.05/1.56 ((c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> (c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 2.05/1.57 inference(rewrite,[status(thm)],[])).
% 2.05/1.57 tff(81,plain,
% 2.05/1.57 (((~![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, 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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))))),
% 2.05/1.57 inference(monotonicity,[status(thm)],[80])).
% 2.05/1.57 tff(82,plain,
% 2.05/1.57 (((~![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, 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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 2.05/1.57 inference(transitivity,[status(thm)],[81, 79])).
% 2.05/1.57 tff(83,plain,
% 2.05/1.57 ((~![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_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), 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(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 2.05/1.57 inference(quant_inst,[status(thm)],[])).
% 2.05/1.57 tff(84,plain,
% 2.05/1.57 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | c_in(c_PropLog_Opl_Ofalse, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_q, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 2.05/1.57 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.05/1.57 tff(85,plain,
% 2.05/1.57 ($false),
% 2.05/1.57 inference(unit_resolution,[status(thm)],[84, 57, 78, 64, 16])).
% 2.05/1.57 % SZS output end Proof
%------------------------------------------------------------------------------