%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL439-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n029.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 03:00:02 PM UTC 2026
% Result : Unsatisfiable 0.45s 0.73s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL439-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.33 % Computer : n029.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 6 01:33:57 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.45/0.73 % SZS status Unsatisfiable
% 0.45/0.73 % SZS output start Proof
% 0.45/0.73 tff(c_in_type, type, (
% 0.45/0.73 c_in: ( $i * $i * $i ) > $o)).
% 0.45/0.73 tff(tc_PropLog_Opl_type, type, (
% 0.45/0.73 tc_PropLog_Opl: $i > $i)).
% 0.45/0.73 tff(t_a_type, type, (
% 0.45/0.73 t_a: $i)).
% 0.45/0.73 tff(c_PropLog_Othms_type, type, (
% 0.45/0.73 c_PropLog_Othms: ( $i * $i ) > $i)).
% 0.45/0.73 tff(c_insert_type, type, (
% 0.45/0.73 c_insert: ( $i * $i * $i ) > $i)).
% 0.45/0.73 tff(v_H_type, type, (
% 0.45/0.73 v_H: $i)).
% 0.45/0.73 tff(v_p_type, type, (
% 0.45/0.73 v_p: $i)).
% 0.45/0.73 tff(c_PropLog_Opl_Oop_A_N_62_type, type, (
% 0.45/0.73 c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i)).
% 0.45/0.73 tff(c_PropLog_Opl_Ofalse_type, type, (
% 0.45/0.73 c_PropLog_Opl_Ofalse: $i)).
% 0.45/0.73 tff(v_q_type, type, (
% 0.45/0.73 v_q: $i)).
% 0.45/0.73 tff(1,plain,
% 0.45/0.73 (^[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))),
% 0.45/0.73 inference(bind,[status(th)],[])).
% 0.45/0.73 tff(2,plain,
% 0.45/0.73 (![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)),
% 0.45/0.73 inference(quant_intro,[status(thm)],[1])).
% 0.45/0.73 tff(3,plain,
% 0.45/0.73 (![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)),
% 0.45/0.73 inference(rewrite,[status(thm)],[])).
% 0.45/0.73 tff(4,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')).
% 0.45/0.73 tff(5,plain,
% 0.45/0.73 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.45/0.73 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.45/0.73 tff(6,plain,(
% 0.45/0.73 ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.45/0.73 inference(skolemize,[status(sab)],[5])).
% 0.45/0.73 tff(7,plain,
% 0.45/0.73 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.45/0.73 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.45/0.73 tff(8,plain,
% 0.45/0.73 ((~![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(v_p, c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 0.45/0.73 inference(quant_inst,[status(thm)],[])).
% 0.45/0.73 tff(9,plain,
% 0.45/0.73 (c_in(v_p, c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 0.45/0.73 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.45/0.73 tff(10,plain,
% 0.45/0.73 (^[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))))),
% 0.45/0.73 inference(bind,[status(th)],[])).
% 0.45/0.73 tff(11,plain,
% 0.45/0.73 (![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)))),
% 0.45/0.73 inference(quant_intro,[status(thm)],[10])).
% 0.45/0.73 tff(12,plain,
% 0.45/0.73 (![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)))),
% 0.45/0.73 inference(rewrite,[status(thm)],[])).
% 0.45/0.73 tff(13,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')).
% 0.45/0.73 tff(14,plain,
% 0.45/0.73 (![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)))),
% 0.45/0.73 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.45/0.73 tff(15,plain,(
% 0.45/0.73 ![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)))),
% 0.45/0.73 inference(skolemize,[status(sab)],[14])).
% 0.45/0.73 tff(16,plain,
% 0.45/0.73 (![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)))),
% 0.45/0.73 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.45/0.73 tff(17,plain,
% 0.45/0.73 (((~![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(v_p, c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(v_p, c_PropLog_Othms(c_insert(v_p, 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(v_p, c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(v_p, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.45/0.74 inference(rewrite,[status(thm)],[])).
% 0.45/0.74 tff(18,plain,
% 0.45/0.74 ((~![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(v_p, c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(v_p, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.45/0.74 inference(quant_inst,[status(thm)],[])).
% 0.45/0.74 tff(19,plain,
% 0.45/0.74 ((~![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(v_p, c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(v_p, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.45/0.74 tff(20,plain,
% 0.45/0.74 (c_in(v_p, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.45/0.74 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.45/0.74 tff(21,assumption,(~c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 0.45/0.74 tff(22,plain,
% 0.45/0.74 (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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))),
% 0.45/0.74 inference(rewrite,[status(thm)],[])).
% 0.45/0.74 tff(23,axiom,(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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.45/0.74 tff(24,plain,
% 0.45/0.74 (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))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.45/0.74 tff(25,plain,
% 0.45/0.74 (^[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))))),
% 0.45/0.74 inference(bind,[status(th)],[])).
% 0.45/0.74 tff(26,plain,
% 0.45/0.74 (![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)))),
% 0.45/0.74 inference(quant_intro,[status(thm)],[25])).
% 0.45/0.74 tff(27,plain,
% 0.45/0.74 (![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)))),
% 0.45/0.74 inference(rewrite,[status(thm)],[])).
% 0.45/0.74 tff(28,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')).
% 0.45/0.74 tff(29,plain,
% 0.45/0.74 (![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)))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.45/0.74 tff(30,plain,(
% 0.45/0.74 ![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)))),
% 0.45/0.74 inference(skolemize,[status(sab)],[29])).
% 0.45/0.74 tff(31,plain,
% 0.45/0.74 (![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)))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.45/0.74 tff(32,plain,
% 0.45/0.74 (((~![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_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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, 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_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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.45/0.74 inference(rewrite,[status(thm)],[])).
% 0.45/0.74 tff(33,plain,
% 0.45/0.74 ((~![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_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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.45/0.74 inference(quant_inst,[status(thm)],[])).
% 0.45/0.74 tff(34,plain,
% 0.45/0.74 ((~![V_a: $i, T_a: $i, V_p: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.45/0.74 tff(35,plain,
% 0.45/0.74 ($false),
% 0.45/0.74 inference(unit_resolution,[status(thm)],[34, 31, 24, 21])).
% 0.45/0.74 tff(36,plain,(c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.74 tff(37,plain,
% 0.45/0.74 ((~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)))),
% 0.45/0.74 inference(rewrite,[status(thm)],[])).
% 0.45/0.74 tff(38,axiom,(~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_conjecture_1')).
% 0.45/0.74 tff(39,plain,
% 0.45/0.74 (~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))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.45/0.74 tff(40,plain,
% 0.45/0.74 (^[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))))),
% 0.45/0.74 inference(bind,[status(th)],[])).
% 0.45/0.74 tff(41,plain,
% 0.45/0.74 (![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)))),
% 0.45/0.74 inference(quant_intro,[status(thm)],[40])).
% 0.45/0.74 tff(42,plain,
% 0.45/0.74 (![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)))),
% 0.45/0.74 inference(rewrite,[status(thm)],[])).
% 0.45/0.74 tff(43,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')).
% 0.45/0.74 tff(44,plain,
% 0.45/0.74 (![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)))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.45/0.74 tff(45,plain,(
% 0.45/0.74 ![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)))),
% 0.45/0.74 inference(skolemize,[status(sab)],[44])).
% 0.45/0.74 tff(46,plain,
% 0.45/0.74 (![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)))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.45/0.74 tff(47,plain,
% 0.45/0.74 (((~![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(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)))) | (~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)))),
% 0.45/0.74 inference(rewrite,[status(thm)],[])).
% 0.45/0.74 tff(48,plain,
% 0.45/0.74 ((~![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(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)))),
% 0.45/0.74 inference(quant_inst,[status(thm)],[])).
% 0.45/0.74 tff(49,plain,
% 0.45/0.74 ((~![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(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))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.45/0.74 tff(50,plain,
% 0.45/0.74 (~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))),
% 0.45/0.74 inference(unit_resolution,[status(thm)],[49, 46, 39])).
% 0.45/0.74 tff(51,plain,
% 0.45/0.74 (^[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, 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_q, 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(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))))),
% 0.45/0.74 inference(bind,[status(th)],[])).
% 0.45/0.74 tff(52,plain,
% 0.45/0.74 (![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, 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(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, 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))))),
% 0.45/0.74 inference(quant_intro,[status(thm)],[51])).
% 0.45/0.74 tff(53,plain,
% 0.45/0.74 (![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, 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(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, 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))))),
% 0.45/0.74 inference(rewrite,[status(thm)],[])).
% 0.45/0.74 tff(54,plain,
% 0.45/0.74 (^[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, 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, 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_p, c_PropLog_Opl_Ofalse, 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, 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_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, 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_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, 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_p, c_PropLog_Opl_Ofalse, 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, 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))))))),
% 0.45/0.74 inference(bind,[status(th)],[])).
% 0.45/0.74 tff(55,plain,
% 0.45/0.74 (![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, c_PropLog_Opl_Ofalse, 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, 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))))),
% 0.45/0.74 inference(quant_intro,[status(thm)],[54])).
% 0.45/0.74 tff(56,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, c_PropLog_Opl_Ofalse, 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__notE_0')).
% 0.45/0.74 tff(57,plain,
% 0.45/0.74 (![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, 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))))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.45/0.74 tff(58,plain,
% 0.45/0.74 (![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, 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))))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.45/0.74 tff(59,plain,(
% 0.45/0.74 ![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, 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))))),
% 0.45/0.74 inference(skolemize,[status(sab)],[58])).
% 0.45/0.74 tff(60,plain,
% 0.45/0.74 (![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, 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))))),
% 0.45/0.74 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.45/0.74 tff(61,plain,
% 0.45/0.74 (((~![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, 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_q, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_p, 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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, 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, 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_q, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_p, 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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.45/0.74 inference(rewrite,[status(thm)],[])).
% 0.45/0.74 tff(62,plain,
% 0.45/0.74 ((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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_p, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), 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(v_p, 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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.45/0.75 inference(rewrite,[status(thm)],[])).
% 0.45/0.75 tff(63,plain,
% 0.45/0.75 (((~![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, 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_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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_p, c_PropLog_Othms(c_insert(v_p, 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, 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_q, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_p, 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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))))),
% 0.45/0.75 inference(monotonicity,[status(thm)],[62])).
% 0.45/0.75 tff(64,plain,
% 0.45/0.75 (((~![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, 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_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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_p, c_PropLog_Othms(c_insert(v_p, 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, 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_q, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_p, 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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.45/0.75 inference(transitivity,[status(thm)],[63, 61])).
% 0.45/0.75 tff(65,plain,
% 0.45/0.75 ((~![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, 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_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, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_p, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.45/0.75 inference(quant_inst,[status(thm)],[])).
% 0.45/0.75 tff(66,plain,
% 0.45/0.75 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | c_in(v_q, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(v_p, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.45/0.75 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.45/0.75 tff(67,plain,
% 0.45/0.75 ($false),
% 0.45/0.75 inference(unit_resolution,[status(thm)],[66, 60, 50, 36, 20])).
% 0.45/0.75 % SZS output end Proof
% 0.45/0.75 % E exiting
%------------------------------------------------------------------------------