%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL441-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n012.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 0.07s 0.33s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL441-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.01 % Command : run_E %s %d THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 5 08:05:44 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.07/0.33 % SZS status Unsatisfiable
% 0.07/0.33 % SZS output start Proof
% 0.07/0.33 tff(c_in_type, type, (
% 0.07/0.33 c_in: ( $i * $i * $i ) > $o)).
% 0.07/0.33 tff(tc_PropLog_Opl_type, type, (
% 0.07/0.33 tc_PropLog_Opl: $i > $i)).
% 0.07/0.33 tff(t_a_type, type, (
% 0.07/0.33 t_a: $i)).
% 0.07/0.33 tff(c_insert_type, type, (
% 0.07/0.33 c_insert: ( $i * $i * $i ) > $i)).
% 0.07/0.33 tff(c_emptyset_type, type, (
% 0.07/0.33 c_emptyset: $i)).
% 0.07/0.33 tff(c_PropLog_Opl_Oop_A_N_62_type, type, (
% 0.07/0.33 c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i)).
% 0.07/0.33 tff(c_PropLog_Opl_Ofalse_type, type, (
% 0.07/0.33 c_PropLog_Opl_Ofalse: $i)).
% 0.07/0.33 tff(c_PropLog_Opl_Ovar_type, type, (
% 0.07/0.33 c_PropLog_Opl_Ovar: ( $i * $i ) > $i)).
% 0.07/0.33 tff(v_a_type, type, (
% 0.07/0.33 v_a: $i)).
% 0.07/0.33 tff(c_PropLog_Othms_type, type, (
% 0.07/0.33 c_PropLog_Othms: ( $i * $i ) > $i)).
% 0.07/0.33 tff(1,plain,
% 0.07/0.33 (^[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))))),
% 0.07/0.33 inference(bind,[status(th)],[])).
% 0.07/0.33 tff(2,plain,
% 0.07/0.33 (![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)))),
% 0.07/0.33 inference(quant_intro,[status(thm)],[1])).
% 0.07/0.33 tff(3,plain,
% 0.07/0.33 (![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)))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(4,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')).
% 0.07/0.33 tff(5,plain,
% 0.07/0.33 (![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)))),
% 0.07/0.33 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.07/0.33 tff(6,plain,(
% 0.07/0.33 ![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)))),
% 0.07/0.33 inference(skolemize,[status(sab)],[5])).
% 0.07/0.33 tff(7,plain,
% 0.07/0.33 (![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)))),
% 0.07/0.33 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.07/0.33 tff(8,assumption,(~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 0.07/0.33 tff(9,plain,
% 0.07/0.33 (^[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))),
% 0.07/0.33 inference(bind,[status(th)],[])).
% 0.07/0.33 tff(10,plain,
% 0.07/0.33 (![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)),
% 0.07/0.33 inference(quant_intro,[status(thm)],[9])).
% 0.07/0.33 tff(11,plain,
% 0.07/0.33 (![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)),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(12,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')).
% 0.07/0.33 tff(13,plain,
% 0.07/0.33 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.07/0.33 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.07/0.33 tff(14,plain,(
% 0.07/0.33 ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.07/0.33 inference(skolemize,[status(sab)],[13])).
% 0.07/0.33 tff(15,plain,
% 0.07/0.33 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.07/0.33 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.07/0.33 tff(16,plain,
% 0.07/0.33 ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 0.07/0.33 inference(quant_inst,[status(thm)],[])).
% 0.07/0.34 tff(17,plain,
% 0.07/0.34 ($false),
% 0.07/0.34 inference(unit_resolution,[status(thm)],[16, 15, 8])).
% 0.07/0.34 tff(18,plain,(c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.07/0.34 tff(19,assumption,(~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 0.07/0.34 tff(20,plain,
% 0.07/0.34 (((~![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_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, 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_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(21,plain,
% 0.07/0.34 ((~![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_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.07/0.34 inference(quant_inst,[status(thm)],[])).
% 0.07/0.34 tff(22,plain,
% 0.07/0.34 ((~![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.07/0.34 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.07/0.34 tff(23,plain,
% 0.07/0.34 ($false),
% 0.07/0.34 inference(unit_resolution,[status(thm)],[22, 19, 7, 18])).
% 0.07/0.34 tff(24,plain,(c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.07/0.34 tff(25,plain,
% 0.07/0.34 (((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))) <=> ((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(26,axiom,((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.07/0.34 tff(27,plain,
% 0.07/0.34 ((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.07/0.34 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.07/0.34 tff(28,plain,
% 0.07/0.34 ((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.07/0.34 inference(modus_ponens,[status(thm)],[27, 25])).
% 0.07/0.34 tff(29,plain,
% 0.07/0.34 ((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.07/0.34 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.07/0.34 tff(30,plain,
% 0.07/0.34 ((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.07/0.34 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.07/0.34 tff(31,plain,
% 0.07/0.34 ((~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.07/0.34 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.07/0.34 tff(32,plain,
% 0.07/0.34 (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.07/0.34 inference(unit_resolution,[status(thm)],[31, 24])).
% 0.07/0.34 tff(33,plain,
% 0.07/0.34 (((~![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(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, 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(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(34,plain,
% 0.07/0.34 ((~![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(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.07/0.34 inference(quant_inst,[status(thm)],[])).
% 0.07/0.34 tff(35,plain,
% 0.07/0.34 ((~![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(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.07/0.34 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.07/0.34 tff(36,plain,
% 0.07/0.34 (~c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 0.07/0.34 inference(unit_resolution,[status(thm)],[35, 32, 7])).
% 0.07/0.34 tff(37,plain,
% 0.07/0.34 ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 0.07/0.34 inference(quant_inst,[status(thm)],[])).
% 0.07/0.34 tff(38,plain,
% 0.07/0.34 ($false),
% 0.07/0.34 inference(unit_resolution,[status(thm)],[37, 15, 36])).
% 0.07/0.34 % SZS output end Proof
% 0.07/0.34 % E exiting
%------------------------------------------------------------------------------