%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n017.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 03:00:01 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 09:05:38 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(c_in_type, type, (
% 0.12/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(tc_PropLog_Opl_type, type, (
% 0.12/0.39 tc_PropLog_Opl: $i > $i)).
% 0.12/0.39 tff(t_a_type, type, (
% 0.12/0.39 t_a: $i)).
% 0.12/0.39 tff(c_PropLog_Othms_type, type, (
% 0.12/0.39 c_PropLog_Othms: ( $i * $i ) > $i)).
% 0.12/0.39 tff(c_insert_type, type, (
% 0.12/0.39 c_insert: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(v_F_type, type, (
% 0.12/0.39 v_F: $i)).
% 0.12/0.39 tff(v_x_type, type, (
% 0.12/0.39 v_x: $i)).
% 0.12/0.39 tff(c_PropLog_Opl_Oop_A_N_62_type, type, (
% 0.12/0.39 c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(v_xa_type, type, (
% 0.12/0.39 v_xa: $i)).
% 0.12/0.39 tff(c_PropLog_Osat_type, type, (
% 0.12/0.39 c_PropLog_Osat: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(1,assumption,(~c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[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))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![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)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![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)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,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')).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.39 tff(7,plain,(
% 0.12/0.39 ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.12/0.39 inference(skolemize,[status(sab)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 ((~![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_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (c_in(v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(14,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')).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.39 tff(16,plain,(
% 0.12/0.39 ![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)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (((~![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_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, 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_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 ((~![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_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 ((~![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[20, 17, 10, 1])).
% 0.12/0.39 tff(22,plain,(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (^[V_q: $i, V_H: $i, T_a: $i, V_p: $i] : refl((c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (^[V_q: $i, V_H: $i, T_a: $i, V_p: $i] : trans(monotonicity(rewrite(((~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (((~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.39 tff(28,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')).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.39 tff(31,plain,(
% 0.12/0.39 ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[30])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) <=> (~c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,axiom,(~c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (~c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, 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_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | (c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : (c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))) | (~c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a))))) | c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 ((~c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) | (~c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 35, 32])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (~c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[39, 22])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (^[V_q: $i, V_H: $i, T_a: $i, V_p: $i] : refl(((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a)) <=> ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a)) <=> ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a)) <=> ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(44,axiom,(![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_PropLog_Osat__imp_0')).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.39 tff(46,plain,(
% 0.12/0.39 ![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))),
% 0.12/0.39 inference(skolemize,[status(sab)],[45])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a) <=> c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,axiom,(c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))) | ((~c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a)) | c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a))) <=> ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))) | (~c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a)) | c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))) | ((~c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a)) | c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 ((~![V_q: $i, V_H: $i, T_a: $i, V_p: $i] : ((~c_PropLog_Osat(c_insert(V_p, V_H, tc_PropLog_Opl(T_a)), V_q, T_a)) | c_PropLog_Osat(V_H, c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), T_a))) | (~c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a)) | c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[53, 50, 47])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (^[V_U: $i] : refl(((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))) <=> ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))) <=> ![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))) <=> ![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (^[V_U: $i] : rewrite((c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Osat(v_F, V_U, t_a))) <=> ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (![V_U: $i] : (c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Osat(v_F, V_U, t_a))) <=> ![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.40 tff(60,axiom,(![V_U: $i] : (c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)) | (~c_PropLog_Osat(v_F, V_U, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.12/0.40 tff(63,plain,(
% 0.12/0.40 ![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[62])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (((~![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))) | ((~c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a)) | c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))) <=> ((~![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))) | (~c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a)) | c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 ((~![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))) | ((~c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a)) | c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 ((~![V_U: $i] : ((~c_PropLog_Osat(v_F, V_U, t_a)) | c_in(V_U, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)))) | (~c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a)) | c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[69])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(72,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')).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.12/0.40 tff(74,plain,(
% 0.12/0.40 ![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)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[73])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (((~![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_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, 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_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 ((~![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_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 ((~![V_a: $i, T_a: $i, V_p: $i, V_G: $i] : ((~c_in(V_p, c_PropLog_Othms(V_G, T_a), tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(c_insert(V_a, V_G, tc_PropLog_Opl(T_a)), T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[78, 75, 68, 40])).
% 0.12/0.40 % SZS output end Proof
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------