TSTP Solution File: LCL441-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL441-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 04:56:17 EDT 2022
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL441-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Sep 1 21:50:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(c_in_type, type, (
% 0.21/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(tc_PropLog_Opl_type, type, (
% 0.21/0.39 tc_PropLog_Opl: $i > $i)).
% 0.21/0.39 tff(t_a_type, type, (
% 0.21/0.39 t_a: $i)).
% 0.21/0.39 tff(c_insert_type, type, (
% 0.21/0.39 c_insert: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(c_emptyset_type, type, (
% 0.21/0.39 c_emptyset: $i)).
% 0.21/0.39 tff(c_PropLog_Opl_Oop_A_N_62_type, type, (
% 0.21/0.39 c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(c_PropLog_Opl_Ofalse_type, type, (
% 0.21/0.39 c_PropLog_Opl_Ofalse: $i)).
% 0.21/0.39 tff(c_PropLog_Opl_Ovar_type, type, (
% 0.21/0.39 c_PropLog_Opl_Ovar: ( $i * $i ) > $i)).
% 0.21/0.39 tff(v_a_type, type, (
% 0.21/0.39 v_a: $i)).
% 0.21/0.39 tff(c_PropLog_Othms_type, type, (
% 0.21/0.39 c_PropLog_Othms: ( $i * $i ) > $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 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/sandbox/benchmark/theBenchmark.p','cls_PropLog_Othms_OH_0')).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.39 tff(6,plain,(
% 0.21/0.39 ![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)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.39 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)).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (^[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))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (![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)),
% 0.21/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![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)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 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/sandbox/benchmark/theBenchmark.p','cls_Set_OinsertCI_1')).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.39 tff(14,plain,(
% 0.21/0.39 ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.21/0.39 inference(skolemize,[status(sab)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[16, 15, 8])).
% 0.21/0.39 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,[]))).
% 0.21/0.39 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)).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (((~![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(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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((~![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(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)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 ((~![V_H: $i, T_a: $i, V_p: $i] : ((~c_in(V_p, V_H, tc_PropLog_Opl(T_a))) | c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)))) | (~c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))) | c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[22, 19, 7, 18])).
% 0.21/0.39 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,[]))).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (((~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))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 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/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 ((~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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 ((~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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[27, 25])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 ((~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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 ((~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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 ((~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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 ((~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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 ((~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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (~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))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[34, 24])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (((~![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 ((~![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)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ((~![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))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (~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))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[38, 35, 7])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[40, 15, 39])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------