TSTP Solution File: LCL443-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL443-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 : 600s
% DateTime : Sun Jul 17 12:52:19 EDT 2022
% Result : Unsatisfiable 1.11s 1.32s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 27
% Syntax : Number of clauses : 81 ( 47 unt; 0 nHn; 47 RR)
% Number of literals : 132 ( 131 equ; 52 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 105 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(A,A,B,C) = B ).
cnf(cls_PropLog_Othms_OMP_0,axiom,
ifeq(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)),true,ifeq(c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),true,c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),true),true) = true ).
cnf(cls_PropLog_Odeduction_0,axiom,
ifeq(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)),true,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)),true) = true ).
cnf(cls_PropLog_Othms_OH_0,axiom,
ifeq(c_in(V_p,V_H,tc_PropLog_Opl(T_a)),true,c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),true) = true ).
cnf(cls_PropLog_Oweaken__left__insert_0,axiom,
ifeq(c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a)),true,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)),true) = true ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a) = true ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true ).
cnf(cls_conjecture_2,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true ).
cnf(refute_0_0,plain,
ifeq(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(subst,[],[cls_PropLog_Odeduction_0:[bind(T_a,$fot(t_a)),bind(V_H,$fot(v_H)),bind(V_p,$fot(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a))),bind(V_q,$fot(c_PropLog_Opl_Ofalse))]]) ).
cnf(refute_0_1,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true,
inference(subst,[],[cls_PropLog_Othms_OMP_0:[bind(T_a,$fot(t_a)),bind(V_H,$fot(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)))),bind(V_p,$fot(v_q)),bind(V_q,$fot(c_PropLog_Opl_Ofalse))]]) ).
cnf(refute_0_2,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(subst,[],[cls_PropLog_Oweaken__left__insert_0:[bind(T_a,$fot(t_a)),bind(V_G,$fot(v_H)),bind(V_a,$fot(X_20)),bind(V_p,$fot(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a)))]]) ).
cnf(refute_0_3,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_4,plain,
( ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
inference(resolve,[$cnf( $equal(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) )],[cls_conjecture_1,refute_0_3]) ).
cnf(refute_0_5,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_7,plain,
( ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) ),[0],$fot(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))]]) ).
cnf(refute_0_8,plain,
( ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) != true
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != true
| ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_11,plain,
( ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != true
| ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true ),
inference(resolve,[$cnf( $equal(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),true) )],[refute_0_1,refute_0_11]) ).
cnf(refute_0_13,plain,
ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_14,plain,
( ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true)
| ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != true
| ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),true) ),[0],$fot(ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true))]]) ).
cnf(refute_0_15,plain,
( ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != true
| ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),true) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
ifeq(c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(subst,[],[refute_0_16:[bind(X_20,$fot(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a)))]]) ).
cnf(refute_0_18,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true,
inference(subst,[],[cls_PropLog_Othms_OMP_0:[bind(T_a,$fot(t_a)),bind(V_H,$fot(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)))),bind(V_p,$fot(v_p)),bind(V_q,$fot(X_94))]]) ).
cnf(refute_0_19,plain,
ifeq(c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(subst,[],[cls_PropLog_Oweaken__left__insert_0:[bind(T_a,$fot(t_a)),bind(V_G,$fot(v_H)),bind(V_a,$fot(X_20)),bind(V_p,$fot(v_p))]]) ).
cnf(refute_0_20,plain,
( c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true
| ifeq(c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_21,plain,
( ifeq(c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
inference(resolve,[$cnf( $equal(c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) )],[cls_conjecture_0,refute_0_20]) ).
cnf(refute_0_22,plain,
ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_24,plain,
( ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) ),[0],$fot(c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))]]) ).
cnf(refute_0_25,plain,
( ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
( c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) != true
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != true
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_28,plain,
( ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != true
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true ),
inference(resolve,[$cnf( $equal(c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_p,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),true) )],[refute_0_18,refute_0_28]) ).
cnf(refute_0_30,plain,
ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_31,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),
introduced(tautology,[refl,[$fot(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true))]]) ).
cnf(refute_0_32,plain,
( ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true)
| ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true)) ),[1,2],$fot(c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))]]) ).
cnf(refute_0_33,plain,
( ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) ),
inference(resolve,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true)
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != true
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),true) ),[0],$fot(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true))]]) ).
cnf(refute_0_36,plain,
( ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) != true
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_94,t_a),c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X_94,c_PropLog_Othms(c_insert(X_20,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),true) )],[refute_0_29,refute_0_36]) ).
cnf(refute_0_38,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(subst,[],[refute_0_37:[bind(X_20,$fot(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a))),bind(X_94,$fot(X_555))]]) ).
cnf(refute_0_39,plain,
ifeq(c_in(X_8,c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),tc_PropLog_Opl(X_6)),true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) = true,
inference(subst,[],[cls_PropLog_Othms_OH_0:[bind(T_a,$fot(X_6)),bind(V_H,$fot(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)))),bind(V_p,$fot(X_8))]]) ).
cnf(refute_0_40,plain,
c_in(X_8,c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),tc_PropLog_Opl(X_6)) = true,
inference(subst,[],[cls_Set_OinsertCI_1:[bind(T_a,$fot(tc_PropLog_Opl(X_6))),bind(V_x,$fot(X_8))]]) ).
cnf(refute_0_41,plain,
( c_in(X_8,c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),tc_PropLog_Opl(X_6)) != true
| ifeq(c_in(X_8,c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),tc_PropLog_Opl(X_6)),true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) != true
| ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(X_8,c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),tc_PropLog_Opl(X_6)),true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_42,plain,
( ifeq(c_in(X_8,c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),tc_PropLog_Opl(X_6)),true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) != true
| ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) = true ),
inference(resolve,[$cnf( $equal(c_in(X_8,c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),tc_PropLog_Opl(X_6)),true) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(X_8,c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),tc_PropLog_Opl(X_6)),true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true),true) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) = c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)))),bind(C,$fot(true))]]) ).
cnf(refute_0_45,plain,
( ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) != c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6))
| ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) != true
| c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true),true) ),[0],$fot(c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)))]]) ).
cnf(refute_0_46,plain,
( ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true) != true
| c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true),c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(X_8,c_PropLog_Othms(c_insert(X_8,V_B,tc_PropLog_Opl(X_6)),X_6),tc_PropLog_Opl(X_6)),true),true) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(subst,[],[refute_0_47:[bind(V_B,$fot(v_H)),bind(X_6,$fot(t_a)),bind(X_8,$fot(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a)))]]) ).
cnf(refute_0_49,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) != true
| ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_50,plain,
( ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
inference(resolve,[$cnf( $equal(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_38,refute_0_50]) ).
cnf(refute_0_52,plain,
ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_53,plain,
( ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) ),[0],$fot(c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))]]) ).
cnf(refute_0_54,plain,
( ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(X_555,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X_555,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(subst,[],[refute_0_55:[bind(X_555,$fot(v_q))]]) ).
cnf(refute_0_57,plain,
( c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) != true
| ifeq(c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_58,plain,
( ifeq(c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true ),
inference(resolve,[$cnf( $equal(c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_17,refute_0_58]) ).
cnf(refute_0_60,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_61,plain,
( ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) ),[0],$fot(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)))]]) ).
cnf(refute_0_62,plain,
( ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) != true
| ifeq(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_65,plain,
( ifeq(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) != true
| ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = true ),
inference(resolve,[$cnf( $equal(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_0,refute_0_65]) ).
cnf(refute_0_67,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_68,plain,
( ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) != c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),true) ),[0],$fot(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)))]]) ).
cnf(refute_0_69,plain,
( ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) != true
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),true) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
$false,
inference(resolve,[$cnf( $equal(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) )],[refute_0_70,cls_conjecture_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL443-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 21:59:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.11/1.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.11/1.32
% 1.11/1.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.18/1.34
%------------------------------------------------------------------------------