%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Sun Sep 27 07:58:56 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 116 ( 13 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(cls_PropLog_Othms_OMP_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_1,VAR_2),c_PropLog_Othms(VAR_3,VAR_2),tc_PropLog_Opl(VAR_2)),true,ifeq(c_in(VAR_0,c_PropLog_Othms(VAR_3,VAR_2),tc_PropLog_Opl(VAR_2)),true,c_in(VAR_1,c_PropLog_Othms(VAR_3,VAR_2),tc_PropLog_Opl(VAR_2)),true),true) = true,
file('theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
cnf(c_2,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(A,B,C),c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),true,ifeq(c_in(A,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),true,c_in(B,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),true),true) = true,
inference(clausify,[status(thm)],[cls_PropLog_Othms_OMP_0]) ).
fof(cls_PropLog_Odeduction_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ifeq(c_in(VAR_0,c_PropLog_Othms(c_insert(VAR_1,VAR_2,tc_PropLog_Opl(VAR_3)),VAR_3),tc_PropLog_Opl(VAR_3)),true,c_in(c_PropLog_Opl_Oop_A_N_62(VAR_1,VAR_0,VAR_3),c_PropLog_Othms(VAR_2,VAR_3),tc_PropLog_Opl(VAR_3)),true) = true,
file('theBenchmark.p',cls_PropLog_Odeduction_0) ).
cnf(c_3,plain,
ifeq(c_in(A,c_PropLog_Othms(c_insert(B,C,tc_PropLog_Opl(D)),D),tc_PropLog_Opl(D)),true,c_in(c_PropLog_Opl_Oop_A_N_62(B,A,D),c_PropLog_Othms(C,D),tc_PropLog_Opl(D)),true) = true,
inference(clausify,[status(thm)],[cls_PropLog_Odeduction_0]) ).
fof(cls_PropLog_Othms_OH_0,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(c_in(VAR_0,VAR_1,tc_PropLog_Opl(VAR_2)),true,c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2)),true) = true,
file('theBenchmark.p',cls_PropLog_Othms_OH_0) ).
cnf(c_4,plain,
ifeq(c_in(A,B,tc_PropLog_Opl(C)),true,c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)),true) = true,
inference(clausify,[status(thm)],[cls_PropLog_Othms_OH_0]) ).
fof(cls_PropLog_Oweaken__left__insert_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ifeq(c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2)),true,c_in(VAR_0,c_PropLog_Othms(c_insert(VAR_3,VAR_1,tc_PropLog_Opl(VAR_2)),VAR_2),tc_PropLog_Opl(VAR_2)),true) = true,
file('theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
cnf(c_5,plain,
ifeq(c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)),true,c_in(A,c_PropLog_Othms(c_insert(D,B,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C)),true) = true,
inference(clausify,[status(thm)],[cls_PropLog_Oweaken__left__insert_0]) ).
fof(cls_Set_OinsertCI_1,axiom,
! [VAR_0,VAR_1,VAR_2] : c_in(VAR_0,c_insert(VAR_0,VAR_1,VAR_2),VAR_2) = true,
file('theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(c_6,plain,
c_in(A,c_insert(A,B,C),C) = true,
inference(clausify,[status(thm)],[cls_Set_OinsertCI_1]) ).
fof(cls_conjecture_0,axiom,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_7,plain,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_8,plain,
true = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(copy,[status(thm)],[c_7]) ).
fof(cls_conjecture_1,axiom,
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,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_9,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,
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_10,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)) = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_8,c_9]) ).
fof(cls_conjecture_2,axiom,
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,
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_11,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(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_12,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)) != c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_8,c_11]) ).
cnf(c_13,plain,
c_in(A,c_insert(A,B,C),C) = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_173,plain,
ifeq(c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(A,c_PropLog_Othms(c_insert(D,B,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C)),true) = true,
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_174,plain,
ifeq(c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(A,c_PropLog_Othms(c_insert(D,B,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))) = true,
inference(paramod,[status(thm)],[c_8,c_173]) ).
cnf(c_14,plain,
ifeq(c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(A,c_PropLog_Othms(c_insert(D,B,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C)),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)),
inference(paramod,[status(thm)],[c_8,c_174]) ).
cnf(c_175,plain,
ifeq(c_in(A,B,tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)),true) = true,
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_176,plain,
ifeq(c_in(A,B,tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))) = true,
inference(paramod,[status(thm)],[c_8,c_175]) ).
cnf(c_15,plain,
ifeq(c_in(A,B,tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)),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)),
inference(paramod,[status(thm)],[c_8,c_176]) ).
cnf(c_177,plain,
ifeq(c_in(A,c_PropLog_Othms(c_insert(B,C,tc_PropLog_Opl(D)),D),tc_PropLog_Opl(D)),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(B,A,D),c_PropLog_Othms(C,D),tc_PropLog_Opl(D)),true) = true,
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_178,plain,
ifeq(c_in(A,c_PropLog_Othms(c_insert(B,C,tc_PropLog_Opl(D)),D),tc_PropLog_Opl(D)),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(B,A,D),c_PropLog_Othms(C,D),tc_PropLog_Opl(D)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))) = true,
inference(paramod,[status(thm)],[c_8,c_177]) ).
cnf(c_16,plain,
ifeq(c_in(A,c_PropLog_Othms(c_insert(B,C,tc_PropLog_Opl(D)),D),tc_PropLog_Opl(D)),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(B,A,D),c_PropLog_Othms(C,D),tc_PropLog_Opl(D)),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)),
inference(paramod,[status(thm)],[c_8,c_178]) ).
cnf(c_179,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(A,B,C),c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),ifeq(c_in(A,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),true,c_in(B,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_180,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(A,B,C),c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),ifeq(c_in(A,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(B,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_179]) ).
cnf(c_181,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(A,B,C),c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),ifeq(c_in(A,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(B,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))),true) = true,
inference(paramod,[status(thm)],[c_8,c_180]) ).
cnf(c_182,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(A,B,C),c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),ifeq(c_in(A,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(B,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),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))) = true,
inference(paramod,[status(thm)],[c_8,c_181]) ).
cnf(c_17,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(A,B,C),c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),ifeq(c_in(A,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),c_in(B,c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),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(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_8,c_182]) ).
cnf(c_183,plain,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = c_in(v_p,c_PropLog_Othms(c_insert(A,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_14,c_1]) ).
cnf(c_18,plain,
c_in(v_p,c_PropLog_Othms(c_insert(A,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(copy,[status(thm)],[c_183]) ).
cnf(c_184,plain,
ifeq(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_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(A,v_H,tc_PropLog_Opl(t_a)),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)),
inference(paramod,[status(thm)],[c_10,c_14]) ).
cnf(c_19,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(A,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_1,c_184]) ).
cnf(c_185,plain,
ifeq(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(A,c_PropLog_Othms(c_insert(A,B,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C)),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)),
inference(paramod,[status(thm)],[c_13,c_15]) ).
cnf(c_23,plain,
c_in(A,c_PropLog_Othms(c_insert(A,B,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C)) = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_1,c_185]) ).
cnf(c_186,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,A,t_a),c_PropLog_Othms(c_insert(B,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),ifeq(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(A,c_PropLog_Othms(c_insert(B,v_H,tc_PropLog_Opl(t_a)),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(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_18,c_17]) ).
cnf(c_33,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,A,t_a),c_PropLog_Othms(c_insert(B,v_H,tc_PropLog_Opl(t_a)),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(A,c_PropLog_Othms(c_insert(B,v_H,tc_PropLog_Opl(t_a)),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)),
inference(paramod,[status(thm)],[c_1,c_186]) ).
cnf(c_187,plain,
ifeq(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)),ifeq(c_in(v_q,c_PropLog_Othms(c_insert(A,v_H,tc_PropLog_Opl(t_a)),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_Ofalse,c_PropLog_Othms(c_insert(A,v_H,tc_PropLog_Opl(t_a)),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(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_19,c_17]) ).
cnf(c_39,plain,
ifeq(c_in(v_q,c_PropLog_Othms(c_insert(A,v_H,tc_PropLog_Opl(t_a)),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_Ofalse,c_PropLog_Othms(c_insert(A,v_H,tc_PropLog_Opl(t_a)),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)),
inference(paramod,[status(thm)],[c_1,c_187]) ).
cnf(c_188,plain,
ifeq(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(A,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,A,t_a),v_H,tc_PropLog_Opl(t_a)),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)),
inference(paramod,[status(thm)],[c_23,c_33]) ).
cnf(c_125,plain,
c_in(A,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,A,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_1,c_188]) ).
cnf(c_189,plain,
ifeq(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_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)),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)),
inference(paramod,[status(thm)],[c_125,c_39]) ).
cnf(c_163,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)) = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_1,c_189]) ).
cnf(c_190,plain,
ifeq(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(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)),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)),
inference(paramod,[status(thm)],[c_163,c_16]) ).
cnf(c_171,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)) = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_1,c_190]) ).
cnf(c_172,plain,
$false,
inference(resolve,[status(thm)],[c_171,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 22:36:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 3636807 was started by sandbox on n026,
% 0.11/0.38 % Fri Sep 25 22:36:55 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.46
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.46
% 0.11/0.46 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.11/0.46 % Length of proof is 26.
% 0.11/0.46 % Level of proof is 8.
% 0.11/0.46 % Maximum clause weight is 87.000.
% 0.11/0.46 % Given clauses 50.
% 0.11/0.46
% 0.11/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------