%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL442-2 : TPTP v9.3.1. Released v3.2.0.
% 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 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 12 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 91 ( 35 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 56 ( 18 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
( ~ c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
( ~ c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
( c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
( c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
( ~ c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_3,plain,
( ~ c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
( c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_4,plain,
( c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_PropLog_Oeval(v_tt,v_pl1,t_a) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_5,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_PropLog_Oeval(v_tt,v_pl1,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_5,axiom,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Oeval(v_tt,v_pl2,t_a) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_6,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Oeval(v_tt,v_pl2,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_9,axiom,
( ~ c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_PropLog_Oeval(v_tt,v_pl2,t_a)
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
file('theBenchmark.p',cls_conjecture_9) ).
cnf(c_7,plain,
( ~ c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_PropLog_Oeval(v_tt,v_pl2,t_a)
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_9]) ).
fof(cls_PropLog_Ofalse__imp_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_3,VAR_1),c_PropLog_Othms(VAR_2,VAR_1),tc_PropLog_Opl(VAR_1))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(VAR_0,c_PropLog_Opl_Ofalse,VAR_1),c_PropLog_Othms(VAR_2,VAR_1),tc_PropLog_Opl(VAR_1)) ),
file('theBenchmark.p',cls_PropLog_Ofalse__imp_0) ).
cnf(c_8,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(A,D,B),c_PropLog_Othms(C,B),tc_PropLog_Opl(B))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Ofalse,B),c_PropLog_Othms(C,B),tc_PropLog_Opl(B)) ),
inference(clausify,[status(thm)],[cls_PropLog_Ofalse__imp_0]) ).
fof(cls_PropLog_Oimp__false_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_3,VAR_2),c_PropLog_Opl_Ofalse,VAR_2),c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(VAR_3,c_PropLog_Opl_Ofalse,VAR_2),c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2)) ),
file('theBenchmark.p',cls_PropLog_Oimp__false_0) ).
cnf(c_9,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,D,C),c_PropLog_Opl_Ofalse,C),c_PropLog_Othms(B,C),tc_PropLog_Opl(C))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(D,c_PropLog_Opl_Ofalse,C),c_PropLog_Othms(B,C),tc_PropLog_Opl(C))
| ~ c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)) ),
inference(clausify,[status(thm)],[cls_PropLog_Oimp__false_0]) ).
fof(cls_PropLog_Oweaken__left__Un1_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_PropLog_Othms(c_union(VAR_1,VAR_3,tc_PropLog_Opl(VAR_2)),VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2)) ),
file('theBenchmark.p',cls_PropLog_Oweaken__left__Un1_0) ).
cnf(c_10,plain,
( c_in(A,c_PropLog_Othms(c_union(B,D,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C))
| ~ c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)) ),
inference(clausify,[status(thm)],[cls_PropLog_Oweaken__left__Un1_0]) ).
fof(cls_PropLog_Oweaken__left__Un2_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_PropLog_Othms(c_union(VAR_3,VAR_1,tc_PropLog_Opl(VAR_2)),VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2)) ),
file('theBenchmark.p',cls_PropLog_Oweaken__left__Un2_0) ).
cnf(c_11,plain,
( c_in(A,c_PropLog_Othms(c_union(D,B,tc_PropLog_Opl(C)),C),tc_PropLog_Opl(C))
| ~ c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)) ),
inference(clausify,[status(thm)],[cls_PropLog_Oweaken__left__Un2_0]) ).
fof(cls_PropLog_Oweaken__right_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_PropLog_Opl_Oop_A_N_62(VAR_3,VAR_0,VAR_2),c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2)) ),
file('theBenchmark.p',cls_PropLog_Oweaken__right_0) ).
cnf(c_12,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(D,A,C),c_PropLog_Othms(B,C),tc_PropLog_Opl(C))
| ~ c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)) ),
inference(clausify,[status(thm)],[cls_PropLog_Oweaken__right_0]) ).
cnf(c_14,plain,
( c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_15,plain,
( c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_16,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_17,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_PropLog_Oeval(v_tt,v_pl2,t_a)
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_24,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,A,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_31,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,A,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_15,c_8]) ).
cnf(c_34,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,A,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),B,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_24,c_10]) ).
cnf(c_37,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,A,t_a),c_PropLog_Othms(c_union(B,c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_31,c_11]) ).
cnf(c_60,plain,
( c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_34,c_5]) ).
cnf(c_356,plain,
( c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_60,c_1]) ).
cnf(c_62,plain,
c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(copy,[status(thm)],[c_356]) ).
cnf(c_65,plain,
c_in(v_pl1,c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),A,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_62,c_10]) ).
cnf(c_80,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,A,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),B,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),B,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_65,c_9]) ).
cnf(c_252,plain,
( c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_80,c_37]) ).
cnf(c_269,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_252,c_17]) ).
cnf(c_277,plain,
( ~ c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_252,c_7]) ).
cnf(c_357,plain,
( c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_269,c_3]) ).
cnf(c_279,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(copy,[status(thm)],[c_357]) ).
cnf(c_289,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,A,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_279,c_8]) ).
cnf(c_294,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,A,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),B,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_289,c_10]) ).
cnf(c_325,plain,
( c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_294,c_5]) ).
cnf(c_358,plain,
( c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_325,c_277]) ).
cnf(c_329,plain,
( c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(copy,[status(thm)],[c_358]) ).
cnf(c_359,plain,
( c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_329,c_3]) ).
cnf(c_331,plain,
c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(copy,[status(thm)],[c_359]) ).
cnf(c_332,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(A,v_pl2,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_331,c_12]) ).
cnf(c_337,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(A,v_pl2,t_a),c_PropLog_Othms(c_union(B,c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_332,c_11]) ).
cnf(c_340,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_337,c_16]) ).
cnf(c_341,plain,
~ c_PropLog_Oeval(v_tt,v_pl2,t_a),
inference(resolve,[status(thm)],[c_337,c_6]) ).
cnf(c_342,plain,
c_PropLog_Oeval(v_tt,v_pl1,t_a),
inference(resolve,[status(thm)],[c_337,c_5]) ).
cnf(c_360,plain,
( ~ c_PropLog_Oeval(v_tt,v_pl1,t_a)
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_341,c_7]) ).
cnf(c_344,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_342,c_360]) ).
cnf(c_345,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_80,c_344]) ).
cnf(c_354,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(A,c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_340,c_11]) ).
cnf(c_355,plain,
$false,
inference(resolve,[status(thm)],[c_354,c_345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL442-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 22:36:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3636294 was started by sandbox on n026,
% 0.09/0.37 % Fri Sep 25 22:36:42 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.42
% 0.14/0.42 % Assigning unary symbol tc_PropLog_Opl kb_weight 0 and highest precedence (12).
% 0.14/0.42
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.42
% 0.14/0.42 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.14/0.42 % Length of proof is 42.
% 0.14/0.42 % Level of proof is 21.
% 0.14/0.42 % Maximum clause weight is 60.000.
% 0.14/0.42 % Given clauses 110.
% 0.14/0.42
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------