%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL446-1 : 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 : n015.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 07:58:57 AM UTC 2026
% Result : Unsatisfiable 79.68s 11.63s
% Output : CNFRefutation 79.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 13 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_PropLog_Othms_OK_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_in(c_PropLog_Opl_Oop_A_N_62(VAR_0,c_PropLog_Opl_Oop_A_N_62(VAR_1,VAR_0,VAR_2),VAR_2),c_PropLog_Othms(VAR_3,VAR_2),tc_PropLog_Opl(VAR_2)),
file('theBenchmark.p',cls_PropLog_Othms_OK_0) ).
cnf(c_1068,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Oop_A_N_62(B,A,C),C),c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),
inference(clausify,[status(thm)],[cls_PropLog_Othms_OK_0]) ).
fof(cls_PropLog_Othms_OMP_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_3,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_3,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_Othms_OMP_0) ).
cnf(c_1069,plain,
( c_in(D,c_PropLog_Othms(B,C),tc_PropLog_Opl(C))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(A,D,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_Othms_OMP_0]) ).
fof(cls_PropLog_Othms_OS_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(VAR_0,c_PropLog_Opl_Oop_A_N_62(VAR_1,VAR_2,VAR_3),VAR_3),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_1,VAR_3),c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_2,VAR_3),VAR_3),VAR_3),c_PropLog_Othms(VAR_4,VAR_3),tc_PropLog_Opl(VAR_3)),
file('theBenchmark.p',cls_PropLog_Othms_OS_0) ).
cnf(c_1070,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Oop_A_N_62(B,C,D),D),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,B,D),c_PropLog_Opl_Oop_A_N_62(A,C,D),D),D),c_PropLog_Othms(E,D),tc_PropLog_Opl(D)),
inference(clausify,[status(thm)],[cls_PropLog_Othms_OS_0]) ).
fof(cls_conjecture_0,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_p,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1071,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_p,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_4236,plain,
( c_in(D,c_PropLog_Othms(E,C),tc_PropLog_Opl(C))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Oop_A_N_62(B,A,C),C),D,C),c_PropLog_Othms(E,C),tc_PropLog_Opl(C)) ),
inference(resolve,[status(thm)],[c_1069,c_1068]) ).
cnf(c_2007,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Oop_A_N_62(B,c_PropLog_Opl_Oop_A_N_62(C,B,D),D),D),c_PropLog_Othms(E,D),tc_PropLog_Opl(D)),
inference(resolve,[status(thm)],[c_4236,c_1068]) ).
cnf(c_4237,plain,
( c_in(D,c_PropLog_Othms(E,C),tc_PropLog_Opl(C))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Oop_A_N_62(B,A,C),C),D,C),c_PropLog_Othms(E,C),tc_PropLog_Opl(C)) ),
inference(resolve,[status(thm)],[c_1069,c_1068]) ).
cnf(c_2010,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,B,C),c_PropLog_Opl_Oop_A_N_62(A,A,C),C),c_PropLog_Othms(D,C),tc_PropLog_Opl(C)),
inference(resolve,[status(thm)],[c_4237,c_1070]) ).
cnf(c_4238,plain,
( c_in(E,c_PropLog_Othms(F,D),tc_PropLog_Opl(D))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Oop_A_N_62(B,c_PropLog_Opl_Oop_A_N_62(C,B,D),D),D),E,D),c_PropLog_Othms(F,D),tc_PropLog_Opl(D)) ),
inference(resolve,[status(thm)],[c_1069,c_2007]) ).
cnf(c_4234,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(A,A,B),c_PropLog_Othms(C,B),tc_PropLog_Opl(B)),
inference(resolve,[status(thm)],[c_4238,c_2010]) ).
cnf(c_4235,plain,
$false,
inference(resolve,[status(thm)],[c_4234,c_1071]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL446-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 22:37:43 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 2442211 was started by sandbox on n015,
% 0.11/0.38 % Fri Sep 25 22:37:43 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.41
% 0.11/0.41 % From the command line: assign(max_seconds, 300).
% 79.68/11.63
% 79.68/11.63 % given #500 (I,wt=14): 1261 -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(76,a,75,a)].
% 79.68/11.63
% 79.68/11.63 % given #1000 (I,wt=16): 1804 c_append(A,B,C) != c_append(A,D,C) | B = D # tptp_name(cls_List_Osame__append__eq__iff1_0) # clausal_fof(1). [assumption].
% 79.68/11.63
% 79.68/11.63 % SZS status Unsatisfiable for theBenchmark
% 79.68/11.63
% 79.68/11.63 % Proof 1 at 2.86 (+ 0.17) seconds.
% 79.68/11.63 % Length of proof is 8.
% 79.68/11.63 % Level of proof is 3.
% 79.68/11.63 % Maximum clause weight is 33.000.
% 79.68/11.63 % Given clauses 1178.
% 79.68/11.63
% 79.68/11.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------