%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL436-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 07:58:54 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 18 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,c_PropLog_Opl_Oop_A_N_62(v_q,v_r,t_a),t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(v_pa,v_r,t_a),t_a),t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,c_PropLog_Opl_Oop_A_N_62(v_q,v_r,t_a),t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(v_pa,v_r,t_a),t_a),t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_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_2,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_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_3,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_4,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,c_PropLog_Opl_Oop_A_N_62(v_q,v_r,t_a),t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(v_pa,v_r,t_a),t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_5,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL436-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 22:31:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2083552 was started by sandbox2 on n007,
% 0.09/0.36 % Fri Sep 25 22:31:09 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 5.
% 0.13/0.37 % Level of proof is 2.
% 0.13/0.37 % Maximum clause weight is 28.000.
% 0.13/0.37 % Given clauses 3.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------