%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL434-2 : 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 : n002.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 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 27 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_PropLog_Othms_OH_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_in(VAR_0,VAR_1,tc_PropLog_Opl(VAR_2)) ),
file('theBenchmark.p',cls_PropLog_Othms_OH_0) ).
cnf(c_3,plain,
( c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C))
| ~ c_in(A,B,tc_PropLog_Opl(C)) ),
inference(clausify,[status(thm)],[cls_PropLog_Othms_OH_0]) ).
fof(cls_PropLog_Othms__I_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_in(c_PropLog_Opl_Oop_A_N_62(VAR_0,VAR_0,VAR_1),c_PropLog_Othms(VAR_2,VAR_1),tc_PropLog_Opl(VAR_1)),
file('theBenchmark.p',cls_PropLog_Othms__I_0) ).
cnf(c_4,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(A,A,B),c_PropLog_Othms(C,B),tc_PropLog_Opl(B)),
inference(clausify,[status(thm)],[cls_PropLog_Othms__I_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_5,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]) ).
fof(cls_Set_OinsertE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_1
| c_in(VAR_0,VAR_2,VAR_3)
| ~ c_in(VAR_0,c_insert(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(c_6,plain,
( A = B
| c_in(A,C,D)
| ~ c_in(A,c_insert(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OinsertE_0]) ).
cnf(c_10,plain,
~ c_in(v_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_11,plain,
( v_pa = v_p
| c_in(v_pa,v_H,tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_15,plain,
~ c_in(v_pa,v_H,tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_3,c_10]) ).
cnf(c_16,plain,
v_pa = v_p,
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_24,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(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_23,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL434-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n002.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 22:35:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 171526 was started by sandbox2 on n002,
% 0.11/0.37 % Fri Sep 25 22:35:36 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 11.
% 0.11/0.38 % Level of proof is 4.
% 0.11/0.38 % Maximum clause weight is 27.000.
% 0.11/0.38 % Given clauses 10.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------