%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL447-1 : 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 : n001.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 18.09s 3.12s
% Output : CNFRefutation 18.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 21 ( 4 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_1,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1220,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1221,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_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_1222,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_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_1223,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]) ).
cnf(c_2026,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(resolve,[status(thm)],[c_1223,c_1222]) ).
cnf(c_3752,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(A,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_2026,c_1221]) ).
cnf(c_3753,plain,
$false,
inference(resolve,[status(thm)],[c_3752,c_1220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL447-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n001.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 22:40:26 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.45 % Process 231190 was started by sandbox2 on n001,
% 0.16/0.45 % Fri Sep 25 22:40:26 2026
% 0.16/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.23/0.51
% 0.23/0.51 % From the command line: assign(max_seconds, 300).
% 18.09/3.12
% 18.09/3.12 % given #500 (I,wt=9): 1241 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # tptp_name(clsrel_Ring__and__Field_Opordered__comm__semiring_2) # clausal_fof(1). [assumption].
% 18.09/3.12
% 18.09/3.12 % given #1000 (I,wt=12): 1771 c_less(c_0,A,tc_nat) | c_0 = A. [copy(1770),flip(b)].
% 18.09/3.12
% 18.09/3.12 % SZS status Unsatisfiable for theBenchmark
% 18.09/3.12
% 18.09/3.12 % Proof 1 at 2.46 (+ 0.09) seconds.
% 18.09/3.12 % Length of proof is 7.
% 18.09/3.12 % Level of proof is 3.
% 18.09/3.12 % Maximum clause weight is 34.000.
% 18.09/3.12 % Given clauses 1210.
% 18.09/3.12
% 18.09/3.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------