%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL431-1 : 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 : n018.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 07:58:53 AM UTC 2026
% Result : Unsatisfiable 58.72s 17.37s
% Output : CNFRefutation 58.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 5 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_1,axiom,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_513,plain,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_PropLog_Osat(c_emptyset,v_p,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_514,plain,
c_PropLog_Osat(c_emptyset,v_p,t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_PropLog_Ocompleteness__0__lemma__dest_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(VAR_0,VAR_2,VAR_1),c_PropLog_Ohyps(VAR_0,VAR_3,VAR_1),tc_set(tc_PropLog_Opl(VAR_1))),VAR_1),tc_PropLog_Opl(VAR_1))
| ~ c_PropLog_Osat(c_emptyset,VAR_0,VAR_1) ),
file('theBenchmark.p',cls_PropLog_Ocompleteness__0__lemma__dest_0) ).
cnf(c_540,plain,
( c_in(A,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(A,C,B),c_PropLog_Ohyps(A,D,B),tc_set(tc_PropLog_Opl(B))),B),tc_PropLog_Opl(B))
| ~ c_PropLog_Osat(c_emptyset,A,B) ),
inference(clausify,[status(thm)],[cls_PropLog_Ocompleteness__0__lemma__dest_0]) ).
fof(cls_Set_ODiff__cancel_0,axiom,
! [VAR_0,VAR_1] : c_minus(VAR_0,VAR_0,tc_set(VAR_1)) = c_emptyset,
file('theBenchmark.p',cls_Set_ODiff__cancel_0) ).
cnf(c_1823,plain,
c_minus(A,A,tc_set(B)) = c_emptyset,
inference(clausify,[status(thm)],[cls_Set_ODiff__cancel_0]) ).
cnf(c_4664,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,A,t_a),c_PropLog_Ohyps(v_p,B,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_540,c_514]) ).
cnf(c_14977,plain,
c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(paramod,[status(thm)],[c_1823,c_4664]) ).
cnf(c_14976,plain,
$false,
inference(resolve,[status(thm)],[c_513,c_14977]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL431-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44 % Computer : n018.cluster.edu
% 0.11/0.44 % Model : x86_64 x86_64
% 0.11/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.44 % Memory : 8046.5625MB
% 0.11/0.44 % OS : Linux 6.8.0-71-generic
% 0.11/0.45 % CPULimit : 300
% 0.11/0.45 % WCLimit : 300
% 0.11/0.45 % DateTime : Fri Sep 25 22:34:35 UTC 2026
% 0.11/0.45 % CPUTime :
% 0.11/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.45 % Process 3007952 was started by sandbox on n018,
% 0.11/0.45 % Fri Sep 25 22:34:35 2026
% 0.11/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.50
% 0.15/0.50 % From the command line: assign(max_seconds, 300).
% 58.72/17.37
% 58.72/17.37 % given #500 (I,wt=4): 806 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # tptp_name(clsrel_Ring__and__Field_Oordered__semidom_0) # clausal_fof(1). [assumption].
% 58.72/17.37
% 58.72/17.37 % given #1000 (I,wt=4): 1306 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A) # tptp_name(clsrel_OrderedGroup_Olordered__ab__group__meet_1) # clausal_fof(1). [assumption].
% 58.72/17.37
% 58.72/17.37 % given #1500 (I,wt=22): 1993 -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,A) | -c_less(c_0,C,A) | -c_lessequals(c_HOL_Oinverse(C,A),c_HOL_Oinverse(B,A),A) | c_lessequals(B,C,A) # tptp_name(cls_Ring__and__Field_Oinverse__le__iff__le_0) # clausal_fof(1). [assumption].
% 58.72/17.37
% 58.72/17.37 % given #2000 (I,wt=11): 2832 c_List_Orev(c_List_Oreplicate(A,B,C),C) = c_List_Oreplicate(A,B,C) # tptp_name(cls_List_Orev__replicate_0) # clausal_fof(1). [assumption].
% 58.72/17.37
% 58.72/17.37 % given #2500 (I,wt=22): 3650 -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(68,b,9,a)].
% 58.72/17.37
% 58.72/17.37 % given #3000 (I,wt=10): 4367 c_Numeral_OBit(c_Numeral_Obin__succ(A),c_Numeral_Obit_OB0) = c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OBit(A,c_Numeral_Obit_OB0))). [back_rewrite(2288),rewrite([2290(5)])].
% 58.72/17.37
% 58.72/17.37 % SZS status Unsatisfiable for theBenchmark
% 58.72/17.37
% 58.72/17.37 % Proof 1 at 6.99 (+ 0.68) seconds.
% 58.72/17.37 % Length of proof is 6.
% 58.72/17.37 % Level of proof is 2.
% 58.72/17.37 % Maximum clause weight is 22.000.
% 58.72/17.37 % Given clauses 3238.
% 58.72/17.37
% 58.72/17.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------