%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 08:00:00 AM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 35 unt; 0 def)
% Number of atoms : 57 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 8 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 11 sgn 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_02,axiom,
! [A,B] : '+'(A,B) = '+'(B,A),
file('theBenchmark.p',sos_02) ).
fof(sos_03,axiom,
! [A] : '+'(A,'0') = A,
file('theBenchmark.p',sos_03) ).
fof(sos_04,axiom,
! [A] : '>='(A,A),
file('theBenchmark.p',sos_04) ).
fof(sos_06,axiom,
! [X3,X4] :
( ( '>='(X4,X3)
& '>='(X3,X4) )
=> X3 = X4 ),
file('theBenchmark.p',sos_06) ).
fof(sos_07,axiom,
! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
<=> '>='(X6,'==>'(X5,X7)) ),
file('theBenchmark.p',sos_07) ).
fof(sos_08,axiom,
! [A] : '>='(A,'0'),
file('theBenchmark.p',sos_08) ).
fof(sos_09,axiom,
! [X8,X9,X10] :
( '>='(X8,X9)
=> '>='('+'(X8,X10),'+'(X9,X10)) ),
file('theBenchmark.p',sos_09) ).
fof(sos_12,axiom,
! [A] : '+'(A,'1') = '1',
file('theBenchmark.p',sos_12) ).
fof(sos_13,axiom,
! [A,B] : '==>'('==>'(A,B),B) = '==>'('==>'(B,A),A),
file('theBenchmark.p',sos_13) ).
fof(goals_14,conjecture,
! [X17] : '==>'('==>'(X17,'1'),'1') = X17,
file('theBenchmark.p',goals_14) ).
fof(goals_14_neg,negated_conjecture,
~ ! [X17] : '==>'('==>'(X17,'1'),'1') = X17,
inference(assume_negation,[status(cth)],[goals_14]) ).
cnf(c_16,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_17,plain,
'+'(A,'0') = A,
inference(clausify,[status(thm)],[sos_03]) ).
cnf(c_18,plain,
'>='(A,A),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_20,plain,
( B = A
| ~ '>='(B,A)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_06]) ).
cnf(c_21,plain,
( '>='(B,'==>'(A,C))
| ~ '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_22,plain,
( ~ '>='(B,'==>'(A,C))
| '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_23,plain,
'>='(A,'0'),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_24,plain,
( '>='('+'(A,C),'+'(B,C))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_27,plain,
'+'(A,'1') = '1',
inference(clausify,[status(thm)],[sos_12]) ).
cnf(c_28,plain,
'==>'('==>'(A,B),B) = '==>'('==>'(B,A),A),
inference(clausify,[status(thm)],[sos_13]) ).
fof(nnf_14,plain,
? [X17] : '==>'('==>'(X17,'1'),'1') != X17,
inference(fof_nnf,[status(thm)],[goals_14_neg]) ).
fof(sk_goals_14_neg,plain,
'==>'('==>'(sK0,'1'),'1') != sK0,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X17,sK0)],[nnf_14]) ).
cnf(c_29,negated_conjecture,
'==>'('==>'(sK0,'1'),'1') != sK0,
inference(split_conjunct,[status(thm)],[sk_goals_14_neg]) ).
cnf(c_30,negated_conjecture,
'==>'('==>'('1',sK0),sK0) != sK0,
inference(paramod,[status(thm)],[c_28,c_29]) ).
cnf(c_152,plain,
A = '+'('0',A),
inference(paramod,[status(thm)],[c_17,c_16]) ).
cnf(c_34,plain,
'+'('0',A) = A,
inference(copy,[status(thm)],[c_152]) ).
cnf(c_38,plain,
( '>='('0','==>'(A,B))
| ~ '>='(A,B) ),
inference(paramod,[status(thm)],[c_17,c_21]) ).
cnf(c_39,plain,
'>='('+'(A,'==>'(A,B)),B),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_153,plain,
'>='('+'(A,B),'+'('0',B)),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_41,plain,
'>='('+'(A,B),B),
inference(paramod,[status(thm)],[c_34,c_153]) ).
cnf(c_154,plain,
'1' = '+'('1',A),
inference(paramod,[status(thm)],[c_27,c_16]) ).
cnf(c_45,plain,
'+'('1',A) = '1',
inference(copy,[status(thm)],[c_154]) ).
cnf(c_73,plain,
'>='(A,'==>'(B,A)),
inference(resolve,[status(thm)],[c_21,c_41]) ).
cnf(c_79,plain,
'>='('1',A),
inference(paramod,[status(thm)],[c_45,c_41]) ).
cnf(c_92,plain,
'>='('0','==>'('1',A)),
inference(resolve,[status(thm)],[c_38,c_79]) ).
cnf(c_155,plain,
( B = '==>'(A,B)
| ~ '>='('==>'(A,B),B) ),
inference(resolve,[status(thm)],[c_20,c_73]) ).
cnf(c_156,negated_conjecture,
sK0 != '==>'('==>'('1',sK0),sK0),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_106,negated_conjecture,
~ '>='('==>'('==>'('1',sK0),sK0),sK0),
inference(resolve,[status(thm)],[c_155,c_156]) ).
cnf(c_157,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_158,plain,
'0' = '==>'('1',A),
inference(resolve,[status(thm)],[c_157,c_92]) ).
cnf(c_121,plain,
'==>'('1',A) = '0',
inference(copy,[status(thm)],[c_158]) ).
cnf(c_122,negated_conjecture,
~ '>='('==>'('0',sK0),sK0),
inference(paramod,[status(thm)],[c_121,c_106]) ).
cnf(c_150,plain,
'>='('==>'('0',A),A),
inference(paramod,[status(thm)],[c_34,c_39]) ).
cnf(c_151,plain,
$false,
inference(resolve,[status(thm)],[c_150,c_122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.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 23:49:27 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 3762990 was started by sandbox on n026,
% 0.09/0.36 % Fri Sep 25 23:49:27 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.40 % Length of proof is 35.
% 0.14/0.40 % Level of proof is 8.
% 0.14/0.40 % Maximum clause weight is 36.000.
% 0.14/0.40 % Given clauses 34.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------