%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 5.94s 1.33s
% Output : CNFRefutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 33 unt; 0 def)
% Number of atoms : 47 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 5 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 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 : 52 ( 1 sgn 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_01,axiom,
! [A,B,C] : '+'('+'(A,B),C) = '+'(A,'+'(B,C)),
file('theBenchmark.p',sos_01) ).
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_13,axiom,
! [A,B] : '==>'('==>'(A,B),B) = '==>'('==>'(B,A),A),
file('theBenchmark.p',sos_13) ).
fof(sos_14,axiom,
! [A] : '+'(A,A) = A,
file('theBenchmark.p',sos_14) ).
fof(goals_15,conjecture,
! [X17] : '==>'('==>'('==>'(X17,'1'),X17),X17) = '0',
file('theBenchmark.p',goals_15) ).
fof(goals_15_neg,negated_conjecture,
~ ! [X17] : '==>'('==>'('==>'(X17,'1'),X17),X17) = '0',
inference(assume_negation,[status(cth)],[goals_15]) ).
cnf(c_16,plain,
'+'('+'(A,B),C) = '+'(A,'+'(B,C)),
inference(clausify,[status(thm)],[sos_01]) ).
cnf(c_17,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_18,plain,
'+'(A,'0') = A,
inference(clausify,[status(thm)],[sos_03]) ).
cnf(c_19,plain,
'>='(A,A),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_21,plain,
( B = A
| ~ '>='(B,A)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_06]) ).
cnf(c_22,plain,
( '>='(B,'==>'(A,C))
| ~ '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_23,plain,
( ~ '>='(B,'==>'(A,C))
| '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_24,plain,
'>='(A,'0'),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_29,plain,
'==>'('==>'(A,B),B) = '==>'('==>'(B,A),A),
inference(clausify,[status(thm)],[sos_13]) ).
cnf(c_30,plain,
'+'(A,A) = A,
inference(clausify,[status(thm)],[sos_14]) ).
fof(nnf_15,plain,
? [X17] : '==>'('==>'('==>'(X17,'1'),X17),X17) != '0',
inference(fof_nnf,[status(thm)],[goals_15_neg]) ).
fof(sk_goals_15_neg,plain,
'==>'('==>'('==>'(sK0,'1'),sK0),sK0) != '0',
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X17,sK0)],[nnf_15]) ).
cnf(c_31,negated_conjecture,
'==>'('==>'('==>'(sK0,'1'),sK0),sK0) != '0',
inference(split_conjunct,[status(thm)],[sk_goals_15_neg]) ).
cnf(c_32,negated_conjecture,
'==>'('==>'(sK0,'==>'(sK0,'1')),'==>'(sK0,'1')) != '0',
inference(paramod,[status(thm)],[c_29,c_31]) ).
cnf(c_6881,plain,
A = '+'('0',A),
inference(paramod,[status(thm)],[c_18,c_17]) ).
cnf(c_36,plain,
'+'('0',A) = A,
inference(copy,[status(thm)],[c_6881]) ).
cnf(c_41,plain,
'>='('+'(A,'==>'(A,B)),B),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_6882,plain,
'+'(A,B) = '+'(A,'+'(A,B)),
inference(paramod,[status(thm)],[c_30,c_16]) ).
cnf(c_51,plain,
'+'(A,'+'(A,B)) = '+'(A,B),
inference(copy,[status(thm)],[c_6882]) ).
cnf(c_6883,plain,
( A = '0'
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_21,c_24]) ).
cnf(c_55,negated_conjecture,
~ '>='('0','==>'('==>'(sK0,'==>'(sK0,'1')),'==>'(sK0,'1'))),
inference(resolve,[status(thm)],[c_6883,c_32]) ).
cnf(c_6884,plain,
~ '>='('+'('==>'(sK0,'==>'(sK0,'1')),'0'),'==>'(sK0,'1')),
inference(resolve,[status(thm)],[c_22,c_55]) ).
cnf(c_6885,plain,
~ '>='('+'('0','==>'(sK0,'==>'(sK0,'1'))),'==>'(sK0,'1')),
inference(paramod,[status(thm)],[c_17,c_6884]) ).
cnf(c_69,plain,
~ '>='('==>'(sK0,'==>'(sK0,'1')),'==>'(sK0,'1')),
inference(paramod,[status(thm)],[c_36,c_6885]) ).
cnf(c_71,plain,
~ '>='('+'(sK0,'==>'(sK0,'==>'(sK0,'1'))),'1'),
inference(resolve,[status(thm)],[c_22,c_69]) ).
cnf(c_165,plain,
'>='('+'(A,'+'(B,'==>'(B,'==>'(A,C)))),C),
inference(resolve,[status(thm)],[c_23,c_41]) ).
cnf(c_6879,plain,
'>='('+'(A,'==>'(A,'==>'(A,B))),B),
inference(paramod,[status(thm)],[c_51,c_165]) ).
cnf(c_6880,plain,
$false,
inference(resolve,[status(thm)],[c_6879,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 23:50:09 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3765080 was started by sandbox2 on n026,
% 0.18/0.45 % Fri Sep 25 23:50:09 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 5.94/1.33
% 5.94/1.33 % SZS status Theorem for theBenchmark
% 5.94/1.33
% 5.94/1.33 % Proof 1 at 0.64 (+ 0.22) seconds.
% 5.94/1.33 % Length of proof is 31.
% 5.94/1.33 % Level of proof is 6.
% 5.94/1.33 % Maximum clause weight is 46.000.
% 5.94/1.33 % Given clauses 252.
% 5.94/1.33
% 5.94/1.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------