%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL903+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 : n012.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 08:00:01 AM UTC 2026
% Result : Theorem 7.44s 1.36s
% Output : CNFRefutation 7.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 51 unt; 0 def)
% Number of atoms : 91 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 18 ~; 14 |; 2 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 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 : 120 ( 15 sgn 26 !; 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_05,axiom,
! [X0,X1,X2] :
( ( '>='(X1,X2)
& '>='(X0,X1) )
=> '>='(X0,X2) ),
file('theBenchmark.p',sos_05) ).
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_10,axiom,
! [X11,X12,X13] :
( '>='(X11,X12)
=> '>='('==>'(X12,X13),'==>'(X11,X13)) ),
file('theBenchmark.p',sos_10) ).
fof(sos_11,axiom,
! [X14,X15,X16] :
( '>='(X14,X15)
=> '>='('==>'(X16,X14),'==>'(X16,X15)) ),
file('theBenchmark.p',sos_11) ).
fof(sos_12,axiom,
! [A] : '+'(A,'1') = '1',
file('theBenchmark.p',sos_12) ).
fof(sos_13,axiom,
! [A] : '==>'('==>'('==>'(A,'1'),A),A) = '0',
file('theBenchmark.p',sos_13) ).
fof(goals_14,conjecture,
! [X17] : '+'(X17,X17) = X17,
file('theBenchmark.p',goals_14) ).
fof(goals_14_neg,negated_conjecture,
~ ! [X17] : '+'(X17,X17) = 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_19,plain,
( '>='(A,C)
| ~ '>='(B,C)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_05]) ).
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_25,plain,
( '>='('==>'(B,C),'==>'(A,C))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_10]) ).
cnf(c_26,plain,
( '>='('==>'(C,A),'==>'(C,B))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_11]) ).
cnf(c_27,plain,
'+'(A,'1') = '1',
inference(clausify,[status(thm)],[sos_12]) ).
cnf(c_28,plain,
'==>'('==>'('==>'(A,'1'),A),A) = '0',
inference(clausify,[status(thm)],[sos_13]) ).
fof(nnf_14,plain,
? [X17] : '+'(X17,X17) != X17,
inference(fof_nnf,[status(thm)],[goals_14_neg]) ).
fof(sk_goals_14_neg,plain,
'+'(sK0,sK0) != sK0,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X17,sK0)],[nnf_14]) ).
cnf(c_29,negated_conjecture,
'+'(sK0,sK0) != sK0,
inference(split_conjunct,[status(thm)],[sk_goals_14_neg]) ).
cnf(c_5921,plain,
A = '+'('0',A),
inference(paramod,[status(thm)],[c_17,c_16]) ).
cnf(c_33,plain,
'+'('0',A) = A,
inference(copy,[status(thm)],[c_5921]) ).
cnf(c_34,plain,
'>='(A,'==>'(B,'+'(B,A))),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_35,plain,
'>='('+'(A,'==>'(A,B)),B),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_5922,plain,
'>='('+'(A,B),'+'('0',B)),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_37,plain,
'>='('+'(A,B),B),
inference(paramod,[status(thm)],[c_33,c_5922]) ).
cnf(c_5923,plain,
'1' = '+'('1',A),
inference(paramod,[status(thm)],[c_27,c_16]) ).
cnf(c_41,plain,
'+'('1',A) = '1',
inference(copy,[status(thm)],[c_5923]) ).
cnf(c_52,plain,
'>='(A,'==>'(B,A)),
inference(resolve,[status(thm)],[c_21,c_37]) ).
cnf(c_57,plain,
'>='('1',A),
inference(paramod,[status(thm)],[c_41,c_37]) ).
cnf(c_58,plain,
'>='('==>'(A,'1'),'==>'(A,B)),
inference(resolve,[status(thm)],[c_26,c_57]) ).
cnf(c_60,plain,
'>='('==>'(A,B),'==>'(A,'==>'(C,'+'(C,B)))),
inference(resolve,[status(thm)],[c_26,c_34]) ).
cnf(c_5924,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_5925,plain,
'0' = '==>'(A,'+'(A,'0')),
inference(resolve,[status(thm)],[c_5924,c_34]) ).
cnf(c_5926,plain,
'0' = '==>'(A,A),
inference(paramod,[status(thm)],[c_17,c_5925]) ).
cnf(c_64,plain,
'==>'(A,A) = '0',
inference(copy,[status(thm)],[c_5926]) ).
cnf(c_68,plain,
'>='(A,'==>'(B,'+'(A,B))),
inference(paramod,[status(thm)],[c_16,c_34]) ).
cnf(c_80,plain,
'>='('+'(A,B),'+'('==>'(C,A),B)),
inference(resolve,[status(thm)],[c_24,c_52]) ).
cnf(c_109,plain,
'>='('==>'('==>'(A,B),C),'==>'('==>'(A,'1'),C)),
inference(resolve,[status(thm)],[c_25,c_58]) ).
cnf(c_5927,plain,
'>='('+'('==>'('==>'(A,'1'),A),'0'),A),
inference(paramod,[status(thm)],[c_28,c_35]) ).
cnf(c_5928,plain,
'>='('+'('0','==>'('==>'(A,'1'),A)),A),
inference(paramod,[status(thm)],[c_16,c_5927]) ).
cnf(c_135,plain,
'>='('==>'('==>'(A,'1'),A),A),
inference(paramod,[status(thm)],[c_33,c_5928]) ).
cnf(c_211,plain,
'>='('+'(A,B),'+'(B,A)),
inference(resolve,[status(thm)],[c_22,c_68]) ).
cnf(c_5929,plain,
( '>='('+'(B,C),D)
| ~ '>='('+'('==>'(A,B),C),D) ),
inference(resolve,[status(thm)],[c_19,c_80]) ).
cnf(c_346,plain,
'>='('+'(A,B),'+'(B,'==>'(C,A))),
inference(resolve,[status(thm)],[c_5929,c_211]) ).
cnf(c_5930,plain,
( '==>'(A,B) = B
| ~ '>='('==>'(A,B),B) ),
inference(resolve,[status(thm)],[c_20,c_52]) ).
cnf(c_570,plain,
'==>'('==>'(A,'1'),A) = A,
inference(resolve,[status(thm)],[c_5930,c_135]) ).
cnf(c_4954,plain,
'>='('==>'('==>'(A,B),A),A),
inference(paramod,[status(thm)],[c_570,c_109]) ).
cnf(c_5931,plain,
( '==>'(A,B) = B
| ~ '>='('==>'(A,B),B) ),
inference(resolve,[status(thm)],[c_20,c_52]) ).
cnf(c_5062,plain,
'==>'('==>'(A,B),A) = A,
inference(resolve,[status(thm)],[c_5931,c_4954]) ).
cnf(c_5236,plain,
'==>'(A,'==>'(A,B)) = '==>'(A,B),
inference(paramod,[status(thm)],[c_5062,c_5062]) ).
cnf(c_5823,plain,
'>='('==>'(A,B),'==>'(A,'+'(A,B))),
inference(paramod,[status(thm)],[c_5236,c_60]) ).
cnf(c_5840,plain,
'>='('+'(A,'==>'(A,B)),'+'(A,B)),
inference(resolve,[status(thm)],[c_22,c_5823]) ).
cnf(c_5932,plain,
( '+'(A,'==>'(B,C)) = '+'(C,A)
| ~ '>='('+'(A,'==>'(B,C)),'+'(C,A)) ),
inference(resolve,[status(thm)],[c_20,c_346]) ).
cnf(c_5933,plain,
'+'(A,'==>'(A,A)) = '+'(A,A),
inference(resolve,[status(thm)],[c_5932,c_5840]) ).
cnf(c_5934,plain,
'+'(A,'0') = '+'(A,A),
inference(paramod,[status(thm)],[c_64,c_5933]) ).
cnf(c_5935,plain,
A = '+'(A,A),
inference(paramod,[status(thm)],[c_17,c_5934]) ).
cnf(c_5919,plain,
'+'(A,A) = A,
inference(copy,[status(thm)],[c_5935]) ).
cnf(c_5920,plain,
$false,
inference(resolve,[status(thm)],[c_5919,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL903+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 23:47:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3340476 was started by sandbox2 on n012,
% 0.08/0.35 % Fri Sep 25 23:47:05 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 7.44/1.36
% 7.44/1.36 % SZS status Theorem for theBenchmark
% 7.44/1.36
% 7.44/1.36 % Proof 1 at 0.75 (+ 0.24) seconds.
% 7.44/1.36 % Length of proof is 51.
% 7.44/1.36 % Level of proof is 13.
% 7.44/1.36 % Maximum clause weight is 33.000.
% 7.44/1.36 % Given clauses 240.
% 7.44/1.36
% 7.44/1.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------