%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL896+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 : n009.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 13.91s 2.25s
% Output : CNFRefutation 13.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 34 unt; 0 def)
% Number of atoms : 56 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 8 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 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 : 86 ( 8 sgn 23 !; 2 ?)
% 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_09,axiom,
! [X8,X9,X10] :
( '>='(X8,X9)
=> '>='('+'(X8,X10),'+'(X9,X10)) ),
file('theBenchmark.p',sos_09) ).
fof(sos_12,axiom,
! [A,B,C] : '+'('+'(A,'==>'(A,B)),'==>'('+'(A,'==>'(A,B)),C)) = '+'(A,'==>'(A,'+'(B,'==>'(B,C)))),
file('theBenchmark.p',sos_12) ).
fof(goals_13,conjecture,
! [X17,X18] : '+'(X17,'==>'(X17,X18)) = '+'(X18,'==>'(X18,X17)),
file('theBenchmark.p',goals_13) ).
fof(goals_13_neg,negated_conjecture,
~ ! [X17,X18] : '+'(X17,'==>'(X17,X18)) = '+'(X18,'==>'(X18,X17)),
inference(assume_negation,[status(cth)],[goals_13]) ).
cnf(c_14,plain,
'+'('+'(A,B),C) = '+'(A,'+'(B,C)),
inference(clausify,[status(thm)],[sos_01]) ).
cnf(c_15,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_16,plain,
'+'(A,'0') = A,
inference(clausify,[status(thm)],[sos_03]) ).
cnf(c_17,plain,
'>='(A,A),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_19,plain,
( B = A
| ~ '>='(B,A)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_06]) ).
cnf(c_20,plain,
( '>='(B,'==>'(A,C))
| ~ '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_21,plain,
( ~ '>='(B,'==>'(A,C))
| '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_22,plain,
'>='(A,'0'),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_23,plain,
( '>='('+'(A,C),'+'(B,C))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_26,plain,
'+'('+'(A,'==>'(A,B)),'==>'('+'(A,'==>'(A,B)),C)) = '+'(A,'==>'(A,'+'(B,'==>'(B,C)))),
inference(clausify,[status(thm)],[sos_12]) ).
cnf(c_27,plain,
'+'(A,'+'('==>'(A,B),'==>'('+'(A,'==>'(A,B)),C))) = '+'(A,'==>'(A,'+'(B,'==>'(B,C)))),
inference(paramod,[status(thm)],[c_14,c_26]) ).
fof(nnf_13,plain,
? [X17,X18] : '+'(X18,'==>'(X18,X17)) != '+'(X17,'==>'(X17,X18)),
inference(fof_nnf,[status(thm)],[goals_13_neg]) ).
fof(sk_goals_13_neg,plain,
'+'(sK0,'==>'(sK0,sK1)) != '+'(sK1,'==>'(sK1,sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X17,sK1),skolemize(X18,sK0)],[nnf_13]) ).
cnf(c_28,negated_conjecture,
'+'(sK0,'==>'(sK0,sK1)) != '+'(sK1,'==>'(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_13_neg]) ).
cnf(c_7533,plain,
A = '+'('0',A),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_32,plain,
'+'('0',A) = A,
inference(copy,[status(thm)],[c_7533]) ).
cnf(c_34,plain,
( '>='(C,'==>'('+'(A,B),D))
| ~ '>='('+'(A,'+'(B,C)),D) ),
inference(paramod,[status(thm)],[c_14,c_20]) ).
cnf(c_37,plain,
'>='('+'(A,'==>'(A,B)),B),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_7534,plain,
'>='('+'(A,B),'+'('0',B)),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_39,plain,
'>='('+'(A,B),B),
inference(paramod,[status(thm)],[c_32,c_7534]) ).
cnf(c_55,plain,
'>='('+'(A,B),A),
inference(paramod,[status(thm)],[c_15,c_39]) ).
cnf(c_84,plain,
'>='(A,'==>'('+'(B,C),B)),
inference(resolve,[status(thm)],[c_34,c_55]) ).
cnf(c_7535,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_7536,plain,
'0' = '==>'('+'(A,B),A),
inference(resolve,[status(thm)],[c_7535,c_84]) ).
cnf(c_186,plain,
'==>'('+'(A,B),A) = '0',
inference(copy,[status(thm)],[c_7536]) ).
cnf(c_7537,plain,
'+'(A,'+'('==>'(A,B),'0')) = '+'(A,'==>'(A,'+'(B,'==>'(B,A)))),
inference(paramod,[status(thm)],[c_186,c_27]) ).
cnf(c_7538,plain,
'+'(A,'+'('0','==>'(A,B))) = '+'(A,'==>'(A,'+'(B,'==>'(B,A)))),
inference(paramod,[status(thm)],[c_15,c_7537]) ).
cnf(c_7539,plain,
'+'(A,'==>'(A,B)) = '+'(A,'==>'(A,'+'(B,'==>'(B,A)))),
inference(paramod,[status(thm)],[c_32,c_7538]) ).
cnf(c_208,plain,
'+'(A,'==>'(A,'+'(B,'==>'(B,A)))) = '+'(A,'==>'(A,B)),
inference(copy,[status(thm)],[c_7539]) ).
cnf(c_7486,plain,
'>='('+'(A,'==>'(A,B)),'+'(B,'==>'(B,A))),
inference(paramod,[status(thm)],[c_208,c_37]) ).
cnf(c_7540,plain,
( '+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A))
| ~ '>='('+'(A,'==>'(A,B)),'+'(B,'==>'(B,A))) ),
inference(resolve,[status(thm)],[c_19,c_7486]) ).
cnf(c_7531,plain,
'+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)),
inference(resolve,[status(thm)],[c_7540,c_7486]) ).
cnf(c_7532,plain,
$false,
inference(resolve,[status(thm)],[c_7531,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL896+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 : n009.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 23:46:59 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 2863771 was started by sandbox on n009,
% 0.09/0.36 % Fri Sep 25 23:46:59 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 13.91/2.25
% 13.91/2.25 % SZS status Theorem for theBenchmark
% 13.91/2.25
% 13.91/2.25 % Proof 1 at 1.26 (+ 0.54) seconds.
% 13.91/2.25 % Length of proof is 33.
% 13.91/2.25 % Level of proof is 10.
% 13.91/2.25 % Maximum clause weight is 37.000.
% 13.91/2.25 % Given clauses 269.
% 13.91/2.25
% 13.91/2.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------