%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL893+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 : n007.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 07:59:59 AM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 20 unt; 0 def)
% Number of atoms : 40 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 4 |; 3 &)
% ( 1 <=>; 3 =>; 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; 2 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_03,axiom,
! [A] : '+'(A,'0') = A,
file('theBenchmark.p',sos_03) ).
fof(sos_05,axiom,
! [A] : '>='(A,A),
file('theBenchmark.p',sos_05) ).
fof(sos_07,axiom,
! [X3,X4] :
( ( '>='(X4,X3)
& '>='(X3,X4) )
=> X3 = X4 ),
file('theBenchmark.p',sos_07) ).
fof(sos_08,axiom,
! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
<=> '>='(X6,'==>'(X5,X7)) ),
file('theBenchmark.p',sos_08) ).
fof(sos_09,axiom,
! [A] : '>='(A,'0'),
file('theBenchmark.p',sos_09) ).
fof(sos_14,axiom,
! [A] : h(A) = '==>'(h(A),A),
file('theBenchmark.p',sos_14) ).
fof(goals_15,conjecture,
! [X17] :
( h(X17) = X17
=> X17 = '0' ),
file('theBenchmark.p',goals_15) ).
fof(goals_15_neg,negated_conjecture,
~ ! [X17] :
( h(X17) = X17
=> X17 = '0' ),
inference(assume_negation,[status(cth)],[goals_15]) ).
cnf(c_18,plain,
'+'(A,'0') = A,
inference(clausify,[status(thm)],[sos_03]) ).
cnf(c_20,plain,
'>='(A,A),
inference(clausify,[status(thm)],[sos_05]) ).
cnf(c_22,plain,
( B = A
| ~ '>='(B,A)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_23,plain,
( '>='(B,'==>'(A,C))
| ~ '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_25,plain,
'>='(A,'0'),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_30,plain,
h(A) = '==>'(h(A),A),
inference(clausify,[status(thm)],[sos_14]) ).
cnf(c_31,plain,
'==>'(h(A),A) = h(A),
inference(copy,[status(thm)],[c_30]) ).
fof(nnf_15,plain,
? [X17] :
( X17 != '0'
& h(X17) = X17 ),
inference(fof_nnf,[status(thm)],[goals_15_neg]) ).
fof(sk_goals_15_neg,plain,
( sK0 != '0'
& h(sK0) = sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X17,sK0)],[nnf_15]) ).
cnf(c_32,negated_conjecture,
h(sK0) = sK0,
inference(split_conjunct,[status(thm)],[sk_goals_15_neg]) ).
cnf(c_33,negated_conjecture,
sK0 != '0',
inference(split_conjunct,[status(thm)],[sk_goals_15_neg]) ).
cnf(c_41,plain,
'>='(A,'==>'(B,'+'(B,A))),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_90,plain,
'==>'(sK0,sK0) = h(sK0),
inference(paramod,[status(thm)],[c_32,c_31]) ).
cnf(c_56,plain,
'==>'(sK0,sK0) = sK0,
inference(paramod,[status(thm)],[c_32,c_90]) ).
cnf(c_91,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_22,c_25]) ).
cnf(c_92,plain,
'0' = '==>'(A,'+'(A,'0')),
inference(resolve,[status(thm)],[c_91,c_41]) ).
cnf(c_93,plain,
'0' = '==>'(A,A),
inference(paramod,[status(thm)],[c_18,c_92]) ).
cnf(c_82,plain,
'==>'(A,A) = '0',
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
'0' = sK0,
inference(paramod,[status(thm)],[c_82,c_56]) ).
cnf(c_88,plain,
sK0 = '0',
inference(copy,[status(thm)],[c_94]) ).
cnf(c_89,plain,
$false,
inference(resolve,[status(thm)],[c_88,c_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL893+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 23:44:08 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.39 % Process 2205086 was started by sandbox on n007,
% 0.15/0.39 % Fri Sep 25 23:44:08 2026
% 0.15/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 0.15/0.40
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40
% 0.15/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.40 % Length of proof is 21.
% 0.15/0.40 % Level of proof is 5.
% 0.15/0.40 % Maximum clause weight is 10.000.
% 0.15/0.40 % Given clauses 24.
% 0.15/0.40
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------