%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO629-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 09:51:07 AM UTC 2026
% Result : Unsatisfiable 0.11s 10.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 26 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 30 ( 3 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_10_06,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),'0')
| 'E'('0',f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s('0')) ),
file('theBenchmark.p',clause_10_06) ).
cnf(c_1,plain,
( 'LE'(f(B),'0')
| 'E'('0',f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s('0')) ),
inference(clausify,[status(thm)],[clause_10_06]) ).
fof(clause_0_02,axiom,
! [VAR_0] : iLEQ(VAR_0,VAR_0),
file('theBenchmark.p',clause_0_02) ).
cnf(c_2,plain,
iLEQ(A,A),
inference(clausify,[status(thm)],[clause_0_02]) ).
fof(clause_3_09,axiom,
! [VAR_0] : iLEQ(VAR_0,g(VAR_0)),
file('theBenchmark.p',clause_3_09) ).
cnf(c_3,plain,
iLEQ(A,g(A)),
inference(clausify,[status(thm)],[clause_3_09]) ).
cnf(c_6,plain,
( 'LE'(f(g(A)),'0')
| 'E'('0',f(g(A)))
| ~ 'LE'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_7,plain,
( 'LE'(f(A),'0')
| 'E'('0',f(A))
| ~ 'LE'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(clause_4_11,axiom,
! [VAR_0] : ~ 'E'(f(VAR_0),f(g(VAR_0))),
file('theBenchmark.p',clause_4_11) ).
cnf(c_8,plain,
~ 'E'(f(A),f(g(A))),
inference(clausify,[status(thm)],[clause_4_11]) ).
fof(clause_1_07,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s('0'),f(g(VAR_0)))
| ~ 'E'(s('0'),f(VAR_0)) ),
file('theBenchmark.p',clause_1_07) ).
cnf(c_10,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s('0'),f(g(A)))
| ~ 'E'(s('0'),f(A)) ),
inference(clausify,[status(thm)],[clause_1_07]) ).
cnf(c_11,plain,
( ~ 'E'(s('0'),f(g(A)))
| ~ 'E'(s('0'),f(A)) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
fof(clause_7_05,axiom,
! [VAR_0] : ~ 'LE'(f(VAR_0),'0'),
file('theBenchmark.p',clause_7_05) ).
cnf(c_12,plain,
~ 'LE'(f(A),'0'),
inference(clausify,[status(thm)],[clause_7_05]) ).
fof(clause_6_04,axiom,
! [VAR_0] :
( 'LE'(f(VAR_0),s('0'))
| 'E'(s('0'),f(VAR_0)) ),
file('theBenchmark.p',clause_6_04) ).
cnf(c_13,plain,
( 'LE'(f(A),s('0'))
| 'E'(s('0'),f(A)) ),
inference(clausify,[status(thm)],[clause_6_04]) ).
fof(clause_11_03,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'('0',f(g(VAR_0)))
| ~ 'E'('0',f(VAR_0)) ),
file('theBenchmark.p',clause_11_03) ).
cnf(c_14,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'('0',f(g(A)))
| ~ 'E'('0',f(A)) ),
inference(clausify,[status(thm)],[clause_11_03]) ).
cnf(c_15,plain,
( ~ 'E'('0',f(g(A)))
| ~ 'E'('0',f(A)) ),
inference(resolve,[status(thm)],[c_8,c_14]) ).
cnf(c_16,plain,
( 'E'('0',f(g(A)))
| ~ 'LE'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_17,plain,
( 'E'('0',f(A))
| ~ 'LE'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_18,plain,
( 'E'(s('0'),f(A))
| 'E'('0',f(g(A))) ),
inference(resolve,[status(thm)],[c_16,c_13]) ).
cnf(c_19,plain,
( 'E'(s('0'),f(A))
| 'E'('0',f(A)) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_21,plain,
( ~ 'E'(s('0'),f(A))
| 'E'('0',f(g(A))) ),
inference(resolve,[status(thm)],[c_19,c_11]) ).
cnf(c_26,plain,
( 'E'('0',f(g(A)))
| 'E'('0',f(g(A))) ),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_23,plain,
'E'('0',f(g(A))),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_24,plain,
~ 'E'('0',f(A)),
inference(resolve,[status(thm)],[c_23,c_15]) ).
cnf(c_25,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO629-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.37 % Computer : n015.cluster.edu
% 0.11/10.37 % Model : x86_64 x86_64
% 0.11/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.37 % Memory : 8046.5625MB
% 0.11/10.37 % OS : Linux 6.8.0-71-generic
% 0.11/10.37 % CPULimit : 300
% 0.11/10.37 % WCLimit : 300
% 0.11/10.37 % DateTime : Sat Sep 26 19:43:56 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.38 % Process 611507 was started by sandbox on n015,
% 0.11/10.38 % Sat Sep 26 19:43:56 2026
% 0.11/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/10.38
% 0.11/10.38 % From the command line: assign(max_seconds, 300).
% 0.11/10.39
% 0.11/10.39 % SZS status Unsatisfiable for theBenchmark
% 0.11/10.39
% 0.11/10.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/10.39 % Length of proof is 20.
% 0.11/10.39 % Level of proof is 7.
% 0.11/10.39 % Maximum clause weight is 15.000.
% 0.11/10.39 % Given clauses 10.
% 0.11/10.39
% 0.11/10.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------