%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 09:51:08 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 143 ( 75 ~; 68 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 98 ( 71 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_4_12,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),VAR_3)),s(s('0')))
| ~ 'E'(f(VAR_2),s(s(s('0'))))
| ~ 'E'(f(VAR_1),s(s(s(s(s('0'))))))
| ~ 'E'(f(VAR_0),s(s(s(s('0'))))) ),
file('theBenchmark.p',clause_4_12) ).
cnf(c_1,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),D)),s(s('0')))
| ~ 'E'(f(C),s(s(s('0'))))
| ~ 'E'(f(B),s(s(s(s(s('0'))))))
| ~ 'E'(f(A),s(s(s(s('0'))))) ),
inference(clausify,[status(thm)],[clause_4_12]) ).
fof(clause_1_10,axiom,
! [VAR_0,VAR_1] :
( 'E'(f(VAR_1),s(s(s('0'))))
| ~ 'E'(f(VAR_1),s(s(s(s(s('0'))))))
| ~ 'E'(f(VAR_0),s(s(s(s('0'))))) ),
file('theBenchmark.p',clause_1_10) ).
cnf(c_2,plain,
( 'E'(f(B),s(s(s('0'))))
| ~ 'E'(f(B),s(s(s(s(s('0'))))))
| ~ 'E'(f(A),s(s(s(s('0'))))) ),
inference(clausify,[status(thm)],[clause_1_10]) ).
fof(clause_12_09,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),VAR_4)),s('0'))
| ~ 'E'(f(VAR_3),s(s('0')))
| ~ 'E'(f(VAR_2),s(s(s('0'))))
| ~ 'E'(f(VAR_1),s(s(s(s(s('0'))))))
| ~ 'E'(f(VAR_0),s(s(s(s('0'))))) ),
file('theBenchmark.p',clause_12_09) ).
cnf(c_3,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),E)),s('0'))
| ~ 'E'(f(D),s(s('0')))
| ~ 'E'(f(C),s(s(s('0'))))
| ~ 'E'(f(B),s(s(s(s(s('0'))))))
| ~ 'E'(f(A),s(s(s(s('0'))))) ),
inference(clausify,[status(thm)],[clause_12_09]) ).
fof(clause_2_07,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),VAR_5)),'0')
| ~ 'E'(f(VAR_4),s(s(s(s(s('0'))))))
| ~ 'E'(f(VAR_3),s('0'))
| ~ 'E'(f(VAR_2),s(s(s('0'))))
| ~ 'E'(f(VAR_1),s(s(s(s('0')))))
| ~ 'E'(f(VAR_0),s(s('0'))) ),
file('theBenchmark.p',clause_2_07) ).
cnf(c_4,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),F)),'0')
| ~ 'E'(f(E),s(s(s(s(s('0'))))))
| ~ 'E'(f(D),s('0'))
| ~ 'E'(f(C),s(s(s('0'))))
| ~ 'E'(f(B),s(s(s(s('0')))))
| ~ 'E'(f(A),s(s('0'))) ),
inference(clausify,[status(thm)],[clause_2_07]) ).
fof(clause_8_05,axiom,
! [VAR_0] : 'E'(f(VAR_0),s(s(s(s(s('0')))))),
file('theBenchmark.p',clause_8_05) ).
cnf(c_5,plain,
'E'(f(A),s(s(s(s(s('0')))))),
inference(clausify,[status(thm)],[clause_8_05]) ).
fof(clause_6_04,axiom,
! [VAR_0] : 'E'(f(VAR_0),s(s(s(s('0'))))),
file('theBenchmark.p',clause_6_04) ).
cnf(c_6,plain,
'E'(f(A),s(s(s(s('0'))))),
inference(clausify,[status(thm)],[clause_6_04]) ).
fof(clause_5_03,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ 'E'(f(VAR_5),s(s(s(s(s('0'))))))
| ~ 'E'(f(VAR_4),'0')
| ~ 'E'(f(VAR_3),s('0'))
| ~ 'E'(f(VAR_2),s(s(s('0'))))
| ~ 'E'(f(VAR_1),s(s(s(s('0')))))
| ~ 'E'(f(VAR_0),s(s('0'))) ),
file('theBenchmark.p',clause_5_03) ).
cnf(c_7,plain,
( ~ 'E'(f(F),s(s(s(s(s('0'))))))
| ~ 'E'(f(E),'0')
| ~ 'E'(f(D),s('0'))
| ~ 'E'(f(C),s(s(s('0'))))
| ~ 'E'(f(B),s(s(s(s('0')))))
| ~ 'E'(f(A),s(s('0'))) ),
inference(clausify,[status(thm)],[clause_5_03]) ).
cnf(c_22,plain,
( ~ 'E'(f(E),s(s(s(s(s('0'))))))
| ~ 'E'(f(D),'0')
| ~ 'E'(f(C),s('0'))
| ~ 'E'(f(B),s(s(s('0'))))
| ~ 'E'(f(A),s(s('0'))) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_8,plain,
( ~ 'E'(f(D),'0')
| ~ 'E'(f(C),s('0'))
| ~ 'E'(f(B),s(s(s('0'))))
| ~ 'E'(f(A),s(s('0'))) ),
inference(resolve,[status(thm)],[c_5,c_22]) ).
cnf(c_23,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),E)),'0')
| ~ 'E'(f(D),s(s(s(s(s('0'))))))
| ~ 'E'(f(C),s('0'))
| ~ 'E'(f(B),s(s(s('0'))))
| ~ 'E'(f(A),s(s('0'))) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_9,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),D)),'0')
| ~ 'E'(f(C),s('0'))
| ~ 'E'(f(B),s(s(s('0'))))
| ~ 'E'(f(A),s(s('0'))) ),
inference(resolve,[status(thm)],[c_5,c_23]) ).
cnf(c_24,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),D)),s('0'))
| ~ 'E'(f(C),s(s('0')))
| ~ 'E'(f(B),s(s(s('0'))))
| ~ 'E'(f(A),s(s(s(s(s('0')))))) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_10,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),C)),s('0'))
| ~ 'E'(f(B),s(s('0')))
| ~ 'E'(f(A),s(s(s('0')))) ),
inference(resolve,[status(thm)],[c_5,c_24]) ).
cnf(c_25,plain,
( 'E'(f(A),s(s(s('0'))))
| ~ 'E'(f(A),s(s(s(s(s('0')))))) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_11,plain,
'E'(f(A),s(s(s('0')))),
inference(resolve,[status(thm)],[c_5,c_25]) ).
cnf(c_26,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),C)),s(s('0')))
| ~ 'E'(f(B),s(s(s('0'))))
| ~ 'E'(f(A),s(s(s(s(s('0')))))) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_27,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),B)),s(s('0')))
| ~ 'E'(f(A),s(s(s('0')))) ),
inference(resolve,[status(thm)],[c_5,c_26]) ).
cnf(c_12,plain,
'E'(f('AP'(s(s(s(s(s(s('0')))))),A)),s(s('0'))),
inference(resolve,[status(thm)],[c_11,c_27]) ).
cnf(c_13,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),B)),s('0'))
| ~ 'E'(f(A),s(s('0'))) ),
inference(resolve,[status(thm)],[c_11,c_10]) ).
cnf(c_14,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),C)),'0')
| ~ 'E'(f(B),s('0'))
| ~ 'E'(f(A),s(s('0'))) ),
inference(resolve,[status(thm)],[c_11,c_9]) ).
cnf(c_15,plain,
( ~ 'E'(f(C),'0')
| ~ 'E'(f(B),s('0'))
| ~ 'E'(f(A),s(s('0'))) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_16,plain,
'E'(f('AP'(s(s(s(s(s(s('0')))))),A)),s('0')),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_17,plain,
( ~ 'E'(f(B),'0')
| ~ 'E'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_15,c_12]) ).
cnf(c_28,plain,
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),B)),'0')
| ~ 'E'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_14,c_12]) ).
cnf(c_19,plain,
'E'(f('AP'(s(s(s(s(s(s('0')))))),A)),'0'),
inference(resolve,[status(thm)],[c_28,c_16]) ).
cnf(c_20,plain,
~ 'E'(f(A),'0'),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_21,plain,
$false,
inference(resolve,[status(thm)],[c_20,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n013.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sat Sep 26 19:40:21 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 3461807 was started by sandbox2 on n013,
% 0.10/0.35 % Sat Sep 26 19:40:21 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.35
% 0.10/0.35 % From the command line: assign(max_seconds, 300).
% 0.14/0.36
% 0.14/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.36
% 0.14/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.36 % Length of proof is 20.
% 0.14/0.36 % Level of proof is 5.
% 0.14/0.36 % Maximum clause weight is 47.000.
% 0.14/0.36 % Given clauses 9.
% 0.14/0.36
% 0.14/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------