%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO617-1 : 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 : n005.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 14.13s 2.23s
% Output : CNFRefutation 14.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 18 unt; 0 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 184 ( 49 ~; 135 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 173 ( 62 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_01,axiom,
! [VAR_0] : le(VAR_0,VAR_0),
file('theBenchmark.p',sos_01) ).
cnf(c_1,plain,
le(A,A),
inference(clausify,[status(thm)],[sos_01]) ).
fof(sos_02,axiom,
! [VAR_0,VAR_1,VAR_2] :
( le(VAR_0,VAR_2)
| ~ le(max(VAR_0,VAR_1),VAR_2) ),
file('theBenchmark.p',sos_02) ).
cnf(c_2,plain,
( le(A,C)
| ~ le(max(A,B),C) ),
inference(clausify,[status(thm)],[sos_02]) ).
fof(sos_03,axiom,
! [VAR_0,VAR_1,VAR_2] :
( le(VAR_1,VAR_2)
| ~ le(max(VAR_0,VAR_1),VAR_2) ),
file('theBenchmark.p',sos_03) ).
cnf(c_3,plain,
( le(B,C)
| ~ le(max(A,B),C) ),
inference(clausify,[status(thm)],[sos_03]) ).
fof(sos_04,axiom,
! [VAR_0] :
( eq(f(VAR_0),a2)
| eq(f(VAR_0),a1)
| eq(f(VAR_0),a0) ),
file('theBenchmark.p',sos_04) ).
cnf(c_4,plain,
( eq(f(A),a2)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(clausify,[status(thm)],[sos_04]) ).
fof(sos_05,axiom,
! [VAR_0,VAR_1] :
( ~ le(s(VAR_0),VAR_1)
| ~ eq(f(VAR_1),a0)
| ~ eq(f(VAR_0),a0) ),
file('theBenchmark.p',sos_05) ).
cnf(c_5,plain,
( ~ le(s(A),B)
| ~ eq(f(B),a0)
| ~ eq(f(A),a0) ),
inference(clausify,[status(thm)],[sos_05]) ).
fof(sos_06,axiom,
! [VAR_0,VAR_1] :
( ~ le(s(VAR_0),VAR_1)
| ~ eq(f(VAR_1),a1)
| ~ eq(f(VAR_0),a1) ),
file('theBenchmark.p',sos_06) ).
cnf(c_6,plain,
( ~ le(s(A),B)
| ~ eq(f(B),a1)
| ~ eq(f(A),a1) ),
inference(clausify,[status(thm)],[sos_06]) ).
fof(sos_07,axiom,
! [VAR_0,VAR_1] :
( ~ le(s(VAR_0),VAR_1)
| ~ eq(f(VAR_1),a2)
| ~ eq(f(VAR_0),a2) ),
file('theBenchmark.p',sos_07) ).
cnf(c_7,plain,
( ~ le(s(A),B)
| ~ eq(f(B),a2)
| ~ eq(f(A),a2) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_11,plain,
le(A,max(A,B)),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_12,plain,
le(A,max(B,A)),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_17,plain,
le(A,max(max(B,A),C)),
inference(resolve,[status(thm)],[c_11,c_3]) ).
cnf(c_1126,plain,
( eq(f(B),a1)
| eq(f(B),a0)
| ~ le(s(B),A)
| ~ eq(f(A),a2) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_1127,plain,
( eq(f(B),a1)
| eq(f(B),a0)
| eq(f(A),a1)
| eq(f(A),a0)
| ~ le(s(A),B) ),
inference(resolve,[status(thm)],[c_1126,c_4]) ).
cnf(c_19,plain,
( eq(f(max(s(A),B)),a1)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_1127,c_11]) ).
cnf(c_20,plain,
le(A,max(B,max(C,A))),
inference(resolve,[status(thm)],[c_12,c_3]) ).
cnf(c_21,plain,
le(A,max(B,max(A,C))),
inference(resolve,[status(thm)],[c_12,c_2]) ).
cnf(c_24,plain,
le(A,max(max(B,max(C,A)),D)),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_34,plain,
le(A,max(B,max(C,max(A,D)))),
inference(resolve,[status(thm)],[c_20,c_2]) ).
cnf(c_37,plain,
le(A,max(B,max(max(A,C),D))),
inference(resolve,[status(thm)],[c_21,c_2]) ).
cnf(c_41,plain,
le(A,max(max(B,max(C,max(D,A))),E)),
inference(resolve,[status(thm)],[c_24,c_3]) ).
cnf(c_1128,plain,
( eq(f(max(s(B),C)),a0)
| eq(f(B),a1)
| eq(f(B),a0)
| ~ le(s(max(s(B),C)),A)
| ~ eq(f(A),a1) ),
inference(resolve,[status(thm)],[c_6,c_19]) ).
cnf(c_1129,plain,
( eq(f(max(s(C),D)),a0)
| eq(f(C),a1)
| eq(f(C),a0)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0)
| ~ le(s(max(s(A),B)),max(s(C),D)) ),
inference(resolve,[status(thm)],[c_1128,c_19]) ).
cnf(c_50,plain,
( eq(f(max(s(C),max(s(max(s(A),B)),D))),a0)
| eq(f(C),a1)
| eq(f(C),a0)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_1129,c_21]) ).
cnf(c_1130,plain,
( eq(f(max(s(B),C)),a0)
| eq(f(B),a1)
| eq(f(B),a0)
| ~ le(s(max(s(B),C)),A)
| ~ eq(f(A),a1) ),
inference(resolve,[status(thm)],[c_6,c_19]) ).
cnf(c_1131,plain,
( eq(f(max(s(C),D)),a0)
| eq(f(C),a1)
| eq(f(C),a0)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0)
| ~ le(s(max(s(A),B)),max(s(C),D)) ),
inference(resolve,[status(thm)],[c_1130,c_19]) ).
cnf(c_52,plain,
( eq(f(max(s(C),s(max(s(A),B)))),a0)
| eq(f(C),a1)
| eq(f(C),a0)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_1131,c_12]) ).
cnf(c_1132,plain,
( eq(f(max(s(A),s(max(s(A),B)))),a0)
| eq(f(A),a1)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(factor,[status(thm)],[c_52]) ).
cnf(c_59,plain,
( eq(f(max(s(A),s(max(s(A),B)))),a0)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(copy,[status(thm)],[c_1132]) ).
cnf(c_78,plain,
le(A,max(B,max(C,max(max(A,D),E)))),
inference(resolve,[status(thm)],[c_34,c_2]) ).
cnf(c_151,plain,
le(A,max(B,max(max(max(A,C),D),E))),
inference(resolve,[status(thm)],[c_37,c_2]) ).
cnf(c_262,plain,
le(A,max(max(B,max(C,max(D,max(E,A)))),F)),
inference(resolve,[status(thm)],[c_41,c_3]) ).
cnf(c_1133,plain,
( eq(f(max(s(B),C)),a0)
| eq(f(B),a1)
| eq(f(B),a0)
| ~ le(s(max(s(B),s(max(s(B),C)))),A)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_5,c_59]) ).
cnf(c_1134,plain,
( eq(f(C),a1)
| eq(f(C),a0)
| eq(f(max(s(D),E)),a0)
| eq(f(D),a1)
| eq(f(D),a0)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0)
| ~ le(s(max(s(A),s(max(s(A),B)))),max(s(C),max(s(max(s(D),E)),F))) ),
inference(resolve,[status(thm)],[c_1133,c_50]) ).
cnf(c_1036,plain,
( eq(f(E),a1)
| eq(f(E),a0)
| eq(f(max(s(C),D)),a0)
| eq(f(C),a1)
| eq(f(C),a0)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_1134,c_78]) ).
cnf(c_1135,plain,
( eq(f(C),a1)
| eq(f(C),a0)
| eq(f(A),a1)
| eq(f(A),a0)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(factor,[status(thm)],[c_1036]) ).
cnf(c_1136,plain,
( eq(f(C),a1)
| eq(f(C),a0)
| eq(f(A),a1)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(copy,[status(thm)],[c_1135]) ).
cnf(c_1056,plain,
( eq(f(C),a1)
| eq(f(C),a0)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(copy,[status(thm)],[c_1136]) ).
cnf(c_1137,plain,
( eq(f(A),a1)
| eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(factor,[status(thm)],[c_1056]) ).
cnf(c_1064,plain,
( eq(f(max(s(A),B)),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(copy,[status(thm)],[c_1137]) ).
cnf(c_1138,plain,
( eq(f(B),a1)
| eq(f(B),a0)
| ~ le(s(max(s(B),C)),A)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_5,c_1064]) ).
cnf(c_1139,plain,
( eq(f(C),a1)
| eq(f(C),a0)
| eq(f(A),a1)
| eq(f(A),a0)
| ~ le(s(max(s(A),B)),max(s(C),D)) ),
inference(resolve,[status(thm)],[c_1138,c_1064]) ).
cnf(c_1070,plain,
( eq(f(B),a1)
| eq(f(B),a0)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_1139,c_151]) ).
cnf(c_1140,plain,
( eq(f(A),a1)
| eq(f(A),a1)
| eq(f(A),a0) ),
inference(factor,[status(thm)],[c_1070]) ).
cnf(c_1073,plain,
( eq(f(A),a1)
| eq(f(A),a0) ),
inference(copy,[status(thm)],[c_1140]) ).
cnf(c_1141,plain,
( eq(f(B),a0)
| ~ le(s(B),A)
| ~ eq(f(A),a1) ),
inference(resolve,[status(thm)],[c_6,c_1073]) ).
cnf(c_1142,plain,
( eq(f(B),a0)
| eq(f(A),a0)
| ~ le(s(A),B) ),
inference(resolve,[status(thm)],[c_1141,c_1073]) ).
cnf(c_1105,plain,
( eq(f(max(B,s(A))),a0)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_1142,c_12]) ).
cnf(c_1143,plain,
( eq(f(B),a0)
| ~ le(s(B),A)
| ~ eq(f(A),a1) ),
inference(resolve,[status(thm)],[c_6,c_1073]) ).
cnf(c_1144,plain,
( eq(f(B),a0)
| eq(f(A),a0)
| ~ le(s(A),B) ),
inference(resolve,[status(thm)],[c_1143,c_1073]) ).
cnf(c_1107,plain,
( eq(f(s(A)),a0)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_1144,c_1]) ).
cnf(c_1111,plain,
le(A,max(max(B,max(C,max(D,max(E,max(A,F))))),V6)),
inference(resolve,[status(thm)],[c_262,c_2]) ).
cnf(c_1145,plain,
( eq(f(B),a0)
| ~ le(s(s(B)),A)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_5,c_1107]) ).
cnf(c_1146,plain,
( eq(f(C),a0)
| eq(f(A),a0)
| ~ le(s(s(A)),max(B,s(C))) ),
inference(resolve,[status(thm)],[c_1145,c_1105]) ).
cnf(c_1120,plain,
( eq(f(B),a0)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_1146,c_262]) ).
cnf(c_1122,plain,
eq(f(A),a0),
inference(factor,[status(thm)],[c_1120]) ).
cnf(c_1147,plain,
( ~ le(s(B),A)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_1122,c_5]) ).
cnf(c_1124,plain,
~ le(s(A),B),
inference(resolve,[status(thm)],[c_1122,c_1147]) ).
cnf(c_1125,plain,
$false,
inference(resolve,[status(thm)],[c_1124,c_1111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO617-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 19:38:31 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2928147 was started by sandbox2 on n005,
% 0.09/0.36 % Sat Sep 26 19:38:31 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 14.13/2.23
% 14.13/2.23 % SZS status Unsatisfiable for theBenchmark
% 14.13/2.23
% 14.13/2.23 % Proof 1 at 1.67 (+ 0.10) seconds.
% 14.13/2.23 % Length of proof is 35.
% 14.13/2.23 % Level of proof is 14.
% 14.13/2.23 % Maximum clause weight is 76.000.
% 14.13/2.23 % Given clauses 92.
% 14.13/2.23
% 14.13/2.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------