%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO614-1 : 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 : n012.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 09:51:06 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.31s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 26 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 25 sgn 12 !; 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),a1)
| eq(f(VAR_0),a0) ),
file('theBenchmark.p',sos_04) ).
cnf(c_4,plain,
( 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]) ).
cnf(c_9,plain,
le(A,max(A,B)),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_10,plain,
le(A,max(B,A)),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_11,plain,
( eq(f(B),a0)
| ~ le(s(B),A)
| ~ eq(f(A),a1) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_17,plain,
le(A,max(B,max(A,C))),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_24,plain,
( eq(f(B),a0)
| eq(f(A),a0)
| ~ le(s(A),B) ),
inference(resolve,[status(thm)],[c_11,c_4]) ).
cnf(c_26,plain,
le(A,max(B,max(max(A,C),D))),
inference(resolve,[status(thm)],[c_17,c_2]) ).
cnf(c_50,plain,
( eq(f(max(s(A),B)),a0)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_24,c_9]) ).
cnf(c_51,plain,
( eq(f(s(A)),a0)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_24,c_1]) ).
cnf(c_57,plain,
le(A,max(B,max(max(max(A,C),D),E))),
inference(resolve,[status(thm)],[c_26,c_2]) ).
cnf(c_60,plain,
( ~ le(s(s(A)),B)
| ~ eq(f(B),a0)
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_51,c_5]) ).
cnf(c_117,plain,
le(A,max(B,max(max(max(max(A,C),D),E),F))),
inference(resolve,[status(thm)],[c_57,c_2]) ).
cnf(c_155,plain,
( eq(f(B),a0)
| ~ le(s(s(A)),max(s(B),C))
| eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_60,c_50]) ).
cnf(c_164,plain,
( ~ le(s(s(A)),max(s(A),B))
| eq(f(A),a0) ),
inference(factor,[status(thm)],[c_155]) ).
cnf(c_173,plain,
eq(f(A),a0),
inference(resolve,[status(thm)],[c_164,c_57]) ).
cnf(c_177,plain,
( ~ le(s(B),A)
| ~ eq(f(A),a0) ),
inference(resolve,[status(thm)],[c_173,c_5]) ).
cnf(c_175,plain,
~ le(s(A),B),
inference(resolve,[status(thm)],[c_173,c_177]) ).
cnf(c_176,plain,
$false,
inference(resolve,[status(thm)],[c_175,c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO614-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 19:38:04 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.29 % Process 1359522 was started by sandbox on n012,
% 0.03/0.29 % Sat Sep 26 19:38:04 2026
% 0.03/0.29 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.29
% 0.03/0.29 % From the command line: assign(max_seconds, 300).
% 0.03/0.31
% 0.03/0.31 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.31
% 0.03/0.31 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.03/0.31 % Length of proof is 22.
% 0.03/0.31 % Level of proof is 9.
% 0.03/0.31 % Maximum clause weight is 16.000.
% 0.03/0.31 % Given clauses 58.
% 0.03/0.31
% 0.03/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------