%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN313-1.001.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 09:37:31 AM UTC 2026
% Result : Unsatisfiable 0.78s 0.57s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 3 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 66 ( 11 ~; 55 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 73 ( 8 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p(VAR_0,f1(VAR_1),VAR_2)
| ~ p(VAR_0,f0(VAR_0),VAR_1) ),
file('theBenchmark.p',clause1) ).
cnf(c_1,plain,
( ~ p(A,f1(B),C)
| ~ p(A,f0(A),B) ),
inference(clausify,[status(thm)],[clause1]) ).
fof(clause2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( p(h2(VAR_2),VAR_1,j2(VAR_1))
| p(h1(VAR_0),VAR_2,j1(VAR_1))
| p(h0,VAR_0,j0(VAR_1)) ),
file('theBenchmark.p',clause2) ).
cnf(c_2,plain,
( p(h2(C),B,j2(B))
| p(h1(A),C,j1(B))
| p(h0,A,j0(B)) ),
inference(clausify,[status(thm)],[clause2]) ).
cnf(c_468,plain,
( p(h2(C),A,j2(A))
| p(h1(f0(h0)),C,j1(A))
| ~ p(h0,f1(j0(A)),B) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
( p(h2(C),D,j2(D))
| p(h1(f1(j0(B))),C,j1(D))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(resolve,[status(thm)],[c_468,c_2]) ).
cnf(c_469,plain,
( p(h2(f0(h1(f1(j0(A))))),B,j2(B))
| p(h2(D),A,j2(A))
| p(h1(f0(h0)),D,j1(A))
| ~ p(h1(f1(j0(A))),f1(j1(B)),C) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_100,plain,
( p(h2(f1(j1(C))),E,j2(E))
| p(h2(D),B,j2(B))
| p(h1(f0(h0)),D,j1(B))
| p(h2(f0(h1(f1(j0(B))))),C,j2(C))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(resolve,[status(thm)],[c_469,c_9]) ).
cnf(c_470,plain,
( p(h2(f1(j1(C))),D,j2(D))
| p(h2(A),B,j2(B))
| p(h2(f0(h1(f1(j0(B))))),C,j2(C))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(factor,[status(thm)],[c_100]) ).
cnf(c_119,plain,
( p(h2(f1(j1(C))),D,j2(D))
| p(h2(f0(h1(f1(j0(B))))),C,j2(C))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(copy,[status(thm)],[c_470]) ).
cnf(c_471,plain,
( p(h2(f0(h1(f1(j0(D))))),A,j2(A))
| p(h2(C),D,j2(D))
| p(h1(f0(h0)),C,j1(D))
| ~ p(h2(f1(j1(A))),f1(j2(f0(h2(f1(j1(A)))))),B) ),
inference(resolve,[status(thm)],[c_1,c_119]) ).
cnf(c_330,plain,
( p(h2(f0(h1(f1(j0(E))))),C,j2(C))
| p(h2(D),E,j2(E))
| p(h1(f0(h0)),D,j1(E))
| p(h2(f0(h1(f1(j0(B))))),C,j2(C))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(resolve,[status(thm)],[c_471,c_119]) ).
cnf(c_472,plain,
( p(h2(f0(h1(f1(j0(B))))),C,j2(C))
| p(h2(A),B,j2(B))
| p(h2(f0(h1(f1(j0(B))))),C,j2(C))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(factor,[status(thm)],[c_330]) ).
cnf(c_473,plain,
( p(h2(f0(h1(f1(j0(B))))),C,j2(C))
| p(h2(f0(h1(f1(j0(B))))),C,j2(C))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(copy,[status(thm)],[c_472]) ).
cnf(c_362,plain,
( p(h2(f0(h1(f1(j0(B))))),C,j2(C))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(copy,[status(thm)],[c_473]) ).
cnf(c_474,plain,
( p(h2(C),A,j2(A))
| p(h1(f0(h0)),C,j1(A))
| ~ p(h2(f0(h1(f1(j0(A))))),f1(j2(f0(h2(f0(h1(f1(j0(A)))))))),B) ),
inference(resolve,[status(thm)],[c_1,c_362]) ).
cnf(c_397,plain,
( p(h2(C),B,j2(B))
| p(h1(f0(h0)),C,j1(B))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(resolve,[status(thm)],[c_474,c_362]) ).
cnf(c_475,plain,
( p(h2(A),B,j2(B))
| p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(factor,[status(thm)],[c_397]) ).
cnf(c_406,plain,
( p(h2(A),B,j2(B))
| p(h1(f0(h0)),A,j1(B)) ),
inference(copy,[status(thm)],[c_475]) ).
cnf(c_476,plain,
( p(h2(f0(h1(f0(h0)))),A,j2(A))
| ~ p(h1(f0(h0)),f1(j1(A)),B) ),
inference(resolve,[status(thm)],[c_1,c_406]) ).
cnf(c_426,plain,
( p(h2(f1(j1(A))),B,j2(B))
| p(h2(f0(h1(f0(h0)))),A,j2(A)) ),
inference(resolve,[status(thm)],[c_476,c_406]) ).
cnf(c_477,plain,
( p(h2(f0(h1(f0(h0)))),A,j2(A))
| ~ p(h2(f1(j1(A))),f1(j2(f0(h2(f1(j1(A)))))),B) ),
inference(resolve,[status(thm)],[c_1,c_426]) ).
cnf(c_478,plain,
( p(h2(f0(h1(f0(h0)))),A,j2(A))
| p(h2(f0(h1(f0(h0)))),A,j2(A)) ),
inference(resolve,[status(thm)],[c_477,c_426]) ).
cnf(c_458,plain,
p(h2(f0(h1(f0(h0)))),A,j2(A)),
inference(copy,[status(thm)],[c_478]) ).
cnf(c_466,plain,
~ p(h2(f0(h1(f0(h0)))),f0(h2(f0(h1(f0(h0))))),A),
inference(resolve,[status(thm)],[c_458,c_1]) ).
cnf(c_467,plain,
$false,
inference(resolve,[status(thm)],[c_466,c_458]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN313-1.001.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 17:27:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1264815 was started by sandbox2 on n017,
% 0.08/0.36 % Sat Sep 26 17:27:48 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.78/0.57
% 0.78/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.78/0.57
% 0.78/0.57 % Proof 1 at 0.12 (+ 0.04) seconds.
% 0.78/0.57 % Length of proof is 13.
% 0.78/0.57 % Level of proof is 11.
% 0.78/0.57 % Maximum clause weight is 76.000.
% 0.78/0.57 % Given clauses 67.
% 0.78/0.57
% 0.78/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------