%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW407-1 : TPTP v9.3.1. Released v5.2.0.
% 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 09:14:12 AM UTC 2026
% Result : Unsatisfiable 32.94s 9.53s
% Output : CNFRefutation 32.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 18 unt; 0 def)
% Number of atoms : 37 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associative_commutative,axiom,
! [VAR_0,VAR_1,VAR_2] : sep(VAR_0,sep(VAR_1,VAR_2)) = sep(VAR_1,sep(VAR_0,VAR_2)),
file('theBenchmark.p',associative_commutative) ).
cnf(c_1,plain,
sep(A,sep(B,C)) = sep(B,sep(A,C)),
inference(clausify,[status(thm)],[associative_commutative]) ).
fof(normalization,axiom,
! [VAR_0,VAR_1] : sep(lseg(VAR_0,VAR_0),VAR_1) = VAR_1,
file('theBenchmark.p',normalization) ).
cnf(c_2,plain,
sep(lseg(A,A),B) = B,
inference(clausify,[status(thm)],[normalization]) ).
fof(unfolding_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( heap(sep(lseg(VAR_0,VAR_2),VAR_3))
| VAR_0 = VAR_1
| ~ heap(sep(next(VAR_0,VAR_1),sep(lseg(VAR_1,VAR_2),VAR_3))) ),
file('theBenchmark.p',unfolding_2) ).
cnf(c_9,plain,
( heap(sep(lseg(A,C),D))
| A = B
| ~ heap(sep(next(A,B),sep(lseg(B,C),D))) ),
inference(clausify,[status(thm)],[unfolding_2]) ).
fof(unfolding_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( heap(sep(lseg(VAR_0,VAR_2),sep(next(VAR_2,VAR_3),VAR_4)))
| ~ heap(sep(lseg(VAR_0,VAR_1),sep(lseg(VAR_1,VAR_2),sep(next(VAR_2,VAR_3),VAR_4)))) ),
file('theBenchmark.p',unfolding_4) ).
cnf(c_11,plain,
( heap(sep(lseg(A,C),sep(next(C,D),E)))
| ~ heap(sep(lseg(A,B),sep(lseg(B,C),sep(next(C,D),E)))) ),
inference(clausify,[status(thm)],[unfolding_4]) ).
fof(premise_5,axiom,
x1 != x2,
file('theBenchmark.p',premise_5) ).
cnf(c_21,plain,
x1 != x2,
inference(clausify,[status(thm)],[premise_5]) ).
cnf(c_22,plain,
x2 != x1,
inference(copy,[status(thm)],[c_21]) ).
fof(premise_9,axiom,
heap(sep(next(x1,x2),sep(lseg(x3,x1),sep(lseg(x4,nil),sep(next(x2,x4),emp))))),
file('theBenchmark.p',premise_9) ).
cnf(c_28,plain,
heap(sep(next(x1,x2),sep(lseg(x3,x1),sep(lseg(x4,nil),sep(next(x2,x4),emp))))),
inference(clausify,[status(thm)],[premise_9]) ).
fof(conclusion_1,axiom,
~ heap(sep(lseg(x4,nil),sep(next(x2,x4),sep(lseg(x3,x2),emp)))),
file('theBenchmark.p',conclusion_1) ).
cnf(c_29,plain,
~ heap(sep(lseg(x4,nil),sep(next(x2,x4),sep(lseg(x3,x2),emp)))),
inference(clausify,[status(thm)],[conclusion_1]) ).
cnf(c_31,plain,
sep(A,sep(B,sep(C,D))) = sep(C,sep(A,sep(B,D))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_42,plain,
( heap(sep(lseg(A,B),C))
| A = B
| ~ heap(sep(next(A,B),C)) ),
inference(paramod,[status(thm)],[c_2,c_9]) ).
cnf(c_47,plain,
( heap(sep(lseg(C,B),sep(next(B,D),E)))
| ~ heap(sep(lseg(A,B),sep(lseg(C,A),sep(next(B,D),E)))) ),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_115,plain,
heap(sep(next(x1,x2),sep(lseg(x3,x1),sep(next(x2,x4),sep(lseg(x4,nil),emp))))),
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_125,plain,
sep(A,sep(B,sep(C,D))) = sep(C,sep(B,sep(A,D))),
inference(paramod,[status(thm)],[c_31,c_1]) ).
cnf(c_298,plain,
~ heap(sep(lseg(x3,x2),sep(next(x2,x4),sep(lseg(x4,nil),emp)))),
inference(paramod,[status(thm)],[c_125,c_29]) ).
cnf(c_1895,plain,
( heap(sep(lseg(x1,x2),sep(lseg(x3,x1),sep(next(x2,x4),sep(lseg(x4,nil),emp)))))
| x1 = x2 ),
inference(resolve,[status(thm)],[c_115,c_42]) ).
cnf(c_1896,plain,
( heap(sep(lseg(x1,x2),sep(lseg(x3,x1),sep(next(x2,x4),sep(lseg(x4,nil),emp)))))
| x2 = x1 ),
inference(copy,[status(thm)],[c_1895]) ).
cnf(c_1155,plain,
heap(sep(lseg(x1,x2),sep(lseg(x3,x1),sep(next(x2,x4),sep(lseg(x4,nil),emp))))),
inference(resolve,[status(thm)],[c_22,c_1896]) ).
cnf(c_1897,plain,
heap(sep(lseg(x3,x2),sep(next(x2,x4),sep(lseg(x4,nil),emp)))),
inference(resolve,[status(thm)],[c_1155,c_47]) ).
cnf(c_1894,plain,
$false,
inference(resolve,[status(thm)],[c_298,c_1897]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW407-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.40 % Computer : n015.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.40 % CPULimit : 300
% 0.08/0.40 % WCLimit : 300
% 0.08/0.40 % DateTime : Sat Sep 26 15:53:13 UTC 2026
% 0.08/0.40 % CPUTime :
% 0.08/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.40 % Process 230887 was started by sandbox on n015,
% 0.08/0.40 % Sat Sep 26 15:53:13 2026
% 0.08/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.40
% 0.08/0.40 % From the command line: assign(max_seconds, 300).
% 32.94/9.53
% 32.94/9.53 % SZS status Unsatisfiable for theBenchmark
% 32.94/9.53
% 32.94/9.53 % Proof 1 at 0.32 (+ 0.16) seconds.
% 32.94/9.53 % Length of proof is 16.
% 32.94/9.53 % Level of proof is 4.
% 32.94/9.53 % Maximum clause weight is 24.000.
% 32.94/9.53 % Given clauses 189.
% 32.94/9.53
% 32.94/9.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------