%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW412-1 : 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 : n016.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 0.99s 0.56s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 39 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 32 ( 0 sgn 7 !; 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(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(premise_4,axiom,
x3 != x2,
file('theBenchmark.p',premise_4) ).
cnf(c_19,plain,
x3 != x2,
inference(clausify,[status(thm)],[premise_4]) ).
cnf(c_20,plain,
x2 != x3,
inference(copy,[status(thm)],[c_19]) ).
fof(premise_6,axiom,
x1 != x4,
file('theBenchmark.p',premise_6) ).
cnf(c_23,plain,
x1 != x4,
inference(clausify,[status(thm)],[premise_6]) ).
fof(premise_8,axiom,
heap(sep(lseg(x3,nil),sep(lseg(x4,nil),sep(next(x1,x4),sep(next(x2,x3),emp))))),
file('theBenchmark.p',premise_8) ).
cnf(c_25,plain,
heap(sep(lseg(x3,nil),sep(lseg(x4,nil),sep(next(x1,x4),sep(next(x2,x3),emp))))),
inference(clausify,[status(thm)],[premise_8]) ).
fof(conclusion_1,axiom,
~ heap(sep(lseg(x2,nil),sep(lseg(x1,nil),emp))),
file('theBenchmark.p',conclusion_1) ).
cnf(c_26,plain,
~ heap(sep(lseg(x2,nil),sep(lseg(x1,nil),emp))),
inference(clausify,[status(thm)],[conclusion_1]) ).
cnf(c_27,plain,
~ heap(sep(lseg(x1,nil),sep(lseg(x2,nil),emp))),
inference(paramod,[status(thm)],[c_1,c_26]) ).
cnf(c_29,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_38,plain,
( heap(sep(lseg(C,B),D))
| C = A
| ~ heap(sep(lseg(A,B),sep(next(C,A),D))) ),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_110,plain,
( heap(sep(lseg(D,B),sep(C,E)))
| D = A
| ~ heap(sep(lseg(A,B),sep(C,sep(next(D,A),E)))) ),
inference(paramod,[status(thm)],[c_29,c_9]) ).
cnf(c_163,plain,
( heap(sep(lseg(D,C),sep(A,E)))
| D = B
| ~ heap(sep(A,sep(lseg(B,C),sep(next(D,B),E)))) ),
inference(paramod,[status(thm)],[c_29,c_38]) ).
cnf(c_1023,plain,
( heap(sep(lseg(x1,nil),sep(lseg(x3,nil),sep(next(x2,x3),emp))))
| x1 = x4 ),
inference(resolve,[status(thm)],[c_163,c_25]) ).
cnf(c_1024,plain,
( heap(sep(lseg(x3,nil),sep(lseg(x1,nil),sep(next(x2,x3),emp))))
| x1 = x4 ),
inference(paramod,[status(thm)],[c_1,c_1023]) ).
cnf(c_1017,plain,
heap(sep(lseg(x3,nil),sep(lseg(x1,nil),sep(next(x2,x3),emp)))),
inference(resolve,[status(thm)],[c_23,c_1024]) ).
cnf(c_1025,plain,
( heap(sep(lseg(x2,nil),sep(lseg(x1,nil),emp)))
| x2 = x3 ),
inference(resolve,[status(thm)],[c_1017,c_110]) ).
cnf(c_1026,plain,
( heap(sep(lseg(x1,nil),sep(lseg(x2,nil),emp)))
| x2 = x3 ),
inference(paramod,[status(thm)],[c_1,c_1025]) ).
cnf(c_1027,plain,
heap(sep(lseg(x1,nil),sep(lseg(x2,nil),emp))),
inference(resolve,[status(thm)],[c_20,c_1026]) ).
cnf(c_1022,plain,
$false,
inference(resolve,[status(thm)],[c_27,c_1027]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW412-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 15:55:16 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1245909 was started by sandbox on n016,
% 0.12/0.36 % Sat Sep 26 15:55:16 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.99/0.56
% 0.99/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.99/0.56
% 0.99/0.56 % Proof 1 at 0.15 (+ 0.05) seconds.
% 0.99/0.56 % Length of proof is 14.
% 0.99/0.56 % Level of proof is 4.
% 0.99/0.56 % Maximum clause weight is 63.000.
% 0.99/0.56 % Given clauses 149.
% 0.99/0.56
% 0.99/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------