%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW425-1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 09:14:13 AM UTC 2026
% Result : Unsatisfiable 113.86s 15.74s
% Output : CNFRefutation 113.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 33 unt; 0 def)
% Number of atoms : 90 ( 56 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 23 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 17 sgn 9 !; 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(wellformedness_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ heap(sep(lseg(VAR_0,VAR_1),sep(lseg(VAR_0,VAR_2),VAR_3))) ),
file('theBenchmark.p',wellformedness_5) ).
cnf(c_8,plain,
( A = C
| A = B
| ~ heap(sep(lseg(A,B),sep(lseg(A,C),D))) ),
inference(clausify,[status(thm)],[wellformedness_5]) ).
fof(premise_2,axiom,
x1 != x7,
file('theBenchmark.p',premise_2) ).
cnf(c_15,plain,
x1 != x7,
inference(clausify,[status(thm)],[premise_2]) ).
cnf(c_16,plain,
x7 != x1,
inference(copy,[status(thm)],[c_15]) ).
fof(premise_3,axiom,
x1 != x10,
file('theBenchmark.p',premise_3) ).
cnf(c_17,plain,
x1 != x10,
inference(clausify,[status(thm)],[premise_3]) ).
cnf(c_18,plain,
x10 != x1,
inference(copy,[status(thm)],[c_17]) ).
fof(premise_8,axiom,
x7 != x10,
file('theBenchmark.p',premise_8) ).
cnf(c_25,plain,
x7 != x10,
inference(clausify,[status(thm)],[premise_8]) ).
fof(premise_12,axiom,
heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x2,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),sep(lseg(x6,x9),emp))))))))),
file('theBenchmark.p',premise_12) ).
cnf(c_32,plain,
heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x2,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),sep(lseg(x6,x9),emp))))))))),
inference(clausify,[status(thm)],[premise_12]) ).
cnf(c_13904,plain,
heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x2,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x6,x9),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_32]) ).
cnf(c_13905,plain,
heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x2,x1),sep(lseg(x9,x1),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_13904]) ).
cnf(c_13906,plain,
heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x2,x1),sep(lseg(x6,x9),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_13905]) ).
cnf(c_13907,plain,
heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x2,x1),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_13906]) ).
cnf(c_13908,plain,
heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x1),sep(lseg(x2,x10),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_13907]) ).
cnf(c_13909,plain,
heap(sep(lseg(x5,x7),sep(lseg(x2,x1),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_13908]) ).
cnf(c_13910,plain,
heap(sep(lseg(x5,x7),sep(lseg(x2,x1),sep(lseg(x2,x10),sep(lseg(x2,x5),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_13909]) ).
cnf(c_13911,plain,
heap(sep(lseg(x2,x1),sep(lseg(x5,x7),sep(lseg(x2,x10),sep(lseg(x2,x5),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_13910]) ).
cnf(c_13912,plain,
heap(sep(lseg(x2,x1),sep(lseg(x2,x10),sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_13911]) ).
cnf(c_33,plain,
heap(sep(lseg(x2,x1),sep(lseg(x2,x10),sep(lseg(x2,x5),sep(lseg(x5,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp))))))))),
inference(paramod,[status(thm)],[c_1,c_13912]) ).
cnf(c_35,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_41,plain,
( A = D
| A = B
| ~ heap(sep(lseg(A,B),sep(C,sep(lseg(A,D),E)))) ),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_13913,plain,
( x10 = A
| ~ heap(sep(lseg(x10,x1),sep(lseg(x10,A),B))) ),
inference(resolve,[status(thm)],[c_8,c_18]) ).
cnf(c_13914,plain,
x10 != x7,
inference(copy,[status(thm)],[c_25]) ).
cnf(c_94,plain,
~ heap(sep(lseg(x10,x1),sep(lseg(x10,x7),A))),
inference(resolve,[status(thm)],[c_13913,c_13914]) ).
cnf(c_13915,plain,
( x2 = x10
| x2 = x1 ),
inference(resolve,[status(thm)],[c_33,c_8]) ).
cnf(c_117,plain,
( x10 = x2
| x2 = x1 ),
inference(copy,[status(thm)],[c_13915]) ).
cnf(c_129,plain,
( B = D
| B = C
| ~ heap(sep(A,sep(lseg(B,C),sep(lseg(B,D),E)))) ),
inference(paramod,[status(thm)],[c_35,c_8]) ).
cnf(c_13916,plain,
( x2 = x5
| x2 = x1 ),
inference(resolve,[status(thm)],[c_41,c_33]) ).
cnf(c_260,plain,
( x5 = x2
| x2 = x1 ),
inference(copy,[status(thm)],[c_13916]) ).
cnf(c_13917,plain,
x1 != x10,
inference(copy,[status(thm)],[c_18]) ).
cnf(c_13918,plain,
( x1 = B
| ~ heap(sep(lseg(x1,x10),sep(A,sep(lseg(x1,B),C)))) ),
inference(resolve,[status(thm)],[c_41,c_13917]) ).
cnf(c_13919,plain,
x1 != x7,
inference(copy,[status(thm)],[c_16]) ).
cnf(c_293,plain,
~ heap(sep(lseg(x1,x10),sep(A,sep(lseg(x1,x7),B)))),
inference(resolve,[status(thm)],[c_13918,c_13919]) ).
cnf(c_317,plain,
( heap(sep(lseg(x2,x1),sep(lseg(x2,x10),sep(lseg(x2,x5),sep(lseg(x2,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp)))))))))
| x2 = x1 ),
inference(paramod,[status(thm)],[c_260,c_33]) ).
cnf(c_561,plain,
( ~ heap(sep(lseg(x2,x1),sep(lseg(x10,x7),A)))
| x2 = x1 ),
inference(paramod,[status(thm)],[c_117,c_94]) ).
cnf(c_13920,plain,
( ~ heap(sep(lseg(x2,x1),sep(lseg(x2,x7),A)))
| x2 = x1
| x2 = x1 ),
inference(paramod,[status(thm)],[c_117,c_561]) ).
cnf(c_572,plain,
( ~ heap(sep(lseg(x2,x1),sep(lseg(x2,x7),A)))
| x2 = x1 ),
inference(copy,[status(thm)],[c_13920]) ).
cnf(c_601,plain,
( ~ heap(sep(lseg(x2,x1),sep(A,sep(B,sep(lseg(x2,x7),C)))))
| x2 = x1 ),
inference(paramod,[status(thm)],[c_35,c_572]) ).
cnf(c_13921,plain,
( x2 = x5
| x2 = x10 ),
inference(resolve,[status(thm)],[c_129,c_33]) ).
cnf(c_13922,plain,
( x2 = x5
| x10 = x2 ),
inference(copy,[status(thm)],[c_13921]) ).
cnf(c_1312,plain,
( x5 = x2
| x10 = x2 ),
inference(copy,[status(thm)],[c_13922]) ).
cnf(c_1358,plain,
( heap(sep(lseg(x2,x1),sep(lseg(x2,x10),sep(lseg(x2,x5),sep(lseg(x2,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp)))))))))
| x10 = x2 ),
inference(paramod,[status(thm)],[c_1312,c_33]) ).
cnf(c_13923,plain,
( x2 = x1
| x2 = x1 ),
inference(resolve,[status(thm)],[c_317,c_601]) ).
cnf(c_13141,plain,
x2 = x1,
inference(copy,[status(thm)],[c_13923]) ).
cnf(c_13924,plain,
( heap(sep(lseg(x2,x1),sep(lseg(x2,x10),sep(lseg(x2,x5),sep(lseg(x2,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp)))))))))
| x10 = x1 ),
inference(paramod,[status(thm)],[c_13141,c_1358]) ).
cnf(c_13925,plain,
( heap(sep(lseg(x1,x1),sep(lseg(x2,x10),sep(lseg(x2,x5),sep(lseg(x2,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp)))))))))
| x10 = x1 ),
inference(paramod,[status(thm)],[c_13141,c_13924]) ).
cnf(c_13926,plain,
( heap(sep(lseg(x1,x1),sep(lseg(x1,x10),sep(lseg(x2,x5),sep(lseg(x2,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp)))))))))
| x10 = x1 ),
inference(paramod,[status(thm)],[c_13141,c_13925]) ).
cnf(c_13927,plain,
( heap(sep(lseg(x1,x1),sep(lseg(x1,x10),sep(lseg(x1,x5),sep(lseg(x2,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp)))))))))
| x10 = x1 ),
inference(paramod,[status(thm)],[c_13141,c_13926]) ).
cnf(c_13928,plain,
( heap(sep(lseg(x1,x1),sep(lseg(x1,x10),sep(lseg(x1,x5),sep(lseg(x1,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp)))))))))
| x10 = x1 ),
inference(paramod,[status(thm)],[c_13141,c_13927]) ).
cnf(c_13929,plain,
( heap(sep(lseg(x1,x10),sep(lseg(x1,x5),sep(lseg(x1,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp))))))))
| x10 = x1 ),
inference(paramod,[status(thm)],[c_2,c_13928]) ).
cnf(c_13930,plain,
heap(sep(lseg(x1,x10),sep(lseg(x1,x5),sep(lseg(x1,x7),sep(lseg(x6,x9),sep(lseg(x7,x6),sep(lseg(x9,x1),sep(lseg(x3,x10),emp)))))))),
inference(resolve,[status(thm)],[c_18,c_13929]) ).
cnf(c_13903,plain,
$false,
inference(resolve,[status(thm)],[c_293,c_13930]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW425-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.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 15:56:15 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 1248130 was started by sandbox2 on n016,
% 0.08/0.36 % Sat Sep 26 15:56:15 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).
% 113.86/15.74
% 113.86/15.74 % given #500 (T,wt=19): 893 x2 = x1 | -heap(sep(A,sep(B,sep(lseg(x1,x2),sep(C,sep(next(x1,D),E)))))). [para(118(a,1),363(b,1,2))].
% 113.86/15.74
% 113.86/15.74 % SZS status Unsatisfiable for theBenchmark
% 113.86/15.74
% 113.86/15.74 % Proof 1 at 11.36 (+ 3.93) seconds.
% 113.86/15.74 % Length of proof is 25.
% 113.86/15.74 % Level of proof is 7.
% 113.86/15.74 % Maximum clause weight is 37.000.
% 113.86/15.74 % Given clauses 700.
% 113.86/15.74
% 113.86/15.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------