%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW410-1 : 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 : 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 09:14:12 AM UTC 2026
% Result : Unsatisfiable 2.18s 0.77s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 30 unt; 0 def)
% Number of atoms : 72 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 22 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 17 !; 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_3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( heap(sep(lseg(VAR_0,nil),VAR_2))
| ~ heap(sep(lseg(VAR_0,VAR_1),sep(lseg(VAR_1,nil),VAR_2))) ),
file('theBenchmark.p',unfolding_3) ).
cnf(c_10,plain,
( heap(sep(lseg(A,nil),C))
| ~ heap(sep(lseg(A,B),sep(lseg(B,nil),C))) ),
inference(clausify,[status(thm)],[unfolding_3]) ).
fof(unfolding_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( heap(sep(lseg(VAR_0,VAR_2),sep(lseg(VAR_2,VAR_3),VAR_4)))
| VAR_2 = VAR_3
| ~ heap(sep(lseg(VAR_0,VAR_1),sep(lseg(VAR_1,VAR_2),sep(lseg(VAR_2,VAR_3),VAR_4)))) ),
file('theBenchmark.p',unfolding_5) ).
cnf(c_12,plain,
( heap(sep(lseg(A,C),sep(lseg(C,D),E)))
| C = D
| ~ heap(sep(lseg(A,B),sep(lseg(B,C),sep(lseg(C,D),E)))) ),
inference(clausify,[status(thm)],[unfolding_5]) ).
fof(premise_2,axiom,
nil != x2,
file('theBenchmark.p',premise_2) ).
cnf(c_15,plain,
nil != x2,
inference(clausify,[status(thm)],[premise_2]) ).
cnf(c_16,plain,
x2 != nil,
inference(copy,[status(thm)],[c_15]) ).
fof(premise_3,axiom,
x1 != x3,
file('theBenchmark.p',premise_3) ).
cnf(c_17,plain,
x1 != x3,
inference(clausify,[status(thm)],[premise_3]) ).
cnf(c_18,plain,
x3 != x1,
inference(copy,[status(thm)],[c_17]) ).
fof(premise_5,axiom,
heap(sep(lseg(x2,x1),sep(lseg(x3,nil),sep(next(x1,x3),emp)))),
file('theBenchmark.p',premise_5) ).
cnf(c_21,plain,
heap(sep(lseg(x2,x1),sep(lseg(x3,nil),sep(next(x1,x3),emp)))),
inference(clausify,[status(thm)],[premise_5]) ).
fof(conclusion_1,axiom,
~ heap(sep(lseg(x3,nil),sep(lseg(x2,x3),emp))),
file('theBenchmark.p',conclusion_1) ).
cnf(c_22,plain,
~ heap(sep(lseg(x3,nil),sep(lseg(x2,x3),emp))),
inference(clausify,[status(thm)],[conclusion_1]) ).
cnf(c_24,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_1925,plain,
sep(A,B) = sep(A,sep(lseg(C,C),B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_25,plain,
sep(A,sep(lseg(B,B),C)) = sep(A,C),
inference(copy,[status(thm)],[c_1925]) ).
cnf(c_33,plain,
( heap(sep(lseg(A,D),sep(C,E)))
| A = B
| ~ heap(sep(next(A,B),sep(C,sep(lseg(B,D),E)))) ),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_35,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_37,plain,
( heap(sep(lseg(B,nil),C))
| ~ heap(sep(lseg(A,nil),sep(lseg(B,A),C))) ),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_43,plain,
( heap(sep(lseg(C,B),sep(lseg(B,D),E)))
| B = D
| ~ heap(sep(lseg(A,B),sep(lseg(C,A),sep(lseg(B,D),E)))) ),
inference(paramod,[status(thm)],[c_1,c_12]) ).
cnf(c_72,plain,
~ heap(sep(lseg(x2,x3),sep(lseg(x3,nil),emp))),
inference(paramod,[status(thm)],[c_1,c_22]) ).
cnf(c_110,plain,
heap(sep(next(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp)))),
inference(paramod,[status(thm)],[c_24,c_21]) ).
cnf(c_122,plain,
sep(lseg(A,A),B) = sep(lseg(C,C),B),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_123,plain,
sep(lseg(A,A),sep(lseg(B,B),C)) = C,
inference(paramod,[status(thm)],[c_2,c_25]) ).
cnf(c_170,plain,
( heap(sep(lseg(A,A),sep(lseg(A,B),C)))
| A = B
| ~ heap(sep(lseg(A,B),C)) ),
inference(paramod,[status(thm)],[c_123,c_12]) ).
cnf(c_1926,plain,
( heap(sep(lseg(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp))))
| x1 = x3 ),
inference(resolve,[status(thm)],[c_110,c_35]) ).
cnf(c_1927,plain,
( heap(sep(lseg(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp))))
| x3 = x1 ),
inference(copy,[status(thm)],[c_1926]) ).
cnf(c_1553,plain,
heap(sep(lseg(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp)))),
inference(resolve,[status(thm)],[c_18,c_1927]) ).
cnf(c_1928,plain,
( heap(sep(lseg(x1,nil),sep(lseg(x2,x1),emp)))
| x1 = x3 ),
inference(resolve,[status(thm)],[c_110,c_33]) ).
cnf(c_1929,plain,
( heap(sep(lseg(x1,nil),sep(lseg(x2,x1),emp)))
| x3 = x1 ),
inference(copy,[status(thm)],[c_1928]) ).
cnf(c_1554,plain,
heap(sep(lseg(x1,nil),sep(lseg(x2,x1),emp))),
inference(resolve,[status(thm)],[c_18,c_1929]) ).
cnf(c_1563,plain,
heap(sep(lseg(x2,nil),emp)),
inference(resolve,[status(thm)],[c_1554,c_37]) ).
cnf(c_1930,plain,
( heap(sep(lseg(x2,x2),sep(lseg(x2,nil),emp)))
| x2 = nil ),
inference(resolve,[status(thm)],[c_1563,c_170]) ).
cnf(c_1568,plain,
heap(sep(lseg(x2,x2),sep(lseg(x2,nil),emp))),
inference(resolve,[status(thm)],[c_16,c_1930]) ).
cnf(c_1575,plain,
heap(sep(lseg(A,A),sep(lseg(x2,nil),emp))),
inference(paramod,[status(thm)],[c_122,c_1568]) ).
cnf(c_1931,plain,
( heap(sep(lseg(x2,x3),sep(lseg(x3,nil),emp)))
| x3 = nil ),
inference(resolve,[status(thm)],[c_1553,c_43]) ).
cnf(c_1872,plain,
x3 = nil,
inference(resolve,[status(thm)],[c_72,c_1931]) ).
cnf(c_1884,plain,
~ heap(sep(lseg(nil,nil),sep(lseg(x2,x3),emp))),
inference(paramod,[status(thm)],[c_1872,c_22]) ).
cnf(c_1932,plain,
~ heap(sep(lseg(nil,nil),sep(lseg(x2,nil),emp))),
inference(paramod,[status(thm)],[c_1872,c_1884]) ).
cnf(c_1924,plain,
$false,
inference(resolve,[status(thm)],[c_1575,c_1932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW410-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n017.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 15:45:49 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 1104731 was started by sandbox on n017,
% 0.08/0.34 % Sat Sep 26 15:45:49 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 2.18/0.77
% 2.18/0.77 % SZS status Unsatisfiable for theBenchmark
% 2.18/0.77
% 2.18/0.77 % Proof 1 at 0.29 (+ 0.12) seconds.
% 2.18/0.77 % Length of proof is 30.
% 2.18/0.77 % Level of proof is 7.
% 2.18/0.77 % Maximum clause weight is 58.000.
% 2.18/0.77 % Given clauses 147.
% 2.18/0.77
% 2.18/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------