%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW400-1 : 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 : n019.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 09:14:11 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.85s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 30 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 12 !; 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(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,
heap(sep(next(x2,nil),sep(lseg(x1,x2),emp))),
file('theBenchmark.p',premise_3) ).
cnf(c_17,plain,
heap(sep(next(x2,nil),sep(lseg(x1,x2),emp))),
inference(clausify,[status(thm)],[premise_3]) ).
fof(conclusion_1,axiom,
~ heap(sep(lseg(x1,nil),emp)),
file('theBenchmark.p',conclusion_1) ).
cnf(c_18,plain,
~ heap(sep(lseg(x1,nil),emp)),
inference(clausify,[status(thm)],[conclusion_1]) ).
cnf(c_31,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_50,plain,
~ heap(sep(lseg(x1,A),sep(lseg(A,nil),emp))),
inference(resolve,[status(thm)],[c_10,c_18]) ).
cnf(c_142,plain,
( heap(sep(lseg(x2,nil),sep(lseg(x1,x2),emp)))
| x2 = nil ),
inference(resolve,[status(thm)],[c_31,c_17]) ).
cnf(c_135,plain,
heap(sep(lseg(x2,nil),sep(lseg(x1,x2),emp))),
inference(resolve,[status(thm)],[c_16,c_142]) ).
cnf(c_143,plain,
heap(sep(lseg(x1,x2),sep(lseg(x2,nil),emp))),
inference(paramod,[status(thm)],[c_1,c_135]) ).
cnf(c_141,plain,
$false,
inference(resolve,[status(thm)],[c_50,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW400-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.81 % Computer : n019.cluster.edu
% 0.17/0.81 % Model : x86_64 x86_64
% 0.17/0.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.81 % Memory : 8046.5625MB
% 0.17/0.81 % OS : Linux 6.8.0-71-generic
% 0.17/0.81 % CPULimit : 300
% 0.17/0.81 % WCLimit : 300
% 0.17/0.81 % DateTime : Sat Sep 26 15:49:34 UTC 2026
% 0.17/0.81 % CPUTime :
% 0.17/0.82 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.82 % Process 1660082 was started by sandbox2 on n019,
% 0.17/0.82 % Sat Sep 26 15:49:34 2026
% 0.17/0.82 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.82
% 0.17/0.82 % From the command line: assign(max_seconds, 300).
% 0.17/0.85
% 0.17/0.85 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.85
% 0.17/0.85 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.85 % Length of proof is 12.
% 0.17/0.85 % Level of proof is 3.
% 0.17/0.85 % Maximum clause weight is 39.000.
% 0.17/0.85 % Given clauses 26.
% 0.17/0.85
% 0.17/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------