%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW409-1 : 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 : n004.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 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 15 unt; 0 def)
% Number of atoms : 32 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 16 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 30 ( 0 sgn 10 !; 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(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_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_20,plain,
heap(sep(lseg(x2,x1),sep(lseg(x3,nil),sep(next(x1,x3),emp)))),
inference(clausify,[status(thm)],[premise_5]) ).
cnf(c_21,plain,
heap(sep(lseg(x3,nil),sep(lseg(x2,x1),sep(next(x1,x3),emp)))),
inference(paramod,[status(thm)],[c_1,c_20]) ).
fof(conclusion_1,axiom,
~ heap(sep(lseg(x2,nil),emp)),
file('theBenchmark.p',conclusion_1) ).
cnf(c_22,plain,
~ heap(sep(lseg(x2,nil),emp)),
inference(clausify,[status(thm)],[conclusion_1]) ).
cnf(c_29,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_31,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_77,plain,
~ heap(sep(lseg(A,nil),sep(lseg(x2,A),emp))),
inference(resolve,[status(thm)],[c_31,c_22]) ).
cnf(c_143,plain,
x1 != x3,
inference(copy,[status(thm)],[c_18]) ).
cnf(c_144,plain,
( heap(sep(lseg(x1,A),B))
| ~ heap(sep(lseg(x3,A),sep(next(x1,x3),B))) ),
inference(resolve,[status(thm)],[c_29,c_143]) ).
cnf(c_145,plain,
~ heap(sep(lseg(x3,nil),sep(next(x1,x3),sep(lseg(x2,x1),emp)))),
inference(resolve,[status(thm)],[c_144,c_77]) ).
cnf(c_146,plain,
~ heap(sep(lseg(x3,nil),sep(lseg(x2,x1),sep(next(x1,x3),emp)))),
inference(paramod,[status(thm)],[c_1,c_145]) ).
cnf(c_142,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW409-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 15:49:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2082851 was started by sandbox on n004,
% 0.10/0.37 % Sat Sep 26 15:49:51 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.45
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45
% 0.10/0.45 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.45 % Length of proof is 12.
% 0.10/0.45 % Level of proof is 3.
% 0.10/0.45 % Maximum clause weight is 29.000.
% 0.10/0.45 % Given clauses 55.
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------