%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM141-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:16:11 AM UTC 2026
% Result : Unsatisfiable 2.22s 0.80s
% Output : CNFRefutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 21 unt; 0 def)
% Number of atoms : 41 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 16 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 2 con; 0-2 aty)
% Number of variables : 32 ( 3 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_successor_of_set_is_set2_2,axiom,
~ member(x,successor(x)),
file('theBenchmark.p',prove_successor_of_set_is_set2_2) ).
cnf(c_53,plain,
~ member(x,successor(x)),
inference(clausify,[status(thm)],[prove_successor_of_set_is_set2_2]) ).
fof(prove_successor_of_set_is_set2_1,axiom,
member(x,universal_class),
file('theBenchmark.p',prove_successor_of_set_is_set2_1) ).
cnf(c_54,plain,
member(x,universal_class),
inference(clausify,[status(thm)],[prove_successor_of_set_is_set2_1]) ).
fof(successor,axiom,
! [VAR_0] : union(VAR_0,singleton(VAR_0)) = successor(VAR_0),
file('theBenchmark.p',successor) ).
cnf(c_151,plain,
union(A,singleton(A)) = successor(A),
inference(clausify,[status(thm)],[successor]) ).
cnf(c_152,plain,
successor(A) = union(A,singleton(A)),
inference(copy,[status(thm)],[c_151]) ).
fof(union,axiom,
! [VAR_0,VAR_1] : complement(intersection(complement(VAR_0),complement(VAR_1))) = union(VAR_0,VAR_1),
file('theBenchmark.p',union) ).
cnf(c_177,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_178,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_177]) ).
fof(complement2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,VAR_1)
| member(VAR_0,complement(VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',complement2) ).
cnf(c_179,plain,
( member(A,B)
| member(A,complement(B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[complement2]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_180,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection2) ).
cnf(c_182,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_193,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_194,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_193]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_196,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
cnf(c_1399,plain,
~ member(x,union(x,singleton(x))),
inference(paramod,[status(thm)],[c_152,c_53]) ).
cnf(c_1400,plain,
~ member(x,union(x,unordered_pair(x,x))),
inference(paramod,[status(thm)],[c_194,c_1399]) ).
cnf(c_240,plain,
~ member(x,complement(intersection(complement(x),complement(unordered_pair(x,x))))),
inference(paramod,[status(thm)],[c_178,c_1400]) ).
cnf(c_310,plain,
( member(x,A)
| member(x,complement(A)) ),
inference(resolve,[status(thm)],[c_179,c_54]) ).
cnf(c_332,plain,
member(x,unordered_pair(A,x)),
inference(resolve,[status(thm)],[c_196,c_54]) ).
cnf(c_586,plain,
member(x,intersection(complement(x),complement(unordered_pair(x,x)))),
inference(resolve,[status(thm)],[c_310,c_240]) ).
cnf(c_1377,plain,
member(x,complement(unordered_pair(x,x))),
inference(resolve,[status(thm)],[c_586,c_182]) ).
cnf(c_1401,plain,
~ member(x,unordered_pair(x,x)),
inference(resolve,[status(thm)],[c_1377,c_180]) ).
cnf(c_1398,plain,
$false,
inference(resolve,[status(thm)],[c_332,c_1401]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM141-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 02:06:32 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 1878225 was started by sandbox on n014,
% 0.10/0.37 % Sat Sep 26 02:06:32 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).
% 2.22/0.80
% 2.22/0.80 % SZS status Unsatisfiable for theBenchmark
% 2.22/0.80
% 2.22/0.80 % Proof 1 at 0.20 (+ 0.05) seconds.
% 2.22/0.80 % Length of proof is 18.
% 2.22/0.80 % Level of proof is 5.
% 2.22/0.80 % Maximum clause weight is 10.000.
% 2.22/0.80 % Given clauses 260.
% 2.22/0.80
% 2.22/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------