%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET102-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:35:47 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 23 unt; 0 def)
% Number of atoms : 31 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 10 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_unordered_pair_member_of_ordered_pair_1,axiom,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
file('theBenchmark.p',prove_unordered_pair_member_of_ordered_pair_1) ).
cnf(c_33,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(clausify,[status(thm)],[prove_unordered_pair_member_of_ordered_pair_1]) ).
fof(unordered_pairs_and_singletons,axiom,
! [VAR_0,VAR_1] : unordered_pair(VAR_0,VAR_1) = union(singleton(VAR_0),singleton(VAR_1)),
file('theBenchmark.p',unordered_pairs_and_singletons) ).
cnf(c_35,plain,
unordered_pair(A,B) = union(singleton(A),singleton(B)),
inference(clausify,[status(thm)],[unordered_pairs_and_singletons]) ).
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_163,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_164,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_163]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(singleton(VAR_0),unordered_pair(VAR_0,singleton(VAR_1))) = ordered_pair(VAR_0,VAR_1),
file('theBenchmark.p',ordered_pair) ).
cnf(c_177,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_491,plain,
unordered_pair(singleton(A),union(singleton(A),singleton(singleton(B)))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_35,c_177]) ).
cnf(c_492,plain,
unordered_pair(singleton(A),complement(intersection(complement(singleton(A)),complement(singleton(singleton(B)))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_164,c_491]) ).
cnf(c_493,plain,
union(singleton(singleton(A)),singleton(complement(intersection(complement(singleton(A)),complement(singleton(singleton(B))))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_35,c_492]) ).
cnf(c_494,plain,
complement(intersection(complement(singleton(singleton(A))),complement(singleton(complement(intersection(complement(singleton(A)),complement(singleton(singleton(B))))))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_164,c_493]) ).
cnf(c_178,plain,
ordered_pair(A,B) = complement(intersection(complement(singleton(singleton(A))),complement(singleton(complement(intersection(complement(singleton(A)),complement(singleton(singleton(B))))))))),
inference(copy,[status(thm)],[c_494]) ).
fof(unordered_pairs_in_universal,axiom,
! [VAR_0,VAR_1] : member(unordered_pair(VAR_0,VAR_1),universal_class),
file('theBenchmark.p',unordered_pairs_in_universal) ).
cnf(c_181,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pairs_in_universal]) ).
cnf(c_495,plain,
member(union(singleton(A),singleton(B)),universal_class),
inference(paramod,[status(thm)],[c_35,c_181]) ).
cnf(c_182,plain,
member(complement(intersection(complement(singleton(A)),complement(singleton(B)))),universal_class),
inference(paramod,[status(thm)],[c_164,c_495]) ).
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_183,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
cnf(c_496,plain,
( member(A,union(singleton(B),singleton(A)))
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_35,c_183]) ).
cnf(c_184,plain,
( member(A,complement(intersection(complement(singleton(B)),complement(singleton(A)))))
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_164,c_496]) ).
cnf(c_497,plain,
~ member(union(singleton(x),singleton(singleton(y))),ordered_pair(x,y)),
inference(paramod,[status(thm)],[c_35,c_33]) ).
cnf(c_498,plain,
~ member(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))),ordered_pair(x,y)),
inference(paramod,[status(thm)],[c_164,c_497]) ).
cnf(c_229,plain,
~ member(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))),complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y)))))))))),
inference(paramod,[status(thm)],[c_178,c_498]) ).
cnf(c_489,plain,
member(complement(intersection(complement(singleton(A)),complement(singleton(B)))),complement(intersection(complement(singleton(C)),complement(singleton(complement(intersection(complement(singleton(A)),complement(singleton(B))))))))),
inference(resolve,[status(thm)],[c_184,c_182]) ).
cnf(c_490,plain,
$false,
inference(resolve,[status(thm)],[c_489,c_229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET102-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:07:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 4159728 was started by sandbox2 on n012,
% 0.09/0.36 % Sat Sep 26 07:07:20 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.42
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.42
% 0.12/0.42 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.12/0.42 % Length of proof is 13.
% 0.12/0.42 % Level of proof is 4.
% 0.12/0.42 % Maximum clause weight is 27.000.
% 0.12/0.42 % Given clauses 61.
% 0.12/0.42
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------