%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET103-7 : 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 : n020.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 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 25 unt; 0 def)
% Number of atoms : 29 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 11 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_property_1_of_ordered_pair_2,axiom,
~ member(y,universal_class),
file('theBenchmark.p',prove_property_1_of_ordered_pair_2) ).
cnf(c_33,plain,
~ member(y,universal_class),
inference(clausify,[status(thm)],[prove_property_1_of_ordered_pair_2]) ).
fof(prove_property_1_of_ordered_pair_1,axiom,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
file('theBenchmark.p',prove_property_1_of_ordered_pair_1) ).
cnf(c_34,plain,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
inference(clausify,[status(thm)],[prove_property_1_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_38,plain,
unordered_pair(A,B) = union(singleton(A),singleton(B)),
inference(clausify,[status(thm)],[unordered_pairs_and_singletons]) ).
fof(singleton_is_null_class,axiom,
! [VAR_0] :
( singleton(VAR_0) = null_class
| member(VAR_0,universal_class) ),
file('theBenchmark.p',singleton_is_null_class) ).
cnf(c_61,plain,
( singleton(A) = null_class
| member(A,universal_class) ),
inference(clausify,[status(thm)],[singleton_is_null_class]) ).
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_166,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_167,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_166]) ).
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_180,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_345,plain,
unordered_pair(singleton(A),union(singleton(A),singleton(singleton(B)))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_38,c_180]) ).
cnf(c_346,plain,
unordered_pair(singleton(A),complement(intersection(complement(singleton(A)),complement(singleton(singleton(B)))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_167,c_345]) ).
cnf(c_347,plain,
union(singleton(singleton(A)),singleton(complement(intersection(complement(singleton(A)),complement(singleton(singleton(B))))))) = ordered_pair(A,B),
inference(paramod,[status(thm)],[c_38,c_346]) ).
cnf(c_348,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_167,c_347]) ).
cnf(c_181,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_348]) ).
cnf(c_349,plain,
unordered_pair(singleton(x),union(singleton(x),singleton(null_class))) != ordered_pair(x,y),
inference(paramod,[status(thm)],[c_38,c_34]) ).
cnf(c_350,plain,
unordered_pair(singleton(x),complement(intersection(complement(singleton(x)),complement(singleton(null_class))))) != ordered_pair(x,y),
inference(paramod,[status(thm)],[c_167,c_349]) ).
cnf(c_351,plain,
union(singleton(singleton(x)),singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))) != ordered_pair(x,y),
inference(paramod,[status(thm)],[c_38,c_350]) ).
cnf(c_352,plain,
complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))) != ordered_pair(x,y),
inference(paramod,[status(thm)],[c_167,c_351]) ).
cnf(c_353,plain,
complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))) != complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))))))),
inference(paramod,[status(thm)],[c_181,c_352]) ).
cnf(c_233,plain,
complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))))))) != complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))),
inference(copy,[status(thm)],[c_353]) ).
cnf(c_339,plain,
singleton(y) = null_class,
inference(resolve,[status(thm)],[c_61,c_33]) ).
cnf(c_354,plain,
complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))) != complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))),
inference(paramod,[status(thm)],[c_339,c_233]) ).
cnf(c_344,plain,
$false,
inference(copy,[status(thm)],[c_354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET103-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.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 07:08:48 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 938521 was started by sandbox2 on n020,
% 0.10/0.37 % Sat Sep 26 07:08:48 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.14/0.44
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.44
% 0.14/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/0.44 % Length of proof is 11.
% 0.14/0.44 % Level of proof is 4.
% 0.14/0.44 % Maximum clause weight is 60.000.
% 0.14/0.44 % Given clauses 19.
% 0.14/0.44
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------