%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET236-6 : 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 : n026.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 08:36:05 AM UTC 2026
% Result : Unsatisfiable 0.76s 0.52s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 21 unt; 0 def)
% Number of atoms : 47 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 8 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_cross_product_property11_3,axiom,
~ subclass(x,y),
file('theBenchmark.p',prove_cross_product_property11_3) ).
cnf(c_36,plain,
~ subclass(x,y),
inference(clausify,[status(thm)],[prove_cross_product_property11_3]) ).
fof(prove_cross_product_property11_2,axiom,
member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),y),
file('theBenchmark.p',prove_cross_product_property11_2) ).
cnf(c_37,plain,
member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),y),
inference(clausify,[status(thm)],[prove_cross_product_property11_2]) ).
fof(prove_cross_product_property11_1,axiom,
subclass(x,cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_cross_product_property11_1) ).
cnf(c_38,plain,
subclass(x,cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_cross_product_property11_1]) ).
fof(cartesian_product4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ordered_pair(first(VAR_0),second(VAR_0)) = VAR_0
| ~ member(VAR_0,cross_product(VAR_1,VAR_2)) ),
file('theBenchmark.p',cartesian_product4) ).
cnf(c_128,plain,
( ordered_pair(first(A),second(A)) = A
| ~ member(A,cross_product(B,C)) ),
inference(clausify,[status(thm)],[cartesian_product4]) ).
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_132,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_133,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_132]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_134,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_135,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_134]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_144,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_145,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_146,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_1420,plain,
( unordered_pair(singleton(first(A)),unordered_pair(first(A),singleton(second(A)))) = A
| ~ member(A,cross_product(B,C)) ),
inference(paramod,[status(thm)],[c_133,c_128]) ).
cnf(c_1421,plain,
( unordered_pair(unordered_pair(first(A),first(A)),unordered_pair(first(A),singleton(second(A)))) = A
| ~ member(A,cross_product(B,C)) ),
inference(paramod,[status(thm)],[c_135,c_1420]) ).
cnf(c_238,plain,
( unordered_pair(unordered_pair(first(A),first(A)),unordered_pair(first(A),unordered_pair(second(A),second(A)))) = A
| ~ member(A,cross_product(B,C)) ),
inference(paramod,[status(thm)],[c_135,c_1421]) ).
cnf(c_1422,plain,
member(unordered_pair(singleton(first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),singleton(second(not_subclass_element(x,y))))),y),
inference(paramod,[status(thm)],[c_133,c_37]) ).
cnf(c_1423,plain,
member(unordered_pair(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),singleton(second(not_subclass_element(x,y))))),y),
inference(paramod,[status(thm)],[c_135,c_1422]) ).
cnf(c_252,plain,
member(unordered_pair(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),unordered_pair(second(not_subclass_element(x,y)),second(not_subclass_element(x,y))))),y),
inference(paramod,[status(thm)],[c_135,c_1423]) ).
cnf(c_314,plain,
member(not_subclass_element(x,y),x),
inference(resolve,[status(thm)],[c_145,c_36]) ).
cnf(c_1424,plain,
( member(A,cross_product(universal_class,universal_class))
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_146,c_38]) ).
cnf(c_672,plain,
member(not_subclass_element(x,y),cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_1424,c_314]) ).
cnf(c_1350,plain,
unordered_pair(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),unordered_pair(second(not_subclass_element(x,y)),second(not_subclass_element(x,y))))) = not_subclass_element(x,y),
inference(resolve,[status(thm)],[c_672,c_238]) ).
cnf(c_1415,plain,
member(not_subclass_element(x,y),y),
inference(paramod,[status(thm)],[c_1350,c_252]) ).
cnf(c_1425,plain,
subclass(x,y),
inference(resolve,[status(thm)],[c_1415,c_144]) ).
cnf(c_1419,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_1425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET236-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.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
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 07:25:27 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 404034 was started by sandbox on n026,
% 0.10/0.38 % Sat Sep 26 07:25:27 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.76/0.52
% 0.76/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.76/0.52
% 0.76/0.52 % Proof 1 at 0.10 (+ 0.02) seconds.
% 0.76/0.52 % Length of proof is 18.
% 0.76/0.52 % Level of proof is 5.
% 0.76/0.52 % Maximum clause weight is 73.000.
% 0.76/0.52 % Given clauses 165.
% 0.76/0.52
% 0.76/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------