%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET234-6 : 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 : n005.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 0.60s 0.55s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 36 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 32 ( 8 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_cross_product_property9_2,axiom,
~ subclass(cross_product(x,y),z),
file('theBenchmark.p',prove_cross_product_property9_2) ).
cnf(c_36,plain,
~ subclass(cross_product(x,y),z),
inference(clausify,[status(thm)],[prove_cross_product_property9_2]) ).
fof(prove_cross_product_property9_1,axiom,
member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),z),
file('theBenchmark.p',prove_cross_product_property9_1) ).
cnf(c_37,plain,
member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),z),
inference(clausify,[status(thm)],[prove_cross_product_property9_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_127,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_131,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_132,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_131]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_133,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_134,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_133]) ).
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_143,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_144,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_1153,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_132,c_127]) ).
cnf(c_1154,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_134,c_1153]) ).
cnf(c_237,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_134,c_1154]) ).
cnf(c_1155,plain,
member(unordered_pair(singleton(first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),singleton(second(not_subclass_element(cross_product(x,y),z))))),z),
inference(paramod,[status(thm)],[c_132,c_37]) ).
cnf(c_1156,plain,
member(unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),singleton(second(not_subclass_element(cross_product(x,y),z))))),z),
inference(paramod,[status(thm)],[c_134,c_1155]) ).
cnf(c_251,plain,
member(unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),unordered_pair(second(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))))),z),
inference(paramod,[status(thm)],[c_134,c_1156]) ).
cnf(c_308,plain,
member(not_subclass_element(cross_product(x,y),z),cross_product(x,y)),
inference(resolve,[status(thm)],[c_144,c_36]) ).
cnf(c_1096,plain,
unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),unordered_pair(second(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))))) = not_subclass_element(cross_product(x,y),z),
inference(resolve,[status(thm)],[c_308,c_237]) ).
cnf(c_1109,plain,
member(not_subclass_element(cross_product(x,y),z),z),
inference(paramod,[status(thm)],[c_1096,c_251]) ).
cnf(c_1157,plain,
subclass(cross_product(x,y),z),
inference(resolve,[status(thm)],[c_1109,c_143]) ).
cnf(c_1152,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_1157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET234-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n005.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sat Sep 26 07:22:32 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.38 % Process 1547221 was started by sandbox2 on n005,
% 0.13/0.38 % Sat Sep 26 07:22:32 2026
% 0.13/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.60/0.55
% 0.60/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.60/0.55
% 0.60/0.55 % Proof 1 at 0.11 (+ 0.03) seconds.
% 0.60/0.55 % Length of proof is 15.
% 0.60/0.55 % Level of proof is 5.
% 0.60/0.55 % Maximum clause weight is 40.000.
% 0.60/0.55 % Given clauses 221.
% 0.60/0.55
% 0.60/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------