%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET231-6 : 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 : 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 08:36:04 AM UTC 2026
% Result : Unsatisfiable 1.48s 0.91s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 30 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 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 : 28 ( 8 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_cross_product_property6_2,axiom,
ordered_pair(first(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),
file('theBenchmark.p',prove_cross_product_property6_2) ).
cnf(c_36,plain,
ordered_pair(first(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(clausify,[status(thm)],[prove_cross_product_property6_2]) ).
fof(prove_cross_product_property6_1,axiom,
~ subclass(cross_product(x,y),z),
file('theBenchmark.p',prove_cross_product_property6_1) ).
cnf(c_37,plain,
~ subclass(cross_product(x,y),z),
inference(clausify,[status(thm)],[prove_cross_product_property6_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_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_1091,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_1092,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_1091]) ).
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_1092]) ).
cnf(c_1093,plain,
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))))) != not_subclass_element(cross_product(x,y),z),
inference(paramod,[status(thm)],[c_132,c_36]) ).
cnf(c_1094,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)),singleton(second(not_subclass_element(cross_product(x,y),z))))) != not_subclass_element(cross_product(x,y),z),
inference(paramod,[status(thm)],[c_134,c_1093]) ).
cnf(c_251,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(paramod,[status(thm)],[c_134,c_1094]) ).
cnf(c_308,plain,
member(not_subclass_element(cross_product(x,y),z),cross_product(x,y)),
inference(resolve,[status(thm)],[c_144,c_37]) ).
cnf(c_1095,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_1090,plain,
$false,
inference(resolve,[status(thm)],[c_251,c_1095]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SET231-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.47 % Computer : n005.cluster.edu
% 0.10/0.47 % Model : x86_64 x86_64
% 0.10/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.47 % Memory : 8046.5625MB
% 0.10/0.47 % OS : Linux 6.8.0-71-generic
% 0.10/0.47 % CPULimit : 300
% 0.10/0.47 % WCLimit : 300
% 0.10/0.47 % DateTime : Sat Sep 26 07:22:48 UTC 2026
% 0.10/0.47 % CPUTime :
% 0.10/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.47 % Process 1548225 was started by sandbox on n005,
% 0.10/0.47 % Sat Sep 26 07:22:48 2026
% 0.10/0.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.49
% 0.10/0.49 % From the command line: assign(max_seconds, 300).
% 1.48/0.91
% 1.48/0.91 % SZS status Unsatisfiable for theBenchmark
% 1.48/0.91
% 1.48/0.91 % Proof 1 at 0.12 (+ 0.04) seconds.
% 1.48/0.91 % Length of proof is 12.
% 1.48/0.91 % Level of proof is 3.
% 1.48/0.91 % Maximum clause weight is 40.000.
% 1.48/0.91 % Given clauses 218.
% 1.48/0.91
% 1.48/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------