%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET108-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 : Fri Sep 25 02:42:19 PM UTC 2026
% Result : Unsatisfiable 24.85s 8.57s
% Output : Proof 24.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 25 unt; 0 def)
% Number of atoms : 49 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 26 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 40 ( 10 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f92,negated_conjecture,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_2) ).
fof(f92_nnf,plain,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f92]) ).
fof(f92_sk,plain,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(skolemisation,[status(esa)],[f92_nnf]) ).
cnf(c92,plain,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f92_sk]) ).
cnf(t76,plain,
member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)) = false,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t332,plain,
member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)) = false,
inference(orient,[status(thm)],[t76]) ).
cnf(f16,axiom,
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f16_nnf,plain,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t71,plain,
ifeq(member(X1,cross_product(X2,X3)),true,ordered_pair(first(X1),second(X1)),X1) = X1,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t107,plain,
ifeq(member(X1,cross_product(X2,X3)),true,ordered_pair(first(X1),second(X1)),X1) = X1,
inference(orient,[status(thm)],[t71]) ).
cnf(f91,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_1) ).
fof(f91_nnf,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(t29,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)) = true,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(t178,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(t179,plain,
ordered_pair(y,z) = ifeq(true,true,ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),ordered_pair(y,z)),
inference(cp,[status(thm)],[t107,t178]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t106,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t6566,plain,
ordered_pair(y,z) = ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),
inference(step,[status(thm)],[t179,t106]) ).
cnf(t5859,plain,
ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))) = ordered_pair(y,z),
inference(orient,[status(thm)],[t6566]) ).
cnf(t6567,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)) = false,
inference(step,[status(thm)],[t332,t5859]) ).
cnf(t6568,plain,
true = false,
inference(step,[status(thm)],[t6567,t178]) ).
cnf(t5888,plain,
true = false,
inference(rw,[status(thm)],[t6568]) ).
cnf(t5889,plain,
false = true,
inference(orient,[status(thm)],[t5888]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c92]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5889]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET108-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n016.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Thu Sep 24 09:56:02 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.85/8.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.85/8.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------