%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 02:41:30 PM UTC 2026
% Result : Unsatisfiable 26.89s 9.55s
% Output : Proof 26.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 30 unt; 0 def)
% Number of atoms : 97 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 74 ( 36 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 16 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,axiom,
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f13_nnf,plain,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(f114,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_2) ).
fof(f114_nnf,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f114]) ).
cnf(c114,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f114_nnf]) ).
cnf(p176,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[c13,c114]) ).
cnf(f9,axiom,
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f9_nnf,plain,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p178,plain,
member(y,unordered_pair(X0,y)),
inference(resolution,[status(thm)],[p176,c9]) ).
cnf(f113,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_1) ).
fof(f113_nnf,plain,
unordered_pair(x,y) = unordered_pair(x,z),
inference(nnf_transformation,[status(thm)],[f113]) ).
cnf(c113,plain,
unordered_pair(x,y) = unordered_pair(x,z),
inference(cnf_transformation,[status(esa)],[f113_nnf]) ).
cnf(f7,axiom,
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f7_nnf,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p140,plain,
( X0 = z
| X0 = x
| ~ member(X0,unordered_pair(x,y)) ),
inference(superposition,[status(thm)],[c113,c7]) ).
cnf(p180,plain,
( y = z
| y = x ),
inference(resolution,[status(thm)],[p178,p140]) ).
cnf(f115,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_3) ).
fof(f115_nnf,plain,
y != z,
inference(nnf_transformation,[status(thm)],[f115]) ).
fof(f115_sk,plain,
y != z,
inference(skolemisation,[status(esa)],[f115_nnf]) ).
cnf(c115,plain,
y != z,
inference(cnf_transformation,[status(esa)],[f115_sk]) ).
cnf(p208,plain,
y = x,
inference(resolution,[status(thm)],[p180,c115]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f11_nnf,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(f14,axiom,
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f14_nnf,plain,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p183,plain,
member(z,universal_class),
inference(resolution,[status(thm)],[c14,c114]) ).
cnf(f8,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f8_nnf,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p184,plain,
member(z,unordered_pair(z,X0)),
inference(resolution,[status(thm)],[p183,c8]) ).
cnf(p186,plain,
member(z,singleton(z)),
inference(superposition,[status(thm)],[c11,p184]) ).
cnf(f109,axiom,
subclass(singleton(Y),unordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
fof(f109_nnf,plain,
! [Y,X] : subclass(singleton(Y),unordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [Y,X] : subclass(singleton(Y),unordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
subclass(singleton(X0),unordered_pair(X1,X0)),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(p139,plain,
subclass(singleton(z),unordered_pair(x,y)),
inference(superposition,[status(thm)],[c113,c109]) ).
cnf(f0,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f0_nnf,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p141,plain,
( member(X0,unordered_pair(x,y))
| ~ member(X0,singleton(z)) ),
inference(resolution,[status(thm)],[p139,c0]) ).
cnf(p187,plain,
member(z,unordered_pair(x,y)),
inference(resolution,[status(thm)],[p186,p141]) ).
cnf(p205,plain,
( z = y
| z = x ),
inference(resolution,[status(thm)],[p187,c7]) ).
cnf(p233,plain,
( z = x
| z = x ),
inference(demodulation,[status(thm)],[p208,p205]) ).
cnf(p245,plain,
z = x,
inference(factoring,[status(thm)],[p233]) ).
cnf(p210,plain,
x != z,
inference(demodulation,[status(thm)],[p208,c115]) ).
cnf(p249,plain,
x != x,
inference(demodulation,[status(thm)],[p245,p210]) ).
cnf(p255,plain,
$false,
inference(equality_resolution,[status(thm)],[p249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.59 % Computer : n017.cluster.edu
% 0.08/5.59 % Model : x86_64 x86_64
% 0.08/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.59 % Memory : 8046.5625MB
% 0.08/5.59 % OS : Linux 6.8.0-71-generic
% 0.08/5.59 % CPULimit : 300
% 0.08/5.59 % WCLimit : 300
% 0.08/5.59 % DateTime : Thu Sep 24 09:06:22 UTC 2026
% 0.08/5.59 % CPUTime :
% 0.08/5.59 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.89/9.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.89/9.55 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------