%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET072-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:41:56 PM UTC 2026
% Result : Unsatisfiable 106.33s 15.84s
% Output : Proof 106.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 22 unt; 0 def)
% Number of atoms : 97 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 81 ( 39 ~; 42 |; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 12 sgn 38 !; 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(f92,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_cancellation_2) ).
fof(f92_nnf,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f92]) ).
cnf(c92,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f92_nnf]) ).
cnf(p151,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[c13,c92]) ).
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(p152,plain,
member(x,unordered_pair(x,X0)),
inference(resolution,[status(thm)],[p151,c8]) ).
cnf(f6,axiom,
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f6_nnf,plain,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f5,axiom,
( subclass(Y,X)
| X != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f5_nnf,plain,
! [X,Y] :
( subclass(Y,X)
| X != Y ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( subclass(Y,X)
| X != Y ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f91,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_cancellation_1) ).
fof(f91_nnf,plain,
unordered_pair(x,z) = unordered_pair(y,z),
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
unordered_pair(x,z) = unordered_pair(y,z),
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(p104,plain,
subclass(unordered_pair(y,z),unordered_pair(x,z)),
inference(resolution,[status(thm)],[c5,c91]) ).
cnf(p111,plain,
( unordered_pair(y,z) = unordered_pair(x,z)
| ~ subclass(unordered_pair(x,z),unordered_pair(y,z)) ),
inference(resolution,[status(thm)],[c6,p104]) ).
cnf(f4,axiom,
( subclass(X,Y)
| X != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass1) ).
fof(f4_nnf,plain,
! [X,Y] :
( subclass(X,Y)
| X != Y ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( subclass(X,Y)
| X != Y ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( subclass(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p101,plain,
subclass(unordered_pair(x,z),unordered_pair(y,z)),
inference(resolution,[status(thm)],[c4,c91]) ).
cnf(p114,plain,
unordered_pair(y,z) = unordered_pair(x,z),
inference(resolution,[status(thm)],[p111,p101]) ).
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(p119,plain,
( X0 = z
| X0 = y
| ~ member(X0,unordered_pair(x,z)) ),
inference(superposition,[status(thm)],[p114,c7]) ).
cnf(p155,plain,
( x = z
| x = y ),
inference(resolution,[status(thm)],[p152,p119]) ).
cnf(f93,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_cancellation_3) ).
fof(f93_nnf,plain,
x != y,
inference(nnf_transformation,[status(thm)],[f93]) ).
fof(f93_sk,plain,
x != y,
inference(skolemisation,[status(esa)],[f93_nnf]) ).
cnf(c93,plain,
x != y,
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(p184,plain,
x = z,
inference(resolution,[status(thm)],[p155,c93]) ).
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(p158,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[c14,c92]) ).
cnf(p159,plain,
member(y,unordered_pair(y,X0)),
inference(resolution,[status(thm)],[p158,c8]) ).
cnf(p162,plain,
member(y,unordered_pair(x,z)),
inference(superposition,[status(thm)],[p114,p159]) ).
cnf(p180,plain,
( y = z
| y = x ),
inference(resolution,[status(thm)],[p162,c7]) ).
cnf(p226,plain,
( y = x
| y = x ),
inference(superposition,[status(thm)],[p184,p180]) ).
cnf(p258,plain,
y = x,
inference(factoring,[status(thm)],[p226]) ).
cnf(p260,plain,
x != x,
inference(demodulation,[status(thm)],[p258,c93]) ).
cnf(p273,plain,
$false,
inference(equality_resolution,[status(thm)],[p260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 09:38:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 106.33/15.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.33/15.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------