%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET072+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 : Theorem 41.48s 5.78s
% Output : Proof 41.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 96 ( 48 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 93 ( 33 ~; 34 |; 22 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 5 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
fof(f2_nnf,plain,
! [X,Y] :
( ( ~ subclass(Y,X)
| ~ subclass(X,Y)
| X = Y )
& ( ( subclass(Y,X)
& subclass(X,Y) )
| X != Y ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( ( ~ subclass(Y,X)
| ~ subclass(X,Y)
| X = Y )
& ( ( subclass(Y,X)
& subclass(X,Y) )
| X != Y ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(c5,plain,
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f43,conjecture,
! [X,Y,Z] :
( ( unordered_pair(X,Z) = unordered_pair(Y,Z)
& member(Y,universal_class)
& member(X,universal_class) )
=> X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation) ).
fof(f43_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( unordered_pair(X,Z) = unordered_pair(Y,Z)
& member(Y,universal_class)
& member(X,universal_class) )
=> X = Y ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [X,Y,Z] :
( X != Y
& unordered_pair(X,Z) = unordered_pair(Y,Z)
& member(Y,universal_class)
& member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
( sk7 != sk8
& unordered_pair(sk7,sk9) = unordered_pair(sk8,sk9)
& member(sk8,universal_class)
& member(sk7,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8,sk9])],[f43_nnf]) ).
cnf(c91,plain,
unordered_pair(sk7,sk9) = unordered_pair(sk8,sk9),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p105,plain,
subclass(unordered_pair(sk8,sk9),unordered_pair(sk7,sk9)),
inference(resolution,[status(thm)],[c5,c91]) ).
cnf(p116,plain,
( ~ subclass(unordered_pair(sk7,sk9),unordered_pair(sk8,sk9))
| unordered_pair(sk8,sk9) = unordered_pair(sk7,sk9) ),
inference(resolution,[status(thm)],[c6,p105]) ).
cnf(c4,plain,
( subclass(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p100,plain,
subclass(unordered_pair(sk7,sk9),unordered_pair(sk8,sk9)),
inference(resolution,[status(thm)],[c4,c91]) ).
cnf(p118,plain,
unordered_pair(sk8,sk9) = unordered_pair(sk7,sk9),
inference(resolution,[status(thm)],[p116,p100]) ).
fof(f3,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f3_nnf,plain,
! [U,X,Y] :
( ( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,X,Y] :
( ( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c9,plain,
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c90,plain,
member(sk8,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p133,plain,
( sk8 != X0
| member(sk8,unordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[c9,c90]) ).
cnf(p167,plain,
member(sk8,unordered_pair(sk8,X0)),
inference(equality_resolution,[status(thm)],[p133]) ).
cnf(p169,plain,
member(sk8,unordered_pair(sk7,sk9)),
inference(superposition,[status(thm)],[p118,p167]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p170,plain,
( sk8 = sk9
| sk8 = sk7 ),
inference(resolution,[status(thm)],[p169,c8]) ).
cnf(c89,plain,
member(sk7,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p132,plain,
( sk7 != X0
| member(sk7,unordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[c9,c89]) ).
cnf(p138,plain,
member(sk7,unordered_pair(sk7,X0)),
inference(equality_resolution,[status(thm)],[p132]) ).
cnf(p125,plain,
( X0 = sk9
| X0 = sk8
| ~ member(X0,unordered_pair(sk7,sk9)) ),
inference(superposition,[status(thm)],[p118,c8]) ).
cnf(p126,plain,
( sk8 != sk9
| X0 = sk8
| ~ member(X0,unordered_pair(sk7,sk9)) ),
inference(equality_factoring,[status(thm)],[p125]) ).
cnf(p141,plain,
( sk8 != sk9
| sk7 = sk8 ),
inference(resolution,[status(thm)],[p138,p126]) ).
cnf(p185,plain,
( sk7 = sk8
| sk8 = sk7 ),
inference(resolution,[status(thm)],[p170,p141]) ).
cnf(c92,plain,
sk7 != sk8,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p193,plain,
( sk7 != sk7
| sk7 = sk8 ),
inference(superposition,[status(thm)],[p185,c92]) ).
cnf(p203,plain,
sk7 = sk8,
inference(equality_resolution,[status(thm)],[p193]) ).
cnf(p216,plain,
$false,
inference(resolution,[status(thm)],[p203,c92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 09:35:26 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 41.48/5.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.48/5.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------