%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET017+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 : n020.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 : Theorem 36.69s 5.74s
% Output : Proof 36.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 28 unt; 0 def)
% Number of atoms : 124 ( 62 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 109 ( 40 ~; 38 |; 26 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 7 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f5_nnf,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c12,plain,
singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f8,axiom,
! [X,Y] :
( ( member(Y,universal_class)
& member(X,universal_class) )
=> ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_second) ).
fof(f8_nnf,plain,
! [X,Y] :
( ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X )
| ~ member(Y,universal_class)
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X )
| ~ member(Y,universal_class)
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c18,plain,
( second(ordered_pair(X0,X1)) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f43,conjecture,
! [X,Y,Z] :
( ( unordered_pair(X,Y) = unordered_pair(X,Z)
& member(Z,universal_class)
& member(Y,universal_class) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
fof(f43_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( unordered_pair(X,Y) = unordered_pair(X,Z)
& member(Z,universal_class)
& member(Y,universal_class) )
=> Y = Z ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [X,Y,Z] :
( Y != Z
& unordered_pair(X,Y) = unordered_pair(X,Z)
& member(Z,universal_class)
& member(Y,universal_class) ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
( sk8 != sk9
& unordered_pair(sk7,sk8) = unordered_pair(sk7,sk9)
& member(sk9,universal_class)
& member(sk8,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8,sk9])],[f43_nnf]) ).
cnf(c90,plain,
member(sk9,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p207,plain,
( second(ordered_pair(sk9,X0)) = X0
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[c18,c90]) ).
fof(f4,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f4_nnf,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c11,plain,
member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p225,plain,
second(ordered_pair(sk9,unordered_pair(X0,X1))) = unordered_pair(X0,X1),
inference(resolution,[status(thm)],[p207,c11]) ).
cnf(p244,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(superposition,[status(thm)],[c12,p225]) ).
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(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p120,plain,
( X0 = X1
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(factoring,[status(thm)],[c8]) ).
cnf(p245,plain,
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(demodulation,[status(thm)],[p244,p120]) ).
cnf(c10,plain,
( X0 != X2
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c89,plain,
member(sk8,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p142,plain,
( sk8 != X1
| member(sk8,unordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[c10,c89]) ).
cnf(p149,plain,
member(sk8,unordered_pair(X0,sk8)),
inference(equality_resolution,[status(thm)],[p142]) ).
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]) ).
cnf(c91,plain,
unordered_pair(sk7,sk8) = unordered_pair(sk7,sk9),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p105,plain,
subclass(unordered_pair(sk7,sk9),unordered_pair(sk7,sk8)),
inference(resolution,[status(thm)],[c5,c91]) ).
cnf(p116,plain,
( ~ subclass(unordered_pair(sk7,sk8),unordered_pair(sk7,sk9))
| unordered_pair(sk7,sk9) = unordered_pair(sk7,sk8) ),
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,sk8),unordered_pair(sk7,sk9)),
inference(resolution,[status(thm)],[c4,c91]) ).
cnf(p118,plain,
unordered_pair(sk7,sk9) = unordered_pair(sk7,sk8),
inference(resolution,[status(thm)],[p116,p100]) ).
cnf(p125,plain,
( X0 = sk9
| X0 = sk7
| ~ member(X0,unordered_pair(sk7,sk8)) ),
inference(superposition,[status(thm)],[p118,c8]) ).
cnf(p150,plain,
( sk8 = sk9
| sk8 = sk7 ),
inference(resolution,[status(thm)],[p149,p125]) ).
cnf(c92,plain,
sk8 != sk9,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p158,plain,
sk8 = sk7,
inference(resolution,[status(thm)],[p150,c92]) ).
cnf(p161,plain,
unordered_pair(sk7,sk9) = unordered_pair(sk7,sk7),
inference(demodulation,[status(thm)],[p158,p118]) ).
cnf(p171,plain,
unordered_pair(sk7,sk7) = singleton(sk7),
inference(superposition,[status(thm)],[c12,p161]) ).
cnf(p172,plain,
unordered_pair(sk7,sk9) = singleton(sk7),
inference(demodulation,[status(thm)],[p171,p161]) ).
cnf(p143,plain,
( sk9 != X1
| member(sk9,unordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[c10,c90]) ).
cnf(p177,plain,
member(sk9,unordered_pair(X0,sk9)),
inference(equality_resolution,[status(thm)],[p143]) ).
cnf(p190,plain,
member(sk9,singleton(sk7)),
inference(superposition,[status(thm)],[p172,p177]) ).
cnf(p252,plain,
sk9 = sk7,
inference(resolution,[status(thm)],[p245,p190]) ).
cnf(p160,plain,
sk7 != sk9,
inference(demodulation,[status(thm)],[p158,c92]) ).
cnf(p253,plain,
sk7 != sk7,
inference(demodulation,[status(thm)],[p252,p160]) ).
cnf(p255,plain,
$false,
inference(equality_resolution,[status(thm)],[p253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET017+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n020.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 09:11:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 36.69/5.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.69/5.74 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------