%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET020+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 02:41:31 PM UTC 2026
% Result : Theorem 47.59s 6.49s
% Output : Proof 47.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 53 ( 30 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 54 ( 21 ~; 14 |; 16 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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,
! [U,V,X] :
( ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) )
=> ( second(X) = V
& first(X) = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(f43_neg,negated_conjecture,
~ ! [U,V,X] :
( ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) )
=> ( second(X) = V
& first(X) = U ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [U,V,X] :
( ( second(X) != V
| first(X) != U )
& X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
( ( second(sk9) != sk8
| first(sk9) != sk7 )
& sk9 = ordered_pair(sk7,sk8)
& member(sk8,universal_class)
& member(sk7,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8,sk9])],[f43_nnf]) ).
cnf(c89,plain,
member(sk7,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p210,plain,
( second(ordered_pair(sk7,X0)) = X0
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[c18,c89]) ).
cnf(c90,plain,
member(sk8,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p251,plain,
second(sk9) = sk8,
inference(resolution,[status(thm)],[p210,c90]) ).
cnf(c17,plain,
( first(ordered_pair(X0,X1)) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p194,plain,
( first(ordered_pair(sk7,X0)) = sk7
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[c17,c89]) ).
cnf(p202,plain,
first(sk9) = sk7,
inference(resolution,[status(thm)],[p194,c90]) ).
cnf(c92,plain,
( second(sk9) != sk8
| first(sk9) != sk7 ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p203,plain,
( second(sk9) != sk8
| sk7 != sk7 ),
inference(demodulation,[status(thm)],[p202,c92]) ).
cnf(p217,plain,
second(sk9) != sk8,
inference(equality_resolution,[status(thm)],[p203]) ).
cnf(p252,plain,
sk8 != sk8,
inference(demodulation,[status(thm)],[p251,p217]) ).
cnf(p258,plain,
$false,
inference(equality_resolution,[status(thm)],[p252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET020+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 09:12:42 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 47.59/6.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.59/6.49 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------