%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET117+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 : 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 02:42:21 PM UTC 2026
% Result : Theorem 23.97s 9.45s
% Output : Proof 23.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 21 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 4 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43,conjecture,
! [X] :
( ordered_pair(first(X),second(X)) = X
=> member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_ordered_pairs_are_sets) ).
fof(f43_neg,negated_conjecture,
~ ! [X] :
( ordered_pair(first(X),second(X)) = X
=> member(X,universal_class) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [X] :
( ~ member(X,universal_class)
& ordered_pair(first(X),second(X)) = X ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
( ~ member(sk7,universal_class)
& ordered_pair(first(sk7),second(sk7)) = sk7 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f43_nnf]) ).
cnf(c89,plain,
ordered_pair(first(sk7),second(sk7)) = sk7,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
fof(f6,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f6_nnf,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c13,plain,
ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
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(p148,plain,
member(ordered_pair(X0,X1),universal_class),
inference(superposition,[status(thm)],[c13,c11]) ).
cnf(p156,plain,
member(sk7,universal_class),
inference(superposition,[status(thm)],[c89,p148]) ).
cnf(c90,plain,
~ member(sk7,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p159,plain,
$false,
inference(resolution,[status(thm)],[p156,c90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET117+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n011.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 09:54:48 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.97/9.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.97/9.45 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------