%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET025+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 : n019.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 02:41:34 PM UTC 2026
% Result : Theorem 10.86s 2.07s
% Output : Proof 10.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 30 unt; 0 def)
% Number of atoms : 82 ( 22 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 78 ( 38 ~; 22 |; 15 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 64 ( 5 sgn 43 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43,conjecture,
! [X,Y] : member(ordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_is_set) ).
fof(f43_neg,negated_conjecture,
~ ! [X,Y] : member(ordered_pair(X,Y),universal_class),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [X,Y] : ~ member(ordered_pair(X,Y),universal_class),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
~ member(ordered_pair(sk7,sk8),universal_class),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8])],[f43_nnf]) ).
cnf(c89,plain,
~ member(ordered_pair(sk7,sk8),universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi89,negated_conjecture,
ifeq(member(ordered_pair(sk7,sk8),universal_class),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c89]) ).
fof(f4,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/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(hi11,axiom,
member(unordered_pair(X0,X1),universal_class) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
fof(f6,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('/export/starexec/sandbox2/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]) ).
cnf(hi13,axiom,
ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f5,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox2/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]) ).
cnf(hi14,axiom,
singleton(X0) = unordered_pair(X0,X0),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi89,hi11,hi13,hi14]) ).
cnf(t1015,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f13,axiom,
! [X,Z] :
( member(Z,complement(X))
<=> ( ~ member(Z,X)
& member(Z,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
fof(f13_nnf,plain,
! [X,Z] :
( ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
& ( ( ~ member(Z,X)
& member(Z,universal_class) )
| ~ member(Z,complement(X)) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Z,X] :
( ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
& ( ( ~ member(Z,X)
& member(Z,universal_class) )
| ~ member(Z,complement(X)) ) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c28,plain,
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f15,axiom,
! [X] : ~ member(X,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
fof(f15_nnf,plain,
! [X] : ~ member(X,null_class),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X] : ~ member(X,null_class),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c31,plain,
~ member(X0,null_class),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f16,axiom,
! [X,Z] :
( member(Z,domain_of(X))
<=> ( restrict(X,singleton(Z),universal_class) != null_class
& member(Z,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of) ).
fof(f16_nnf,plain,
! [X,Z] :
( ( restrict(X,singleton(Z),universal_class) = null_class
| ~ member(Z,universal_class)
| member(Z,domain_of(X)) )
& ( ( restrict(X,singleton(Z),universal_class) != null_class
& member(Z,universal_class) )
| ~ member(Z,domain_of(X)) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Z,X] :
( ( restrict(X,singleton(Z),universal_class) = null_class
| ~ member(Z,universal_class)
| member(Z,domain_of(X)) )
& ( ( restrict(X,singleton(Z),universal_class) != null_class
& member(Z,universal_class) )
| ~ member(Z,domain_of(X)) ) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c33,plain,
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f39,axiom,
! [X,Y] :
( disjoint(X,Y)
<=> ! [U] :
~ ( member(U,Y)
& member(U,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f39_nnf,plain,
! [X,Y] :
( ( ? [U] :
( member(U,Y)
& member(U,X) )
| disjoint(X,Y) )
& ( ! [U] :
( ~ member(U,Y)
| ~ member(U,X) )
| ~ disjoint(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [X,Y,U] :
( ( ( member(sk4(X,Y),Y)
& member(sk4(X,Y),X) )
| disjoint(X,Y) )
& ( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f39_nnf]) ).
cnf(c80,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c28,c31,c33,c80,c89]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1015]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET025+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Thu Sep 24 09:15:35 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.86/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.86/2.07 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------