%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET108+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 : n007.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 02:42:19 PM UTC 2026
% Result : Theorem 9.31s 1.96s
% Output : Proof 9.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 27 unt; 0 def)
% Number of atoms : 123 ( 52 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 132 ( 56 ~; 40 |; 33 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 82 ( 1 sgn 39 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43,conjecture,
! [X] :
? [U,V] :
( ( V = X
& U = X
& ~ ? [Y,Z] :
( X = ordered_pair(Y,Z)
& member(Z,universal_class)
& member(Y,universal_class) ) )
| ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_first_and_second) ).
fof(f43_neg,negated_conjecture,
~ ! [X] :
? [U,V] :
( ( V = X
& U = X
& ~ ? [Y,Z] :
( X = ordered_pair(Y,Z)
& member(Z,universal_class)
& member(Y,universal_class) ) )
| ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [X] :
! [U,V] :
( ( V != X
| U != X
| ? [Y,Z] :
( X = ordered_pair(Y,Z)
& member(Z,universal_class)
& member(Y,universal_class) ) )
& ( X != ordered_pair(U,V)
| ~ member(V,universal_class)
| ~ member(U,universal_class) ) ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
! [U,V] :
( ( V != sk7
| U != sk7
| ( sk7 = ordered_pair(sk8(U,V),sk9(U,V))
& member(sk9(U,V),universal_class)
& member(sk8(U,V),universal_class) ) )
& ( sk7 != ordered_pair(U,V)
| ~ member(V,universal_class)
| ~ member(U,universal_class) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8,sk9])],[f43_nnf]) ).
cnf(c92,plain,
( X2 != sk7
| X1 != sk7
| sk7 = ordered_pair(sk8(X1,X2),sk9(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi87,negated_conjecture,
ifeq(X0,sk7,ifeq(X1,sk7,sk7,ordered_pair(sk8(X0,X1),sk9(X0,X1))),ordered_pair(sk8(X0,X1),sk9(X0,X1))) = ordered_pair(sk8(X0,X1),sk9(X0,X1)),
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(hi100,axiom,
or(false,X0) = X0,
introduced(definition) ).
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(h87,plain,
sk7 = unordered_pair(unordered_pair(sk8(or(false,sk7),or(false,sk7)),sk8(or(false,sk7),or(false,sk7))),unordered_pair(sk8(or(false,sk7),or(false,sk7)),unordered_pair(sk9(or(false,sk7),or(false,sk7)),sk9(or(false,sk7),or(false,sk7))))),
inference(hyper_resolution,[status(thm)],[hi87,hi100,hi100,hi13,hi14]) ).
cnf(c91,plain,
( X2 != sk7
| X1 != sk7
| member(sk9(X1,X2),universal_class) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi86,negated_conjecture,
ifeq(X0,sk7,ifeq(X1,sk7,member(sk9(X0,X1),universal_class),true),true) = true,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(h88,plain,
member(sk9(or(false,sk7),or(false,sk7)),universal_class) = true,
inference(hyper_resolution,[status(thm)],[hi86,hi100,hi100]) ).
cnf(c90,plain,
( X2 != sk7
| X1 != sk7
| member(sk8(X1,X2),universal_class) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi85,negated_conjecture,
ifeq(X0,sk7,ifeq(X1,sk7,member(sk8(X0,X1),universal_class),true),true) = true,
inference(equality_encoding,[status(esa)],[c90]) ).
cnf(h89,plain,
member(sk8(or(false,sk7),or(false,sk7)),universal_class) = true,
inference(hyper_resolution,[status(thm)],[hi85,hi100,hi100]) ).
cnf(c89,plain,
( sk7 != ordered_pair(X1,X2)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi92,negated_conjecture,
ifeq(member(X0,universal_class),true,ifeq(member(X1,universal_class),true,ifeq(sk7,ordered_pair(X0,X1),false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c89]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi92,h89,h88,h87,hi13,hi14]) ).
cnf(t300,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,t300]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET108+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 09:48:53 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.31/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.31/1.96 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------