%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET102-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 02:42:14 PM UTC 2026
% Result : Unsatisfiable 0.07s 15.85s
% Output : Proof 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 35 unt; 0 def)
% Number of atoms : 59 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 26 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 72 ( 17 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f91,negated_conjecture,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unordered_pair_member_of_ordered_pair_1) ).
fof(f91_nnf,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(nnf_transformation,[status(thm)],[f91]) ).
fof(f91_sk,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(skolemisation,[status(esa)],[f91_nnf]) ).
cnf(c91,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(cnf_transformation,[status(esa)],[f91_sk]) ).
cnf(u11,axiom,
member(unordered_pair(x,singleton(y)),ordered_pair(x,y)) = false,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f11_nnf,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(d0,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f12,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f12_nnf,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(u0,axiom,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(d1,axiom,
unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = ordered_pair(X0,X1),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(t56,plain,
member(unordered_pair(x,unordered_pair(y,y)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(definition_unfolding,[status(thm)],[u11,d0,d1]) ).
cnf(f9,axiom,
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f9_nnf,plain,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t40,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X2,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t324,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X2,X1)),true) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(f10,axiom,
member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f10_nnf,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t12,plain,
member(unordered_pair(X1,X2),universal_class) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t110,plain,
member(unordered_pair(X1,X2),universal_class) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t326,plain,
true = ifeq(true,true,member(unordered_pair(X1,X2),unordered_pair(X3,unordered_pair(X1,X2))),true),
inference(cp,[status(thm)],[t324,t110]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t109,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t1261,plain,
true = member(unordered_pair(X1,X2),unordered_pair(X3,unordered_pair(X1,X2))),
inference(step,[status(thm)],[t326,t109]) ).
cnf(t470,plain,
member(unordered_pair(X1,X2),unordered_pair(X3,unordered_pair(X1,X2))) = true,
inference(orient,[status(thm)],[t1261]) ).
cnf(t1409,plain,
true = false,
inference(step,[status(thm)],[t56,t470]) ).
cnf(t1085,plain,
false = true,
inference(orient,[status(thm)],[t1409]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c91]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1085]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET102-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/15.32 % Computer : n012.cluster.edu
% 0.03/15.32 % Model : x86_64 x86_64
% 0.03/15.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/15.32 % Memory : 8046.5625MB
% 0.03/15.32 % OS : Linux 6.8.0-71-generic
% 0.03/15.32 % CPULimit : 300
% 0.03/15.32 % WCLimit : 300
% 0.03/15.32 % DateTime : Thu Sep 24 09:49:27 UTC 2026
% 0.03/15.32 % CPUTime :
% 0.03/15.32 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/15.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/15.85 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------