%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET096-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 02:42:13 PM UTC 2026
% Result : Unsatisfiable 17.03s 7.91s
% Output : Proof 17.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 77 ( 53 unt; 0 def)
% Number of atoms : 101 ( 64 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 91 ( 67 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-4 aty)
% Number of variables : 73 ( 12 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t150,axiom,
sF3 = ifeq(x,null_class,false,true),
introduced(definition) ).
cnf(t147,axiom,
sF0 = eq(x,null_class),
introduced(definition) ).
cnf(f140,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_2) ).
fof(f140_nnf,plain,
x != null_class,
inference(nnf_transformation,[status(thm)],[f140]) ).
fof(f140_sk,plain,
x != null_class,
inference(skolemisation,[status(esa)],[f140_nnf]) ).
cnf(c140,plain,
x != null_class,
inference(cnf_transformation,[status(esa)],[f140_sk]) ).
cnf(t5,plain,
eq(x,null_class) = false,
inference(equality_encoding,[status(esa)],[c140]) ).
cnf(t158,plain,
eq(x,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t4449,plain,
sF0 = false,
inference(step,[status(thm)],[t147,t158]) ).
cnf(t169,plain,
false = sF0,
inference(orient,[status(thm)],[t4449]) ).
cnf(t4466,plain,
sF3 = ifeq(x,null_class,sF0,true),
inference(step,[status(thm)],[t150,t169]) ).
cnf(t18,plain,
ifeq(x,null_class,false,true) = true,
inference(equality_encoding,[status(esa)],[c140]) ).
cnf(t4461,plain,
ifeq(x,null_class,sF0,true) = true,
inference(step,[status(thm)],[t18,t169]) ).
cnf(t185,plain,
ifeq(x,null_class,sF0,true) = true,
inference(orient,[status(thm)],[t4461]) ).
cnf(t4467,plain,
sF3 = true,
inference(step,[status(thm)],[t4466,t185]) ).
cnf(t197,plain,
true = sF3,
inference(orient,[status(thm)],[t4467]) ).
cnf(f141,negated_conjecture,
singleton(y) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_3) ).
fof(f141_nnf,plain,
singleton(y) != x,
inference(nnf_transformation,[status(thm)],[f141]) ).
fof(f141_sk,plain,
singleton(y) != x,
inference(skolemisation,[status(esa)],[f141_nnf]) ).
cnf(c141,plain,
singleton(y) != x,
inference(cnf_transformation,[status(esa)],[f141_sk]) ).
cnf(u35,axiom,
eq(singleton(y),x) = false,
inference(equality_encoding,[status(esa)],[c141]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/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(t16,plain,
eq(unordered_pair(y,y),x) = false,
inference(definition_unfolding,[status(thm)],[u35,d0]) ).
cnf(t148,axiom,
sF1 = unordered_pair(y,y),
introduced(definition) ).
cnf(t180,plain,
unordered_pair(y,y) = sF1,
inference(orient,[status(thm)],[t148]) ).
cnf(t4459,plain,
eq(sF1,x) = false,
inference(step,[status(thm)],[t16,t180]) ).
cnf(t4460,plain,
eq(sF1,x) = sF0,
inference(step,[status(thm)],[t4459,t169]) ).
cnf(t183,plain,
eq(sF1,x) = sF0,
inference(orient,[status(thm)],[t4460]) ).
cnf(t3912,plain,
eq(sF1,sF1) = sF0,
inference(rw,[status(thm)],[t183]) ).
cnf(t4,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t157,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t4473,plain,
eq(X1,X1) = sF3,
inference(step,[status(thm)],[t157,t197]) ).
cnf(t203,plain,
eq(X1,X1) = sF3,
inference(orient,[status(thm)],[t4473]) ).
cnf(t5205,plain,
sF3 = sF0,
inference(step,[status(thm)],[t3912,t203]) ).
cnf(t3943,plain,
sF3 = sF0,
inference(orient,[status(thm)],[t5205]) ).
cnf(t5232,plain,
true = sF0,
inference(step,[status(thm)],[t197,t3943]) ).
cnf(t3970,plain,
true = sF0,
inference(orient,[status(thm)],[t5232]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f101,axiom,
~ member(Y,intersection(complement(X),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f101_nnf,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c101,plain,
~ member(X0,intersection(complement(X1),X1)),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(f102,axiom,
~ member(Z,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f102_nnf,plain,
! [Z] : ~ member(Z,null_class),
inference(nnf_transformation,[status(thm)],[f102]) ).
fof(f102_sk,plain,
! [Z] : ~ member(Z,null_class),
inference(skolemisation,[status(esa)],[f102_nnf]) ).
cnf(c102,plain,
~ member(X0,null_class),
inference(cnf_transformation,[status(esa)],[f102_sk]) ).
cnf(f115,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f115_nnf,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f115]) ).
fof(f115_sk,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f115_nnf]) ).
cnf(c115,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f115_sk]) ).
cnf(f116,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f116_nnf,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
( unordered_pair(X1,X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f117,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
fof(f117_nnf,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(nnf_transformation,[status(thm)],[f117]) ).
fof(f117_sk,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(skolemisation,[status(esa)],[f117_nnf]) ).
cnf(c117,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f117_sk]) ).
cnf(f122,axiom,
( singleton(X) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(f122_nnf,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f122]) ).
fof(f122_sk,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f122_nnf]) ).
cnf(c122,plain,
( singleton(X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f122_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102,c115,c116,c117,c122,c140,c141]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t3970]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t169]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET096-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/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 09:46:33 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.03/7.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.03/7.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------