%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET102-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:42:15 PM UTC 2026
% Result : Unsatisfiable 10.85s 2.08s
% Output : Proof 10.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 98 ( 70 unt; 0 def)
% Number of atoms : 126 ( 73 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 94 ( 66 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 128 ( 31 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f145,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(f145_nnf,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(nnf_transformation,[status(thm)],[f145]) ).
fof(f145_sk,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(skolemisation,[status(esa)],[f145_nnf]) ).
cnf(c145,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(cnf_transformation,[status(esa)],[f145_sk]) ).
cnf(u39,axiom,
member(unordered_pair(x,singleton(y)),ordered_pair(x,y)) = false,
inference(equality_encoding,[status(esa)],[c145]) ).
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(t96,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)],[u39,d0,d1]) ).
cnf(t150,axiom,
sF0 = unordered_pair(y,y),
introduced(definition) ).
cnf(t171,plain,
unordered_pair(y,y) = sF0,
inference(orient,[status(thm)],[t150]) ).
cnf(t2839,plain,
member(unordered_pair(x,sF0),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t96,t171]) ).
cnf(f107,axiom,
unordered_pair(X,Y) = unordered_pair(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f107_nnf,plain,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
inference(nnf_transformation,[status(thm)],[f107]) ).
fof(f107_sk,plain,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
inference(skolemisation,[status(esa)],[f107_nnf]) ).
cnf(c107,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f107_sk]) ).
cnf(t21,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(t188,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t21]) ).
cnf(t2840,plain,
member(unordered_pair(sF0,x),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2839,t188]) ).
cnf(t151,axiom,
sF1 = unordered_pair(x,unordered_pair(y,y)),
introduced(definition) ).
cnf(t2438,plain,
sF1 = unordered_pair(x,sF0),
inference(step,[status(thm)],[t151,t171]) ).
cnf(t185,plain,
unordered_pair(x,sF0) = sF1,
inference(orient,[status(thm)],[t2438]) ).
cnf(t2439,plain,
unordered_pair(sF0,x) = sF1,
inference(step,[status(thm)],[t185,t188]) ).
cnf(t189,plain,
unordered_pair(sF0,x) = sF1,
inference(rw,[status(thm)],[t2439]) ).
cnf(t190,plain,
unordered_pair(sF0,x) = sF1,
inference(orient,[status(thm)],[t189]) ).
cnf(t2841,plain,
member(sF1,unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2840,t190]) ).
cnf(t152,axiom,
sF2 = unordered_pair(x,x),
introduced(definition) ).
cnf(t172,plain,
unordered_pair(x,x) = sF2,
inference(orient,[status(thm)],[t152]) ).
cnf(t2842,plain,
member(sF1,unordered_pair(sF2,unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2841,t172]) ).
cnf(t2843,plain,
member(sF1,unordered_pair(sF2,unordered_pair(x,sF0))) = false,
inference(step,[status(thm)],[t2842,t171]) ).
cnf(t2844,plain,
member(sF1,unordered_pair(sF2,unordered_pair(sF0,x))) = false,
inference(step,[status(thm)],[t2843,t188]) ).
cnf(t2845,plain,
member(sF1,unordered_pair(sF2,sF1)) = false,
inference(step,[status(thm)],[t2844,t190]) ).
cnf(f8,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f8_nnf,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t61,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t604,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(orient,[status(thm)],[t61]) ).
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(t18,plain,
member(unordered_pair(X1,X2),universal_class) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t179,plain,
member(unordered_pair(X1,X2),universal_class) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t186,plain,
true = member(sF1,universal_class),
inference(cp,[status(thm)],[t179,t185]) ).
cnf(t187,plain,
member(sF1,universal_class) = true,
inference(orient,[status(thm)],[t186]) ).
cnf(t611,plain,
true = ifeq(true,true,member(sF1,unordered_pair(sF1,X1)),true),
inference(cp,[status(thm)],[t604,t187]) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t173,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t2510,plain,
true = member(sF1,unordered_pair(sF1,X1)),
inference(step,[status(thm)],[t611,t173]) ).
cnf(t632,plain,
member(sF1,unordered_pair(sF1,X1)) = true,
inference(orient,[status(thm)],[t2510]) ).
cnf(t634,plain,
true = member(sF1,unordered_pair(X1,sF1)),
inference(cp,[status(thm)],[t632,t188]) ).
cnf(t663,plain,
member(sF1,unordered_pair(X1,sF1)) = true,
inference(orient,[status(thm)],[t634]) ).
cnf(t2846,plain,
true = false,
inference(step,[status(thm)],[t2845,t663]) ).
cnf(t2277,plain,
false = true,
inference(orient,[status(thm)],[t2846]) ).
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(f101,axiom,
~ member(Y,intersection(complement(X),X)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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,c145]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2277]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET102-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.40 % Computer : n019.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.40 % CPULimit : 300
% 0.08/0.40 % WCLimit : 300
% 0.08/0.40 % DateTime : Thu Sep 24 09:49:55 UTC 2026
% 0.08/0.41 % CPUTime :
% 0.08/0.41 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.85/2.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.85/2.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------