%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET114-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:42:20 PM UTC 2026
% Result : Unsatisfiable 23.63s 3.52s
% Output : Proof 23.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 27
% Syntax : Number of formulae : 211 ( 175 unt; 0 def)
% Number of atoms : 247 ( 198 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 103 ( 67 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 13 con; 0-4 aty)
% Number of variables : 129 ( 14 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t168,axiom,
sF2 = ifeq(second(x),x,false,true),
introduced(definition) ).
cnf(t166,axiom,
sF0 = second(x),
introduced(definition) ).
cnf(t181,plain,
second(x) = sF0,
inference(orient,[status(thm)],[t166]) ).
cnf(t7136,plain,
sF2 = ifeq(sF0,x,false,true),
inference(step,[status(thm)],[t168,t181]) ).
cnf(t167,axiom,
sF1 = eq(second(x),x),
introduced(definition) ).
cnf(t7113,plain,
sF1 = eq(sF0,x),
inference(step,[status(thm)],[t167,t181]) ).
cnf(f160,negated_conjecture,
second(x) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_2nd_in_pair_of_non_sets) ).
fof(f160_nnf,plain,
second(x) != x,
inference(nnf_transformation,[status(thm)],[f160]) ).
fof(f160_sk,plain,
second(x) != x,
inference(skolemisation,[status(esa)],[f160_nnf]) ).
cnf(c160,plain,
second(x) != x,
inference(cnf_transformation,[status(esa)],[f160_sk]) ).
cnf(t15,plain,
eq(second(x),x) = false,
inference(equality_encoding,[status(esa)],[c160]) ).
cnf(t7112,plain,
eq(sF0,x) = false,
inference(step,[status(thm)],[t15,t181]) ).
cnf(t195,plain,
eq(sF0,x) = false,
inference(orient,[status(thm)],[t7112]) ).
cnf(t7114,plain,
sF1 = false,
inference(step,[status(thm)],[t7113,t195]) ).
cnf(t196,plain,
false = sF1,
inference(orient,[status(thm)],[t7114]) ).
cnf(t7137,plain,
sF2 = ifeq(sF0,x,sF1,true),
inference(step,[status(thm)],[t7136,t196]) ).
cnf(t24,plain,
ifeq(second(x),x,false,true) = true,
inference(equality_encoding,[status(esa)],[c160]) ).
cnf(t7133,plain,
ifeq(sF0,x,false,true) = true,
inference(step,[status(thm)],[t24,t181]) ).
cnf(t7134,plain,
ifeq(sF0,x,sF1,true) = true,
inference(step,[status(thm)],[t7133,t196]) ).
cnf(t226,plain,
ifeq(sF0,x,sF1,true) = true,
inference(orient,[status(thm)],[t7134]) ).
cnf(t7138,plain,
sF2 = true,
inference(step,[status(thm)],[t7137,t226]) ).
cnf(t228,plain,
true = sF2,
inference(orient,[status(thm)],[t7138]) ).
cnf(f154,axiom,
( second(X) = X
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_3) ).
fof(f154_nnf,plain,
! [X] :
( second(X) = X
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
inference(nnf_transformation,[status(thm)],[f154]) ).
fof(f154_sk,plain,
! [X] :
( second(X) = X
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
inference(skolemisation,[status(esa)],[f154_nnf]) ).
cnf(c154,plain,
( second(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[status(esa)],[f154_sk]) ).
cnf(u69,axiom,
or(member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)),eq(second(X0),X0)) = true,
inference(equality_encoding,[status(esa)],[c154]) ).
cnf(f12,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox2/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(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(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(t140,plain,
or(member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),cross_product(universal_class,universal_class)),eq(second(X1),X1)) = true,
inference(definition_unfolding,[status(thm)],[u69,d1]) ).
cnf(t174,axiom,
sF8 = cross_product(universal_class,universal_class),
introduced(definition) ).
cnf(t194,plain,
cross_product(universal_class,universal_class) = sF8,
inference(orient,[status(thm)],[t174]) ).
cnf(t8232,plain,
or(member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),sF8),eq(second(X1),X1)) = true,
inference(step,[status(thm)],[t140,t194]) ).
cnf(t8233,plain,
or(member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),sF8),eq(second(X1),X1)) = sF2,
inference(step,[status(thm)],[t8232,t228]) ).
cnf(t6378,plain,
or(member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),sF8),eq(second(X1),X1)) = sF2,
inference(orient,[status(thm)],[t8233]) ).
cnf(t28,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t7180,plain,
ifeq(eq(X1,X2),sF2,X1,X2) = X2,
inference(step,[status(thm)],[t28,t228]) ).
cnf(t287,plain,
ifeq(eq(X1,X2),sF2,X1,X2) = X2,
inference(orient,[status(thm)],[t7180]) ).
cnf(f153,axiom,
( first(X) = X
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
fof(f153_nnf,plain,
! [X] :
( first(X) = X
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
inference(nnf_transformation,[status(thm)],[f153]) ).
fof(f153_sk,plain,
! [X] :
( first(X) = X
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
inference(skolemisation,[status(esa)],[f153_nnf]) ).
cnf(c153,plain,
( first(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[status(esa)],[f153_sk]) ).
cnf(u68,axiom,
or(member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)),eq(first(X0),X0)) = true,
inference(equality_encoding,[status(esa)],[c153]) ).
cnf(t139,plain,
or(member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),cross_product(universal_class,universal_class)),eq(first(X1),X1)) = true,
inference(definition_unfolding,[status(thm)],[u68,d1]) ).
cnf(t8141,plain,
or(member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),sF8),eq(first(X1),X1)) = true,
inference(step,[status(thm)],[t139,t194]) ).
cnf(t8142,plain,
or(member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),sF8),eq(first(X1),X1)) = sF2,
inference(step,[status(thm)],[t8141,t228]) ).
cnf(t6223,plain,
or(member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),sF8),eq(first(X1),X1)) = sF2,
inference(orient,[status(thm)],[t8142]) ).
cnf(t6224,plain,
sF2 = or(member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(sF0,second(x)))),sF8),eq(first(x),x)),
inference(cp,[status(thm)],[t6223,t181]) ).
cnf(t169,axiom,
sF3 = first(x),
introduced(definition) ).
cnf(t182,plain,
first(x) = sF3,
inference(orient,[status(thm)],[t169]) ).
cnf(t8143,plain,
sF2 = or(member(unordered_pair(unordered_pair(sF3,first(x)),unordered_pair(first(x),unordered_pair(sF0,second(x)))),sF8),eq(first(x),x)),
inference(step,[status(thm)],[t6224,t182]) ).
cnf(t8144,plain,
sF2 = or(member(unordered_pair(unordered_pair(sF3,sF3),unordered_pair(first(x),unordered_pair(sF0,second(x)))),sF8),eq(first(x),x)),
inference(step,[status(thm)],[t8143,t182]) ).
cnf(t170,axiom,
sF4 = unordered_pair(first(x),first(x)),
introduced(definition) ).
cnf(t7127,plain,
sF4 = unordered_pair(sF3,first(x)),
inference(step,[status(thm)],[t170,t182]) ).
cnf(t7128,plain,
sF4 = unordered_pair(sF3,sF3),
inference(step,[status(thm)],[t7127,t182]) ).
cnf(t216,plain,
unordered_pair(sF3,sF3) = sF4,
inference(orient,[status(thm)],[t7128]) ).
cnf(t8145,plain,
sF2 = or(member(unordered_pair(sF4,unordered_pair(first(x),unordered_pair(sF0,second(x)))),sF8),eq(first(x),x)),
inference(step,[status(thm)],[t8144,t216]) ).
cnf(t8146,plain,
sF2 = or(member(unordered_pair(sF4,unordered_pair(sF3,unordered_pair(sF0,second(x)))),sF8),eq(first(x),x)),
inference(step,[status(thm)],[t8145,t182]) ).
cnf(t8147,plain,
sF2 = or(member(unordered_pair(sF4,unordered_pair(sF3,unordered_pair(sF0,sF0))),sF8),eq(first(x),x)),
inference(step,[status(thm)],[t8146,t181]) ).
cnf(t171,axiom,
sF5 = unordered_pair(second(x),second(x)),
introduced(definition) ).
cnf(t7129,plain,
sF5 = unordered_pair(sF0,second(x)),
inference(step,[status(thm)],[t171,t181]) ).
cnf(t7130,plain,
sF5 = unordered_pair(sF0,sF0),
inference(step,[status(thm)],[t7129,t181]) ).
cnf(t220,plain,
unordered_pair(sF0,sF0) = sF5,
inference(orient,[status(thm)],[t7130]) ).
cnf(t8148,plain,
sF2 = or(member(unordered_pair(sF4,unordered_pair(sF3,sF5)),sF8),eq(first(x),x)),
inference(step,[status(thm)],[t8147,t220]) ).
cnf(t172,axiom,
sF6 = unordered_pair(first(x),unordered_pair(second(x),second(x))),
introduced(definition) ).
cnf(t7211,plain,
sF6 = unordered_pair(sF3,unordered_pair(second(x),second(x))),
inference(step,[status(thm)],[t172,t182]) ).
cnf(t7212,plain,
sF6 = unordered_pair(sF3,unordered_pair(sF0,second(x))),
inference(step,[status(thm)],[t7211,t181]) ).
cnf(t7213,plain,
sF6 = unordered_pair(sF3,unordered_pair(sF0,sF0)),
inference(step,[status(thm)],[t7212,t181]) ).
cnf(t7214,plain,
sF6 = unordered_pair(sF3,sF5),
inference(step,[status(thm)],[t7213,t220]) ).
cnf(t360,plain,
unordered_pair(sF3,sF5) = sF6,
inference(orient,[status(thm)],[t7214]) ).
cnf(t8149,plain,
sF2 = or(member(unordered_pair(sF4,sF6),sF8),eq(first(x),x)),
inference(step,[status(thm)],[t8148,t360]) ).
cnf(f156,axiom,
( second(X) = X
| ordered_pair(first(X),second(X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).
fof(f156_nnf,plain,
! [X] :
( second(X) = X
| ordered_pair(first(X),second(X)) = X ),
inference(nnf_transformation,[status(thm)],[f156]) ).
fof(f156_sk,plain,
! [X] :
( second(X) = X
| ordered_pair(first(X),second(X)) = X ),
inference(skolemisation,[status(esa)],[f156_nnf]) ).
cnf(c156,plain,
( second(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f156_sk]) ).
cnf(u71,axiom,
or(eq(ordered_pair(first(X0),second(X0)),X0),eq(second(X0),X0)) = true,
inference(equality_encoding,[status(esa)],[c156]) ).
cnf(t129,plain,
or(eq(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),X1),eq(second(X1),X1)) = true,
inference(definition_unfolding,[status(thm)],[u71,d1]) ).
cnf(t8056,plain,
or(eq(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),X1),eq(second(X1),X1)) = sF2,
inference(step,[status(thm)],[t129,t228]) ).
cnf(t5446,plain,
or(eq(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),X1),eq(second(X1),X1)) = sF2,
inference(orient,[status(thm)],[t8056]) ).
cnf(t5447,plain,
sF2 = or(eq(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(sF0,second(x)))),x),eq(second(x),x)),
inference(cp,[status(thm)],[t5446,t181]) ).
cnf(t8059,plain,
sF2 = or(eq(unordered_pair(unordered_pair(sF3,first(x)),unordered_pair(first(x),unordered_pair(sF0,second(x)))),x),eq(second(x),x)),
inference(step,[status(thm)],[t5447,t182]) ).
cnf(t8060,plain,
sF2 = or(eq(unordered_pair(unordered_pair(sF3,sF3),unordered_pair(first(x),unordered_pair(sF0,second(x)))),x),eq(second(x),x)),
inference(step,[status(thm)],[t8059,t182]) ).
cnf(t8061,plain,
sF2 = or(eq(unordered_pair(sF4,unordered_pair(first(x),unordered_pair(sF0,second(x)))),x),eq(second(x),x)),
inference(step,[status(thm)],[t8060,t216]) ).
cnf(t8062,plain,
sF2 = or(eq(unordered_pair(sF4,unordered_pair(sF3,unordered_pair(sF0,second(x)))),x),eq(second(x),x)),
inference(step,[status(thm)],[t8061,t182]) ).
cnf(t8063,plain,
sF2 = or(eq(unordered_pair(sF4,unordered_pair(sF3,unordered_pair(sF0,sF0))),x),eq(second(x),x)),
inference(step,[status(thm)],[t8062,t181]) ).
cnf(t8064,plain,
sF2 = or(eq(unordered_pair(sF4,unordered_pair(sF3,sF5)),x),eq(second(x),x)),
inference(step,[status(thm)],[t8063,t220]) ).
cnf(t8065,plain,
sF2 = or(eq(unordered_pair(sF4,sF6),x),eq(second(x),x)),
inference(step,[status(thm)],[t8064,t360]) ).
cnf(t8066,plain,
sF2 = or(eq(unordered_pair(sF4,sF6),x),eq(sF0,x)),
inference(step,[status(thm)],[t8065,t181]) ).
cnf(t7122,plain,
eq(sF0,x) = sF1,
inference(step,[status(thm)],[t195,t196]) ).
cnf(t204,plain,
eq(sF0,x) = sF1,
inference(orient,[status(thm)],[t7122]) ).
cnf(t8067,plain,
sF2 = or(eq(unordered_pair(sF4,sF6),x),sF1),
inference(step,[status(thm)],[t8066,t204]) ).
cnf(t8,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t187,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t7120,plain,
or(X1,sF1) = X1,
inference(step,[status(thm)],[t187,t196]) ).
cnf(t202,plain,
or(X1,sF1) = X1,
inference(rw,[status(thm)],[t7120]) ).
cnf(t208,plain,
or(X1,sF1) = X1,
inference(orient,[status(thm)],[t202]) ).
cnf(t8068,plain,
sF2 = eq(unordered_pair(sF4,sF6),x),
inference(step,[status(thm)],[t8067,t208]) ).
cnf(t5457,plain,
eq(unordered_pair(sF4,sF6),x) = sF2,
inference(orient,[status(thm)],[t8068]) ).
cnf(t5459,plain,
x = ifeq(sF2,sF2,unordered_pair(sF4,sF6),x),
inference(cp,[status(thm)],[t287,t5457]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t207,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t8069,plain,
x = unordered_pair(sF4,sF6),
inference(step,[status(thm)],[t5459,t207]) ).
cnf(t5462,plain,
unordered_pair(sF4,sF6) = x,
inference(orient,[status(thm)],[t8069]) ).
cnf(t8150,plain,
sF2 = or(member(x,sF8),eq(first(x),x)),
inference(step,[status(thm)],[t8149,t5462]) ).
cnf(f159,negated_conjecture,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets2_1) ).
fof(f159_nnf,plain,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
inference(nnf_transformation,[status(thm)],[f159]) ).
fof(f159_sk,plain,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
inference(skolemisation,[status(esa)],[f159_nnf]) ).
cnf(c159,plain,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f159_sk]) ).
cnf(u77,axiom,
member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) = false,
inference(equality_encoding,[status(esa)],[c159]) ).
cnf(t115,plain,
member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)) = false,
inference(definition_unfolding,[status(thm)],[u77,d1]) ).
cnf(t7870,plain,
member(unordered_pair(unordered_pair(sF3,first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)) = false,
inference(step,[status(thm)],[t115,t182]) ).
cnf(t7871,plain,
member(unordered_pair(unordered_pair(sF3,sF3),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)) = false,
inference(step,[status(thm)],[t7870,t182]) ).
cnf(t7872,plain,
member(unordered_pair(sF4,unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)) = false,
inference(step,[status(thm)],[t7871,t216]) ).
cnf(t7873,plain,
member(unordered_pair(sF4,unordered_pair(sF3,unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)) = false,
inference(step,[status(thm)],[t7872,t182]) ).
cnf(t7874,plain,
member(unordered_pair(sF4,unordered_pair(sF3,unordered_pair(sF0,second(x)))),cross_product(universal_class,universal_class)) = false,
inference(step,[status(thm)],[t7873,t181]) ).
cnf(t7875,plain,
member(unordered_pair(sF4,unordered_pair(sF3,unordered_pair(sF0,sF0))),cross_product(universal_class,universal_class)) = false,
inference(step,[status(thm)],[t7874,t181]) ).
cnf(t7876,plain,
member(unordered_pair(sF4,unordered_pair(sF3,sF5)),cross_product(universal_class,universal_class)) = false,
inference(step,[status(thm)],[t7875,t220]) ).
cnf(t7877,plain,
member(unordered_pair(sF4,sF6),cross_product(universal_class,universal_class)) = false,
inference(step,[status(thm)],[t7876,t360]) ).
cnf(t7878,plain,
member(unordered_pair(sF4,sF6),sF8) = false,
inference(step,[status(thm)],[t7877,t194]) ).
cnf(t7879,plain,
member(unordered_pair(sF4,sF6),sF8) = sF1,
inference(step,[status(thm)],[t7878,t196]) ).
cnf(t3758,plain,
member(unordered_pair(sF4,sF6),sF8) = sF1,
inference(orient,[status(thm)],[t7879]) ).
cnf(t8070,plain,
member(x,sF8) = sF1,
inference(step,[status(thm)],[t3758,t5462]) ).
cnf(t5463,plain,
member(x,sF8) = sF1,
inference(rw,[status(thm)],[t8070]) ).
cnf(t5521,plain,
member(x,sF8) = sF1,
inference(orient,[status(thm)],[t5463]) ).
cnf(t8151,plain,
sF2 = or(sF1,eq(first(x),x)),
inference(step,[status(thm)],[t8150,t5521]) ).
cnf(t10,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t189,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t7121,plain,
or(sF1,X1) = X1,
inference(step,[status(thm)],[t189,t196]) ).
cnf(t203,plain,
or(sF1,X1) = X1,
inference(rw,[status(thm)],[t7121]) ).
cnf(t209,plain,
or(sF1,X1) = X1,
inference(orient,[status(thm)],[t203]) ).
cnf(t8152,plain,
sF2 = eq(first(x),x),
inference(step,[status(thm)],[t8151,t209]) ).
cnf(t8153,plain,
sF2 = eq(sF3,x),
inference(step,[status(thm)],[t8152,t182]) ).
cnf(t6227,plain,
eq(sF3,x) = sF2,
inference(orient,[status(thm)],[t8153]) ).
cnf(t6228,plain,
x = ifeq(sF2,sF2,sF3,x),
inference(cp,[status(thm)],[t287,t6227]) ).
cnf(t8154,plain,
x = sF3,
inference(step,[status(thm)],[t6228,t207]) ).
cnf(t6231,plain,
x = sF3,
inference(orient,[status(thm)],[t8154]) ).
cnf(t8155,plain,
second(sF3) = sF0,
inference(step,[status(thm)],[t181,t6231]) ).
cnf(t6232,plain,
second(sF3) = sF0,
inference(rw,[status(thm)],[t8155]) ).
cnf(t6298,plain,
second(sF3) = sF0,
inference(orient,[status(thm)],[t6232]) ).
cnf(t6381,plain,
sF2 = or(member(unordered_pair(unordered_pair(first(sF3),first(sF3)),unordered_pair(first(sF3),unordered_pair(sF0,second(sF3)))),sF8),eq(second(sF3),sF3)),
inference(cp,[status(thm)],[t6378,t6298]) ).
cnf(t8156,plain,
first(sF3) = sF3,
inference(step,[status(thm)],[t182,t6231]) ).
cnf(t6233,plain,
first(sF3) = sF3,
inference(rw,[status(thm)],[t8156]) ).
cnf(t6303,plain,
first(sF3) = sF3,
inference(orient,[status(thm)],[t6233]) ).
cnf(t8234,plain,
sF2 = or(member(unordered_pair(unordered_pair(sF3,first(sF3)),unordered_pair(first(sF3),unordered_pair(sF0,second(sF3)))),sF8),eq(second(sF3),sF3)),
inference(step,[status(thm)],[t6381,t6303]) ).
cnf(t8235,plain,
sF2 = or(member(unordered_pair(unordered_pair(sF3,sF3),unordered_pair(first(sF3),unordered_pair(sF0,second(sF3)))),sF8),eq(second(sF3),sF3)),
inference(step,[status(thm)],[t8234,t6303]) ).
cnf(t8236,plain,
sF2 = or(member(unordered_pair(sF4,unordered_pair(first(sF3),unordered_pair(sF0,second(sF3)))),sF8),eq(second(sF3),sF3)),
inference(step,[status(thm)],[t8235,t216]) ).
cnf(t8237,plain,
sF2 = or(member(unordered_pair(sF4,unordered_pair(sF3,unordered_pair(sF0,second(sF3)))),sF8),eq(second(sF3),sF3)),
inference(step,[status(thm)],[t8236,t6303]) ).
cnf(t8238,plain,
sF2 = or(member(unordered_pair(sF4,unordered_pair(sF3,unordered_pair(sF0,sF0))),sF8),eq(second(sF3),sF3)),
inference(step,[status(thm)],[t8237,t6298]) ).
cnf(t8239,plain,
sF2 = or(member(unordered_pair(sF4,unordered_pair(sF3,sF5)),sF8),eq(second(sF3),sF3)),
inference(step,[status(thm)],[t8238,t220]) ).
cnf(t8240,plain,
sF2 = or(member(unordered_pair(sF4,sF6),sF8),eq(second(sF3),sF3)),
inference(step,[status(thm)],[t8239,t360]) ).
cnf(t8159,plain,
unordered_pair(sF4,sF6) = sF3,
inference(step,[status(thm)],[t5462,t6231]) ).
cnf(t6237,plain,
unordered_pair(sF4,sF6) = sF3,
inference(orient,[status(thm)],[t8159]) ).
cnf(t8241,plain,
sF2 = or(member(sF3,sF8),eq(second(sF3),sF3)),
inference(step,[status(thm)],[t8240,t6237]) ).
cnf(t8161,plain,
member(sF3,sF8) = sF1,
inference(step,[status(thm)],[t5521,t6231]) ).
cnf(t6239,plain,
member(sF3,sF8) = sF1,
inference(rw,[status(thm)],[t8161]) ).
cnf(t6314,plain,
member(sF3,sF8) = sF1,
inference(orient,[status(thm)],[t6239]) ).
cnf(t8242,plain,
sF2 = or(sF1,eq(second(sF3),sF3)),
inference(step,[status(thm)],[t8241,t6314]) ).
cnf(t8243,plain,
sF2 = eq(second(sF3),sF3),
inference(step,[status(thm)],[t8242,t209]) ).
cnf(t8244,plain,
sF2 = eq(sF0,sF3),
inference(step,[status(thm)],[t8243,t6298]) ).
cnf(t8157,plain,
eq(sF0,sF3) = sF1,
inference(step,[status(thm)],[t204,t6231]) ).
cnf(t6234,plain,
eq(sF0,sF3) = sF1,
inference(rw,[status(thm)],[t8157]) ).
cnf(t6305,plain,
eq(sF0,sF3) = sF1,
inference(orient,[status(thm)],[t6234]) ).
cnf(t8245,plain,
sF2 = sF1,
inference(step,[status(thm)],[t8244,t6305]) ).
cnf(t6382,plain,
sF2 = sF1,
inference(orient,[status(thm)],[t8245]) ).
cnf(t8274,plain,
true = sF1,
inference(step,[status(thm)],[t228,t6382]) ).
cnf(t6411,plain,
true = sF1,
inference(orient,[status(thm)],[t8274]) ).
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,c159,c160]) ).
cnf(g0_0,plain,
sF1 != false,
inference(rw,[status(thm)],[goal_0,t6411]) ).
cnf(g0_1,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_0,t196]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET114-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 09:56:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.63/3.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.63/3.52 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------