%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET115-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 02:42:21 PM UTC 2026
% Result : Unsatisfiable 15.19s 2.45s
% Output : Proof 15.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 31 unt; 0 def)
% Number of atoms : 87 ( 50 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 94 ( 66 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 72 ( 12 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f155,axiom,
( first(X) = X
| ordered_pair(first(X),second(X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).
fof(f155_nnf,plain,
! [X] :
( first(X) = X
| ordered_pair(first(X),second(X)) = X ),
inference(nnf_transformation,[status(thm)],[f155]) ).
fof(f155_sk,plain,
! [X] :
( first(X) = X
| ordered_pair(first(X),second(X)) = X ),
inference(skolemisation,[status(esa)],[f155_nnf]) ).
cnf(c155,plain,
( first(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f155_sk]) ).
cnf(t109,plain,
or(eq(ordered_pair(first(X1),second(X1)),X1),eq(first(X1),X1)) = true,
inference(equality_encoding,[status(esa)],[c155]) ).
cnf(t652,plain,
or(eq(ordered_pair(first(X1),second(X1)),X1),eq(first(X1),X1)) = true,
inference(orient,[status(thm)],[t109]) ).
cnf(f160,negated_conjecture,
first(x) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_in_pair_of_non_sets) ).
fof(f160_nnf,plain,
first(x) != x,
inference(nnf_transformation,[status(thm)],[f160]) ).
fof(f160_sk,plain,
first(x) != x,
inference(skolemisation,[status(esa)],[f160_nnf]) ).
cnf(c160,plain,
first(x) != x,
inference(cnf_transformation,[status(esa)],[f160_sk]) ).
cnf(t16,plain,
eq(first(x),x) = false,
inference(equality_encoding,[status(esa)],[c160]) ).
cnf(t953,plain,
eq(first(x),x) = false,
inference(orient,[status(thm)],[t16]) ).
cnf(t957,plain,
true = or(eq(ordered_pair(first(x),second(x)),x),false),
inference(cp,[status(thm)],[t652,t953]) ).
cnf(t8,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t205,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t1161,plain,
true = eq(ordered_pair(first(x),second(x)),x),
inference(step,[status(thm)],[t957,t205]) ).
cnf(f159,negated_conjecture,
ordered_pair(first(x),second(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets3_1) ).
fof(f159_nnf,plain,
ordered_pair(first(x),second(x)) != x,
inference(nnf_transformation,[status(thm)],[f159]) ).
fof(f159_sk,plain,
ordered_pair(first(x),second(x)) != x,
inference(skolemisation,[status(esa)],[f159_nnf]) ).
cnf(c159,plain,
ordered_pair(first(x),second(x)) != x,
inference(cnf_transformation,[status(esa)],[f159_sk]) ).
cnf(t38,plain,
eq(ordered_pair(first(x),second(x)),x) = false,
inference(equality_encoding,[status(esa)],[c159]) ).
cnf(t942,plain,
eq(ordered_pair(first(x),second(x)),x) = false,
inference(orient,[status(thm)],[t38]) ).
cnf(t1162,plain,
true = false,
inference(step,[status(thm)],[t1161,t942]) ).
cnf(t1134,plain,
false = true,
inference(orient,[status(thm)],[t1162]) ).
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,
true != true,
inference(rw,[status(thm)],[goal_0,t1134]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET115-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 09:59:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.19/2.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.19/2.45 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------