%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET075-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 02:41:59 PM UTC 2026
% Result : Unsatisfiable 8.83s 1.62s
% Output : Proof 8.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 46 unt; 0 def)
% Number of atoms : 78 ( 38 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 50 ( 34 ~; 16 |; 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 : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 84 ( 24 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/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(t75,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t150,plain,
ifeq(member(X1,universal_class),true,member(X1,unordered_pair(X1,X2)),true) = true,
inference(orient,[status(thm)],[t75]) ).
cnf(f116,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
fof(f116_nnf,plain,
unordered_pair(x,y) = null_class,
inference(nnf_transformation,[status(thm)],[f116]) ).
cnf(c116,plain,
unordered_pair(x,y) = null_class,
inference(cnf_transformation,[status(esa)],[f116_nnf]) ).
cnf(t15,plain,
unordered_pair(x,y) = null_class,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(t617,plain,
unordered_pair(x,y) = null_class,
inference(orient,[status(thm)],[t15]) ).
cnf(t641,plain,
unordered_pair(x,y) = null_class,
inference(rw,[status(thm)],[t617]) ).
cnf(f107,axiom,
unordered_pair(X,Y) = unordered_pair(Y,X),
file('/export/starexec/sandbox2/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(t24,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(t631,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t24]) ).
cnf(t863,plain,
unordered_pair(y,x) = null_class,
inference(step,[status(thm)],[t641,t631]) ).
cnf(t826,plain,
unordered_pair(y,x) = null_class,
inference(orient,[status(thm)],[t863]) ).
cnf(t832,plain,
true = ifeq(member(y,universal_class),true,member(y,null_class),true),
inference(cp,[status(thm)],[t150,t826]) ).
cnf(f94,axiom,
( member(V,universal_class)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f94_nnf,plain,
! [U,V,X,Y] :
( member(V,universal_class)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f94]) ).
fof(f94_sk,plain,
! [U,V,X,Y] :
( member(V,universal_class)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(skolemisation,[status(esa)],[f94_nnf]) ).
cnf(c94,plain,
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t90,plain,
ifeq(member(ordered_pair(X1,X2),cross_product(X3,X4)),true,member(X2,universal_class),true) = true,
inference(equality_encoding,[status(esa)],[c94]) ).
cnf(t168,plain,
ifeq(member(ordered_pair(X1,X2),cross_product(X3,X4)),true,member(X2,universal_class),true) = true,
inference(orient,[status(thm)],[t90]) ).
cnf(f115,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
fof(f115_nnf,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(nnf_transformation,[status(thm)],[f115]) ).
cnf(c115,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(cnf_transformation,[status(esa)],[f115_nnf]) ).
cnf(t40,plain,
member(ordered_pair(x,y),cross_product(u,v)) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(t222,plain,
member(ordered_pair(x,y),cross_product(u,v)) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t232,plain,
true = ifeq(true,true,member(y,universal_class),true),
inference(cp,[status(thm)],[t168,t222]) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t131,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(t860,plain,
true = member(y,universal_class),
inference(step,[status(thm)],[t232,t131]) ).
cnf(t770,plain,
member(y,universal_class) = true,
inference(orient,[status(thm)],[t860]) ).
cnf(t864,plain,
true = ifeq(true,true,member(y,null_class),true),
inference(step,[status(thm)],[t832,t770]) ).
cnf(t865,plain,
true = member(y,null_class),
inference(step,[status(thm)],[t864,t131]) ).
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(t5,plain,
member(X1,null_class) = false,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t476,plain,
member(X1,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t866,plain,
true = false,
inference(step,[status(thm)],[t865,t476]) ).
cnf(t838,plain,
false = true,
inference(orient,[status(thm)],[t866]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t838]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET075-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.29 % Computer : n012.cluster.edu
% 0.06/0.29 % Model : x86_64 x86_64
% 0.06/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.29 % Memory : 8046.5625MB
% 0.06/0.29 % OS : Linux 6.8.0-71-generic
% 0.06/0.29 % CPULimit : 300
% 0.06/0.29 % WCLimit : 300
% 0.06/0.29 % DateTime : Thu Sep 24 09:36:36 UTC 2026
% 0.06/0.30 % CPUTime :
% 0.06/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.83/1.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.83/1.62 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------