%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET238-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 02:42:56 PM UTC 2026
% Result : Unsatisfiable 82.74s 16.05s
% Output : Proof 82.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 46 unt; 0 def)
% Number of atoms : 78 ( 46 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 46 ( 30 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-4 aty)
% Number of variables : 90 ( 11 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f113,negated_conjecture,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_2) ).
fof(f113_nnf,plain,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(u35,axiom,
ifeq(member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
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(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(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(f27,axiom,
intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f27_nnf,plain,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(d4,axiom,
intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t192,plain,
ifeq(member(unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),unordered_pair(second(z),second(z)))),intersection(xr,cross_product(x,y))),true,false,true) = true,
inference(definition_unfolding,[status(thm)],[u35,d1,d4]) ).
cnf(f21,axiom,
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f21_nnf,plain,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(member(X0,intersection(X1,X2)),true,member(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(f112,negated_conjecture,
member(z,restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_1) ).
fof(f112_nnf,plain,
member(z,restrict(xr,x,y)),
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
member(z,restrict(xr,x,y)),
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(hi102,negated_conjecture,
member(z,restrict(xr,x,y)) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(hi25,axiom,
intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h83,plain,
member(z,cross_product(x,y)) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi102,hi25]) ).
cnf(f16,axiom,
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f16_nnf,plain,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(member(X0,cross_product(X1,X2)),true,ordered_pair(first(X0),second(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(hi12,axiom,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(hi13,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t151,plain,
unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),unordered_pair(second(z),second(z)))) = z,
inference(hyper_resolution,[status(thm)],[hi16,h83,hi12,hi13]) ).
cnf(t1510,plain,
unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),unordered_pair(second(z),second(z)))) = z,
inference(orient,[status(thm)],[t151]) ).
cnf(t2907,plain,
ifeq(member(z,intersection(xr,cross_product(x,y))),true,false,true) = true,
inference(step,[status(thm)],[t192,t1510]) ).
cnf(u40,axiom,
member(z,restrict(xr,x,y)) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t73,plain,
member(z,intersection(xr,cross_product(x,y))) = true,
inference(definition_unfolding,[status(thm)],[u40,d4]) ).
cnf(t1600,plain,
member(z,intersection(xr,cross_product(x,y))) = true,
inference(orient,[status(thm)],[t73]) ).
cnf(t2908,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t2907,t1600]) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t240,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t23]) ).
cnf(t2909,plain,
false = true,
inference(step,[status(thm)],[t2908,t240]) ).
cnf(t2896,plain,
false = true,
inference(orient,[status(thm)],[t2909]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c113]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2896]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET238-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n008.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 10:21:32 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 82.74/16.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 82.74/16.05 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------