%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET239-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 5.57s 6.21s
% Output : Proof 5.57s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t110,axiom,
sF1 = ifeq(member(z,xr),true,false,true),
introduced(definition) ).
cnf(f113,negated_conjecture,
~ member(z,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_alternate_defn2_2) ).
fof(f113_nnf,plain,
~ member(z,xr),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
~ member(z,xr),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
~ member(z,xr),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(t6,plain,
member(z,xr) = false,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t120,plain,
member(z,xr) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t109,axiom,
sF0 = member(z,xr),
introduced(definition) ).
cnf(t480,plain,
sF0 = false,
inference(step,[status(thm)],[t109,t120]) ).
cnf(t126,plain,
false = sF0,
inference(orient,[status(thm)],[t480]) ).
cnf(t484,plain,
member(z,xr) = sF0,
inference(step,[status(thm)],[t120,t126]) ).
cnf(t130,plain,
member(z,xr) = sF0,
inference(orient,[status(thm)],[t484]) ).
cnf(t496,plain,
sF1 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t110,t130]) ).
cnf(t497,plain,
sF1 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t496,t126]) ).
cnf(t22,plain,
ifeq(member(z,xr),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t491,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t22,t130]) ).
cnf(t492,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t491,t126]) ).
cnf(t165,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t492]) ).
cnf(t498,plain,
sF1 = true,
inference(step,[status(thm)],[t497,t165]) ).
cnf(t187,plain,
true = sF1,
inference(orient,[status(thm)],[t498]) ).
cnf(f20,axiom,
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f20_nnf,plain,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t47,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t596,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X2),true) = true,
inference(step,[status(thm)],[t47,t187]) ).
cnf(t597,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X2),sF1) = true,
inference(step,[status(thm)],[t596,t187]) ).
cnf(t598,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X2),sF1) = sF1,
inference(step,[status(thm)],[t597,t187]) ).
cnf(t354,plain,
ifeq(member(X1,intersection(X2,X3)),sF1,member(X1,X2),sF1) = sF1,
inference(orient,[status(thm)],[t598]) ).
cnf(t356,plain,
sF1 = ifeq(member(z,intersection(xr,X1)),sF1,sF0,sF1),
inference(cp,[status(thm)],[t354,t130]) ).
cnf(t371,plain,
ifeq(member(z,intersection(xr,X1)),sF1,sF0,sF1) = sF1,
inference(orient,[status(thm)],[t356]) ).
cnf(f28,axiom,
intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
fof(f28_nnf,plain,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(u35,axiom,
intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f27,axiom,
intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/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(t41,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(definition_unfolding,[status(thm)],[u35,d4]) ).
cnf(t300,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(orient,[status(thm)],[t41]) ).
cnf(t111,axiom,
sF2 = cross_product(x,y),
introduced(definition) ).
cnf(t135,plain,
cross_product(x,y) = sF2,
inference(orient,[status(thm)],[t111]) ).
cnf(t301,plain,
intersection(X1,cross_product(x,y)) = intersection(sF2,X1),
inference(cp,[status(thm)],[t300,t135]) ).
cnf(t573,plain,
intersection(X1,sF2) = intersection(sF2,X1),
inference(step,[status(thm)],[t301,t135]) ).
cnf(t302,plain,
intersection(X1,sF2) = intersection(sF2,X1),
inference(orient,[status(thm)],[t573]) ).
cnf(t372,plain,
sF1 = ifeq(member(z,intersection(sF2,xr)),sF1,sF0,sF1),
inference(cp,[status(thm)],[t371,t302]) ).
cnf(t112,axiom,
sF3 = intersection(xr,cross_product(x,y)),
introduced(definition) ).
cnf(t488,plain,
sF3 = intersection(xr,sF2),
inference(step,[status(thm)],[t112,t135]) ).
cnf(t143,plain,
intersection(xr,sF2) = sF3,
inference(orient,[status(thm)],[t488]) ).
cnf(t574,plain,
intersection(sF2,xr) = sF3,
inference(step,[status(thm)],[t143,t302]) ).
cnf(t303,plain,
intersection(sF2,xr) = sF3,
inference(rw,[status(thm)],[t574]) ).
cnf(t304,plain,
intersection(sF2,xr) = sF3,
inference(orient,[status(thm)],[t303]) ).
cnf(t599,plain,
sF1 = ifeq(member(z,sF3),sF1,sF0,sF1),
inference(step,[status(thm)],[t372,t304]) ).
cnf(f112,negated_conjecture,
member(z,restrict(xr,x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_alternate_defn2_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(u38,axiom,
member(z,restrict(xr,x,y)) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t27,plain,
member(z,intersection(xr,cross_product(x,y))) = true,
inference(definition_unfolding,[status(thm)],[u38,d4]) ).
cnf(t493,plain,
member(z,intersection(xr,sF2)) = true,
inference(step,[status(thm)],[t27,t135]) ).
cnf(t494,plain,
member(z,sF3) = true,
inference(step,[status(thm)],[t493,t143]) ).
cnf(t174,plain,
member(z,sF3) = true,
inference(orient,[status(thm)],[t494]) ).
cnf(t528,plain,
member(z,sF3) = sF1,
inference(step,[status(thm)],[t174,t187]) ).
cnf(t227,plain,
member(z,sF3) = sF1,
inference(orient,[status(thm)],[t528]) ).
cnf(t600,plain,
sF1 = ifeq(sF1,sF1,sF0,sF1),
inference(step,[status(thm)],[t599,t227]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t138,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t601,plain,
sF1 = sF0,
inference(step,[status(thm)],[t600,t138]) ).
cnf(t373,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t601]) ).
cnf(t636,plain,
true = sF0,
inference(step,[status(thm)],[t187,t373]) ).
cnf(t408,plain,
true = sF0,
inference(orient,[status(thm)],[t636]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c113]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t408]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t126]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET239-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n011.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 10:21:49 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.57/6.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.57/6.21 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------