%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET060-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 02:41:48 PM UTC 2026
% Result : Unsatisfiable 6.12s 1.52s
% Output : Proof 6.12s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t101,axiom,
sF2 = member(y,intersection(complement(x),x)),
introduced(definition) ).
cnf(t99,axiom,
sF0 = complement(x),
introduced(definition) ).
cnf(t106,plain,
complement(x) = sF0,
inference(orient,[status(thm)],[t99]) ).
cnf(t331,plain,
sF2 = member(y,intersection(sF0,x)),
inference(step,[status(thm)],[t101,t106]) ).
cnf(t100,axiom,
sF1 = intersection(complement(x),x),
introduced(definition) ).
cnf(t328,plain,
sF1 = intersection(sF0,x),
inference(step,[status(thm)],[t100,t106]) ).
cnf(t115,plain,
intersection(sF0,x) = sF1,
inference(orient,[status(thm)],[t328]) ).
cnf(t332,plain,
sF2 = member(y,sF1),
inference(step,[status(thm)],[t331,t115]) ).
cnf(f101,negated_conjecture,
member(y,intersection(complement(x),x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_special_classes_lemma_1) ).
fof(f101_nnf,plain,
member(y,intersection(complement(x),x)),
inference(nnf_transformation,[status(thm)],[f101]) ).
cnf(c101,plain,
member(y,intersection(complement(x),x)),
inference(cnf_transformation,[status(esa)],[f101_nnf]) ).
cnf(t17,plain,
member(y,intersection(complement(x),x)) = true,
inference(equality_encoding,[status(esa)],[c101]) ).
cnf(t329,plain,
member(y,intersection(sF0,x)) = true,
inference(step,[status(thm)],[t17,t106]) ).
cnf(t330,plain,
member(y,sF1) = true,
inference(step,[status(thm)],[t329,t115]) ).
cnf(t123,plain,
member(y,sF1) = true,
inference(orient,[status(thm)],[t330]) ).
cnf(t333,plain,
sF2 = true,
inference(step,[status(thm)],[t332,t123]) ).
cnf(t129,plain,
true = sF2,
inference(orient,[status(thm)],[t333]) ).
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(t40,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t425,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),true) = true,
inference(step,[status(thm)],[t40,t129]) ).
cnf(t426,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = true,
inference(step,[status(thm)],[t425,t129]) ).
cnf(t427,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = sF2,
inference(step,[status(thm)],[t426,t129]) ).
cnf(t286,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X3),sF2) = sF2,
inference(orient,[status(thm)],[t427]) ).
cnf(t288,plain,
sF2 = ifeq(member(X1,sF1),sF2,member(X1,x),sF2),
inference(cp,[status(thm)],[t286,t115]) ).
cnf(t304,plain,
ifeq(member(X1,sF1),sF2,member(X1,x),sF2) = sF2,
inference(orient,[status(thm)],[t288]) ).
cnf(t358,plain,
member(y,sF1) = sF2,
inference(step,[status(thm)],[t123,t129]) ).
cnf(t155,plain,
member(y,sF1) = sF2,
inference(orient,[status(thm)],[t358]) ).
cnf(t305,plain,
sF2 = ifeq(sF2,sF2,member(y,x),sF2),
inference(cp,[status(thm)],[t304,t155]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t116,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t428,plain,
sF2 = member(y,x),
inference(step,[status(thm)],[t305,t116]) ).
cnf(t16,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t120,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t16]) ).
cnf(t355,plain,
ifeq(not(X1),sF2,X1,false) = false,
inference(step,[status(thm)],[t120,t129]) ).
cnf(t153,plain,
ifeq(not(X1),sF2,X1,false) = false,
inference(rw,[status(thm)],[t355]) ).
cnf(t164,plain,
ifeq(not(X1),sF2,X1,false) = false,
inference(orient,[status(thm)],[t153]) ).
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(t37,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t399,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF2,
inference(step,[status(thm)],[t37,t129]) ).
cnf(t227,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF2,
inference(orient,[status(thm)],[t399]) ).
cnf(t228,plain,
sF2 = or(not(member(X1,sF0)),not(member(X1,x))),
inference(cp,[status(thm)],[t227,t106]) ).
cnf(t252,plain,
or(not(member(X1,sF0)),not(member(X1,x))) = sF2,
inference(orient,[status(thm)],[t228]) ).
cnf(f20,axiom,
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/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(t39,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t415,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X2),true) = true,
inference(step,[status(thm)],[t39,t129]) ).
cnf(t416,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X2),sF2) = true,
inference(step,[status(thm)],[t415,t129]) ).
cnf(t417,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X2),sF2) = sF2,
inference(step,[status(thm)],[t416,t129]) ).
cnf(t256,plain,
ifeq(member(X1,intersection(X2,X3)),sF2,member(X1,X2),sF2) = sF2,
inference(orient,[status(thm)],[t417]) ).
cnf(t258,plain,
sF2 = ifeq(member(X1,sF1),sF2,member(X1,sF0),sF2),
inference(cp,[status(thm)],[t256,t115]) ).
cnf(t269,plain,
ifeq(member(X1,sF1),sF2,member(X1,sF0),sF2) = sF2,
inference(orient,[status(thm)],[t258]) ).
cnf(t270,plain,
sF2 = ifeq(sF2,sF2,member(y,sF0),sF2),
inference(cp,[status(thm)],[t269,t155]) ).
cnf(t418,plain,
sF2 = member(y,sF0),
inference(step,[status(thm)],[t270,t116]) ).
cnf(t271,plain,
member(y,sF0) = sF2,
inference(orient,[status(thm)],[t418]) ).
cnf(t273,plain,
sF2 = or(not(sF2),not(member(y,x))),
inference(cp,[status(thm)],[t252,t271]) ).
cnf(t3,plain,
not(true) = false,
introduced(definition) ).
cnf(t105,plain,
not(true) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t340,plain,
not(sF2) = false,
inference(step,[status(thm)],[t105,t129]) ).
cnf(t136,plain,
not(sF2) = false,
inference(rw,[status(thm)],[t340]) ).
cnf(t159,plain,
not(sF2) = false,
inference(orient,[status(thm)],[t136]) ).
cnf(t419,plain,
sF2 = or(false,not(member(y,x))),
inference(step,[status(thm)],[t273,t159]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t111,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t420,plain,
sF2 = not(member(y,x)),
inference(step,[status(thm)],[t419,t111]) ).
cnf(t275,plain,
not(member(y,x)) = sF2,
inference(orient,[status(thm)],[t420]) ).
cnf(t276,plain,
false = ifeq(sF2,sF2,member(y,x),false),
inference(cp,[status(thm)],[t164,t275]) ).
cnf(t421,plain,
false = member(y,x),
inference(step,[status(thm)],[t276,t116]) ).
cnf(t277,plain,
member(y,x) = false,
inference(orient,[status(thm)],[t421]) ).
cnf(t429,plain,
sF2 = false,
inference(step,[status(thm)],[t428,t277]) ).
cnf(t306,plain,
false = sF2,
inference(orient,[status(thm)],[t429]) ).
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]) ).
cnf(g0_0,plain,
sF2 != false,
inference(rw,[status(thm)],[goal_0,t129]) ).
cnf(g0_1,plain,
sF2 != sF2,
inference(rw,[status(thm)],[g0_0,t306]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET060-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.58 % Computer : n007.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Thu Sep 24 09:27:24 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.59 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.12/1.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.12/1.52 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------