%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET153-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 02:42:37 PM UTC 2026
% Result : Unsatisfiable 0.95s 1.17s
% Output : Proof 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 119 ( 99 unt; 0 def)
% Number of atoms : 139 ( 106 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 51 ( 31 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-4 aty)
% Number of variables : 107 ( 16 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t111,axiom,
sF3 = ifeq(intersection(complement(x),x),null_class,false,true),
introduced(definition) ).
cnf(t108,axiom,
sF0 = complement(x),
introduced(definition) ).
cnf(t116,plain,
complement(x) = sF0,
inference(orient,[status(thm)],[t108]) ).
cnf(t585,plain,
sF3 = ifeq(intersection(sF0,x),null_class,false,true),
inference(step,[status(thm)],[t111,t116]) ).
cnf(t109,axiom,
sF1 = intersection(complement(x),x),
introduced(definition) ).
cnf(t565,plain,
sF1 = intersection(sF0,x),
inference(step,[status(thm)],[t109,t116]) ).
cnf(t124,plain,
intersection(sF0,x) = sF1,
inference(orient,[status(thm)],[t565]) ).
cnf(t586,plain,
sF3 = ifeq(sF1,null_class,false,true),
inference(step,[status(thm)],[t585,t124]) ).
cnf(t110,axiom,
sF2 = eq(intersection(complement(x),x),null_class),
introduced(definition) ).
cnf(t568,plain,
sF2 = eq(intersection(sF0,x),null_class),
inference(step,[status(thm)],[t110,t116]) ).
cnf(t569,plain,
sF2 = eq(sF1,null_class),
inference(step,[status(thm)],[t568,t124]) ).
cnf(f112,negated_conjecture,
intersection(complement(x),x) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_with_complement_1) ).
fof(f112_nnf,plain,
intersection(complement(x),x) != null_class,
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
intersection(complement(x),x) != null_class,
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
intersection(complement(x),x) != null_class,
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(t16,plain,
eq(intersection(complement(x),x),null_class) = false,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t566,plain,
eq(intersection(sF0,x),null_class) = false,
inference(step,[status(thm)],[t16,t116]) ).
cnf(t567,plain,
eq(sF1,null_class) = false,
inference(step,[status(thm)],[t566,t124]) ).
cnf(t130,plain,
eq(sF1,null_class) = false,
inference(orient,[status(thm)],[t567]) ).
cnf(t570,plain,
sF2 = false,
inference(step,[status(thm)],[t569,t130]) ).
cnf(t135,plain,
false = sF2,
inference(orient,[status(thm)],[t570]) ).
cnf(t587,plain,
sF3 = ifeq(sF1,null_class,sF2,true),
inference(step,[status(thm)],[t586,t135]) ).
cnf(t31,plain,
ifeq(intersection(complement(x),x),null_class,false,true) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t581,plain,
ifeq(intersection(sF0,x),null_class,false,true) = true,
inference(step,[status(thm)],[t31,t116]) ).
cnf(t582,plain,
ifeq(sF1,null_class,false,true) = true,
inference(step,[status(thm)],[t581,t124]) ).
cnf(t583,plain,
ifeq(sF1,null_class,sF2,true) = true,
inference(step,[status(thm)],[t582,t135]) ).
cnf(t198,plain,
ifeq(sF1,null_class,sF2,true) = true,
inference(orient,[status(thm)],[t583]) ).
cnf(t588,plain,
sF3 = true,
inference(step,[status(thm)],[t587,t198]) ).
cnf(t208,plain,
true = sF3,
inference(orient,[status(thm)],[t588]) ).
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(t47,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t702,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X3),true) = true,
inference(step,[status(thm)],[t47,t208]) ).
cnf(t703,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X3),sF3) = true,
inference(step,[status(thm)],[t702,t208]) ).
cnf(t704,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X3),sF3) = sF3,
inference(step,[status(thm)],[t703,t208]) ).
cnf(t424,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X3),sF3) = sF3,
inference(orient,[status(thm)],[t704]) ).
cnf(t426,plain,
sF3 = ifeq(member(X1,sF1),sF3,member(X1,x),sF3),
inference(cp,[status(thm)],[t424,t124]) ).
cnf(t444,plain,
ifeq(member(X1,sF1),sF3,member(X1,x),sF3) = sF3,
inference(orient,[status(thm)],[t426]) ).
cnf(f65,axiom,
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f65_nnf,plain,
! [X] :
( member(regular(X),X)
| X = null_class ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [X] :
( member(regular(X),X)
| X = null_class ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(t32,plain,
or(eq(X1,null_class),member(regular(X1),X1)) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t199,plain,
or(eq(X1,null_class),member(regular(X1),X1)) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t576,plain,
eq(sF1,null_class) = sF2,
inference(step,[status(thm)],[t130,t135]) ).
cnf(t141,plain,
eq(sF1,null_class) = sF2,
inference(orient,[status(thm)],[t576]) ).
cnf(t200,plain,
true = or(sF2,member(regular(sF1),sF1)),
inference(cp,[status(thm)],[t199,t141]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t121,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t575,plain,
or(sF2,X1) = X1,
inference(step,[status(thm)],[t121,t135]) ).
cnf(t140,plain,
or(sF2,X1) = X1,
inference(rw,[status(thm)],[t575]) ).
cnf(t147,plain,
or(sF2,X1) = X1,
inference(orient,[status(thm)],[t140]) ).
cnf(t584,plain,
true = member(regular(sF1),sF1),
inference(step,[status(thm)],[t200,t147]) ).
cnf(t201,plain,
member(regular(sF1),sF1) = true,
inference(orient,[status(thm)],[t584]) ).
cnf(t629,plain,
member(regular(sF1),sF1) = sF3,
inference(step,[status(thm)],[t201,t208]) ).
cnf(t268,plain,
member(regular(sF1),sF1) = sF3,
inference(orient,[status(thm)],[t629]) ).
cnf(t445,plain,
sF3 = ifeq(sF3,sF3,member(regular(sF1),x),sF3),
inference(cp,[status(thm)],[t444,t268]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t125,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t705,plain,
sF3 = member(regular(sF1),x),
inference(step,[status(thm)],[t445,t125]) ).
cnf(t17,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t131,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t17]) ).
cnf(t143,plain,
ifeq(not(X1),true,X1,sF2) = false,
inference(rw,[status(thm)],[t131]) ).
cnf(t579,plain,
ifeq(not(X1),true,X1,sF2) = sF2,
inference(step,[status(thm)],[t143,t135]) ).
cnf(t149,plain,
ifeq(not(X1),true,X1,sF2) = sF2,
inference(orient,[status(thm)],[t579]) ).
cnf(t614,plain,
ifeq(not(X1),sF3,X1,sF2) = sF2,
inference(step,[status(thm)],[t149,t208]) ).
cnf(t235,plain,
ifeq(not(X1),sF3,X1,sF2) = sF2,
inference(rw,[status(thm)],[t614]) ).
cnf(t284,plain,
ifeq(not(X1),sF3,X1,sF2) = sF2,
inference(orient,[status(thm)],[t235]) ).
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(t44,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t676,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF3,
inference(step,[status(thm)],[t44,t208]) ).
cnf(t360,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = sF3,
inference(orient,[status(thm)],[t676]) ).
cnf(t361,plain,
sF3 = or(not(member(X1,sF0)),not(member(X1,x))),
inference(cp,[status(thm)],[t360,t116]) ).
cnf(t387,plain,
or(not(member(X1,sF0)),not(member(X1,x))) = sF3,
inference(orient,[status(thm)],[t361]) ).
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(t46,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t692,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X2),true) = true,
inference(step,[status(thm)],[t46,t208]) ).
cnf(t693,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X2),sF3) = true,
inference(step,[status(thm)],[t692,t208]) ).
cnf(t694,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X2),sF3) = sF3,
inference(step,[status(thm)],[t693,t208]) ).
cnf(t392,plain,
ifeq(member(X1,intersection(X2,X3)),sF3,member(X1,X2),sF3) = sF3,
inference(orient,[status(thm)],[t694]) ).
cnf(t394,plain,
sF3 = ifeq(member(X1,sF1),sF3,member(X1,sF0),sF3),
inference(cp,[status(thm)],[t392,t124]) ).
cnf(t407,plain,
ifeq(member(X1,sF1),sF3,member(X1,sF0),sF3) = sF3,
inference(orient,[status(thm)],[t394]) ).
cnf(t408,plain,
sF3 = ifeq(sF3,sF3,member(regular(sF1),sF0),sF3),
inference(cp,[status(thm)],[t407,t268]) ).
cnf(t695,plain,
sF3 = member(regular(sF1),sF0),
inference(step,[status(thm)],[t408,t125]) ).
cnf(t409,plain,
member(regular(sF1),sF0) = sF3,
inference(orient,[status(thm)],[t695]) ).
cnf(t411,plain,
sF3 = or(not(sF3),not(member(regular(sF1),x))),
inference(cp,[status(thm)],[t387,t409]) ).
cnf(t3,plain,
not(true) = false,
introduced(definition) ).
cnf(t115,plain,
not(true) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t572,plain,
not(true) = sF2,
inference(step,[status(thm)],[t115,t135]) ).
cnf(t137,plain,
not(true) = sF2,
inference(orient,[status(thm)],[t572]) ).
cnf(t593,plain,
not(sF3) = sF2,
inference(step,[status(thm)],[t137,t208]) ).
cnf(t213,plain,
not(sF3) = sF2,
inference(rw,[status(thm)],[t593]) ).
cnf(t274,plain,
not(sF3) = sF2,
inference(orient,[status(thm)],[t213]) ).
cnf(t696,plain,
sF3 = or(sF2,not(member(regular(sF1),x))),
inference(step,[status(thm)],[t411,t274]) ).
cnf(t697,plain,
sF3 = not(member(regular(sF1),x)),
inference(step,[status(thm)],[t696,t147]) ).
cnf(t413,plain,
not(member(regular(sF1),x)) = sF3,
inference(orient,[status(thm)],[t697]) ).
cnf(t414,plain,
sF2 = ifeq(sF3,sF3,member(regular(sF1),x),sF2),
inference(cp,[status(thm)],[t284,t413]) ).
cnf(t698,plain,
sF2 = member(regular(sF1),x),
inference(step,[status(thm)],[t414,t125]) ).
cnf(t415,plain,
member(regular(sF1),x) = sF2,
inference(orient,[status(thm)],[t698]) ).
cnf(t706,plain,
sF3 = sF2,
inference(step,[status(thm)],[t705,t415]) ).
cnf(t446,plain,
sF3 = sF2,
inference(orient,[status(thm)],[t706]) ).
cnf(t747,plain,
true = sF2,
inference(step,[status(thm)],[t208,t446]) ).
cnf(t487,plain,
true = sF2,
inference(orient,[status(thm)],[t747]) ).
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,c112]) ).
cnf(g0_0,plain,
sF2 != false,
inference(rw,[status(thm)],[goal_0,t487]) ).
cnf(g0_1,plain,
sF2 != sF2,
inference(rw,[status(thm)],[g0_0,t135]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET153-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n006.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
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 10:02:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.95/1.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.95/1.17 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------