%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET166-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 02:42:40 PM UTC 2026
% Result : Unsatisfiable 68.93s 9.11s
% Output : Proof 68.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 91 ( 71 unt; 0 def)
% Number of atoms : 123 ( 59 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 46 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 94 ( 5 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f22,axiom,
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f22_nnf,plain,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t167,plain,
ifeq(member(X1,X2),true,ifeq(member(X1,X3),true,member(X1,intersection(X2,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t1973,plain,
ifeq(member(X1,X2),true,ifeq(member(X1,X3),true,member(X1,intersection(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t167]) ).
cnf(t53,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t3291,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t53]) ).
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(t131,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t1922,plain,
or(not(member(X1,complement(X2))),not(member(X1,X2))) = true,
inference(orient,[status(thm)],[t131]) ).
cnf(f112,negated_conjecture,
member(x,union(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_members_of_union1_1) ).
fof(f112_nnf,plain,
member(x,union(y,z)),
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
member(x,union(y,z)),
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(u35,axiom,
member(x,union(y,z)) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(f25,axiom,
complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f25_nnf,plain,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(d2,axiom,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t113,plain,
member(x,complement(intersection(complement(y),complement(z)))) = true,
inference(definition_unfolding,[status(thm)],[u35,d2]) ).
cnf(t1602,plain,
member(x,complement(intersection(complement(y),complement(z)))) = true,
inference(orient,[status(thm)],[t113]) ).
cnf(t1923,plain,
true = or(not(true),not(member(x,intersection(complement(y),complement(z))))),
inference(cp,[status(thm)],[t1922,t1602]) ).
cnf(t4,plain,
not(true) = false,
introduced(definition) ).
cnf(t3292,plain,
not(true) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t6977,plain,
true = or(false,not(member(x,intersection(complement(y),complement(z))))),
inference(step,[status(thm)],[t1923,t3292]) ).
cnf(t12,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t239,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t6978,plain,
true = not(member(x,intersection(complement(y),complement(z)))),
inference(step,[status(thm)],[t6977,t239]) ).
cnf(t6594,plain,
not(member(x,intersection(complement(y),complement(z)))) = true,
inference(orient,[status(thm)],[t6978]) ).
cnf(t6595,plain,
false = ifeq(true,true,member(x,intersection(complement(y),complement(z))),false),
inference(cp,[status(thm)],[t3291,t6594]) ).
cnf(t25,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t240,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t25]) ).
cnf(t6979,plain,
false = member(x,intersection(complement(y),complement(z))),
inference(step,[status(thm)],[t6595,t240]) ).
cnf(t6596,plain,
member(x,intersection(complement(y),complement(z))) = false,
inference(orient,[status(thm)],[t6979]) ).
cnf(t6606,plain,
true = ifeq(member(x,complement(y)),true,ifeq(member(x,complement(z)),true,false,true),true),
inference(cp,[status(thm)],[t1973,t6596]) ).
cnf(f0,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f0_nnf,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(subclass(X0,X1),true,ifeq(member(X2,X0),true,member(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f3,axiom,
subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f3_nnf,plain,
! [X] : subclass(X,universal_class),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : subclass(X,universal_class),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
subclass(X0,universal_class) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(hi102,negated_conjecture,
member(x,union(y,z)) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(hi36,axiom,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h88,plain,
member(x,universal_class) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi102,hi36]) ).
cnf(f24,axiom,
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f24_nnf,plain,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi23,axiom,
ifeq(member(X0,universal_class),true,or(member(X0,complement(X1)),member(X0,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t117,plain,
or(member(x,complement(X1)),member(x,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi23,h88]) ).
cnf(t1746,plain,
or(member(x,complement(X1)),member(x,X1)) = true,
inference(orient,[status(thm)],[t117]) ).
cnf(f113,negated_conjecture,
~ member(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_members_of_union1_2) ).
fof(f113_nnf,plain,
~ member(x,y),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
~ member(x,y),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
~ member(x,y),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(t8,plain,
member(x,y) = false,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t3218,plain,
member(x,y) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t3224,plain,
true = or(member(x,complement(y)),false),
inference(cp,[status(thm)],[t1746,t3218]) ).
cnf(t10,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t238,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t6764,plain,
true = member(x,complement(y)),
inference(step,[status(thm)],[t3224,t238]) ).
cnf(t3389,plain,
member(x,complement(y)) = true,
inference(orient,[status(thm)],[t6764]) ).
cnf(t6980,plain,
true = ifeq(true,true,ifeq(member(x,complement(z)),true,false,true),true),
inference(step,[status(thm)],[t6606,t3389]) ).
cnf(t6981,plain,
true = ifeq(member(x,complement(z)),true,false,true),
inference(step,[status(thm)],[t6980,t240]) ).
cnf(f114,negated_conjecture,
~ member(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_members_of_union1_3) ).
fof(f114_nnf,plain,
~ member(x,z),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
~ member(x,z),
inference(skolemisation,[status(esa)],[f114_nnf]) ).
cnf(c114,plain,
~ member(x,z),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(t9,plain,
member(x,z) = false,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(t3235,plain,
member(x,z) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t3241,plain,
true = or(member(x,complement(z)),false),
inference(cp,[status(thm)],[t1746,t3235]) ).
cnf(t6765,plain,
true = member(x,complement(z)),
inference(step,[status(thm)],[t3241,t238]) ).
cnf(t3405,plain,
member(x,complement(z)) = true,
inference(orient,[status(thm)],[t6765]) ).
cnf(t6982,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t6981,t3405]) ).
cnf(t6983,plain,
true = false,
inference(step,[status(thm)],[t6982,t240]) ).
cnf(t6613,plain,
false = true,
inference(orient,[status(thm)],[t6983]) ).
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,c114]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6613]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET166-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 10:06:17 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 68.93/9.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.93/9.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------