%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET242-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 02:42:58 PM UTC 2026
% Result : Unsatisfiable 9.46s 2.18s
% Output : Proof 9.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 25 unt; 0 def)
% Number of atoms : 53 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 30 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 46 ( 0 sgn 20 !; 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(hi22,axiom,
ifeq(member(X0,X1),true,ifeq(member(X0,X2),true,member(X0,intersection(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(f112,negated_conjecture,
member(z,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_alternate_defn5_1) ).
fof(f112_nnf,plain,
member(z,xr),
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
member(z,xr),
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(hi102,negated_conjecture,
member(z,xr) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(f113,negated_conjecture,
member(z,cross_product(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_alternate_defn5_2) ).
fof(f113_nnf,plain,
member(z,cross_product(x,y)),
inference(nnf_transformation,[status(thm)],[f113]) ).
cnf(c113,plain,
member(z,cross_product(x,y)),
inference(cnf_transformation,[status(esa)],[f113_nnf]) ).
cnf(hi103,negated_conjecture,
member(z,cross_product(x,y)) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h148,plain,
member(z,intersection(xr,cross_product(x,y))) = true,
inference(hyper_resolution,[status(thm)],[hi22,hi102,hi103]) ).
cnf(f114,negated_conjecture,
~ member(z,restrict(xr,x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_alternate_defn5_3) ).
fof(f114_nnf,plain,
~ member(z,restrict(xr,x,y)),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
~ member(z,restrict(xr,x,y)),
inference(skolemisation,[status(esa)],[f114_nnf]) ).
cnf(c114,plain,
~ member(z,restrict(xr,x,y)),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(hi106,negated_conjecture,
ifeq(member(z,restrict(xr,x,y)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
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(hi25,axiom,
intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi106,h148,hi25]) ).
cnf(t280,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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,c114]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t280]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET242-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.77 % Computer : n026.cluster.edu
% 0.10/0.77 % Model : x86_64 x86_64
% 0.10/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.77 % Memory : 8046.5625MB
% 0.10/0.77 % OS : Linux 6.8.0-71-generic
% 0.10/0.77 % CPULimit : 300
% 0.10/0.77 % WCLimit : 300
% 0.10/0.77 % DateTime : Thu Sep 24 10:24:10 UTC 2026
% 0.10/0.78 % CPUTime :
% 0.10/0.78 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.46/2.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.46/2.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------