%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET643+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 03:32:27 PM UTC 2025
% Result : Theorem 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 42 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relset_1_5,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_5) ).
fof(prove_relset_1_5_negated,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_5]) ).
cnf(41,plain,
ilf_type(sK16,set_type),
inference(cnf,[status(esa)],[prove_relset_1_5_negated]) ).
cnf(l0,plain,
ilf_type(sK16,set_type),
inference(instantiation,[status(thm)],[41]) ).
fof(p1,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( subset(B,cross_product(C,D))
=> ilf_type(B,relation_type(C,D)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
cnf(0,plain,
( ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf,[status(esa)],[p1]) ).
cnf(l1,plain,
( ~ subset(cross_product(sK16,sK17),cross_product(sK16,sK17))
| ~ ilf_type(cross_product(sK16,sK17),set_type)
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| ilf_type(cross_product(sK16,sK17),relation_type(sK16,sK17)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(43,plain,
~ ilf_type(cross_product(sK16,sK17),relation_type(sK16,sK17)),
inference(cnf,[status(esa)],[prove_relset_1_5_negated]) ).
cnf(l20,plain,
~ ilf_type(cross_product(sK16,sK17),relation_type(sK16,sK17)),
inference(instantiation,[status(thm)],[43]) ).
fof(p3,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
cnf(7,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(cross_product(X0,X1),set_type) ),
inference(cnf,[status(esa)],[p3]) ).
cnf(l28,plain,
( ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK17,set_type)
| ilf_type(cross_product(sK16,sK17),set_type) ),
inference(instantiation,[status(thm)],[7]) ).
fof(p10,plain,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
cnf(19,plain,
( ~ ilf_type(X0,set_type)
| subset(X0,X0) ),
inference(cnf,[status(esa)],[p10]) ).
cnf(l5,plain,
( ~ ilf_type(cross_product(sK16,sK17),set_type)
| subset(cross_product(sK16,sK17),cross_product(sK16,sK17)) ),
inference(instantiation,[status(thm)],[19]) ).
fof(p19,plain,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
cnf(40,plain,
ilf_type(X0,set_type),
inference(cnf,[status(esa)],[p19]) ).
cnf(l34,plain,
ilf_type(sK17,set_type),
inference(instantiation,[status(thm)],[40]) ).
cnf(42,plain,
ilf_type(sK17,set_type),
inference(cnf,[status(esa)],[prove_relset_1_5_negated]) ).
cnf(l6,plain,
ilf_type(sK17,set_type),
inference(instantiation,[status(thm)],[42]) ).
cnf(l22,plain,
ilf_type(cross_product(sK16,sK17),set_type),
inference(instantiation,[status(thm)],[40]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l20,l28,l5,l34,l6,l22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET643+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 22:11:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.33 % launching worker at depth: 6
% 0.18/0.34 % launching worker at depth: 9
% 0.18/0.36 % launching worker at depth: 10
% 0.18/0.45 % SZS status Theorem for theBenchmark
% 0.18/0.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------