%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET662+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 03:32:29 PM UTC 2025
% Result : Theorem 248.86s 31.60s
% Output : CNFRefutation 248.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 21 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 46 ~; 40 |; 3 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 1 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relset_1_25,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_25) ).
fof(prove_relset_1_25_negated,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_25]) ).
cnf(38,plain,
ilf_type(sK12,set_type),
inference(cnf,[status(esa)],[prove_relset_1_25_negated]) ).
cnf(l0,plain,
ilf_type(sK12,set_type),
inference(instantiation,[status(thm)],[38]) ).
fof(p2,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
cnf(1,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf,[status(esa)],[p2]) ).
cnf(l1,plain,
( ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(empty_set,subset_type(cross_product(sK12,sK13)))
| ilf_type(empty_set,relation_type(sK12,sK13)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(39,plain,
ilf_type(sK13,set_type),
inference(cnf,[status(esa)],[prove_relset_1_25_negated]) ).
cnf(l156,plain,
ilf_type(sK13,set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(40,plain,
~ ilf_type(empty_set,relation_type(sK12,sK13)),
inference(cnf,[status(esa)],[prove_relset_1_25_negated]) ).
cnf(l3,plain,
~ ilf_type(empty_set,relation_type(sK12,sK13)),
inference(instantiation,[status(thm)],[40]) ).
fof(p7,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
cnf(9,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(cnf,[status(esa)],[p7]) ).
cnf(l2,plain,
( ~ ilf_type(cross_product(sK12,sK13),set_type)
| ~ ilf_type(empty_set,set_type)
| ~ ilf_type(empty_set,member_type(power_set(cross_product(sK12,sK13))))
| ilf_type(empty_set,subset_type(cross_product(sK12,sK13))) ),
inference(instantiation,[status(thm)],[9]) ).
fof(p20,plain,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
cnf(37,plain,
ilf_type(X0,set_type),
inference(cnf,[status(esa)],[p20]) ).
cnf(l4,plain,
ilf_type(cross_product(sK12,sK13),set_type),
inference(instantiation,[status(thm)],[37]) ).
cnf(l88,plain,
ilf_type(empty_set,set_type),
inference(instantiation,[status(thm)],[37]) ).
fof(p14,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
cnf(26,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| empty(X1)
| ilf_type(X0,member_type(X1)) ),
inference(cnf,[status(esa)],[p14]) ).
cnf(l10,plain,
( ~ ilf_type(empty_set,set_type)
| ~ ilf_type(power_set(cross_product(sK12,sK13)),set_type)
| ~ member(empty_set,power_set(cross_product(sK12,sK13)))
| empty(power_set(cross_product(sK12,sK13)))
| ilf_type(empty_set,member_type(power_set(cross_product(sK12,sK13)))) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l14,plain,
ilf_type(empty_set,set_type),
inference(instantiation,[status(thm)],[37]) ).
cnf(l12,plain,
ilf_type(power_set(cross_product(sK12,sK13)),set_type),
inference(instantiation,[status(thm)],[37]) ).
fof(p13,plain,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
cnf(23,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf,[status(esa)],[p13]) ).
cnf(l91,plain,
( ~ empty(power_set(cross_product(sK12,sK13)))
| ~ ilf_type(cross_product(sK12,sK13),set_type) ),
inference(instantiation,[status(thm)],[23]) ).
fof(p6,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
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)],[p6]) ).
cnf(l100,plain,
( ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK13,set_type)
| ilf_type(cross_product(sK12,sK13),set_type) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l400,plain,
ilf_type(sK13,set_type),
inference(instantiation,[status(thm)],[39]) ).
fof(p12,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
cnf(21,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| member(sK5(X0,X1),X0) ),
inference(cnf,[status(esa)],[p12]) ).
cnf(l39,plain,
( ~ ilf_type(empty_set,set_type)
| ~ ilf_type(cross_product(sK12,sK13),set_type)
| member(empty_set,power_set(cross_product(sK12,sK13)))
| member(sK5(empty_set,cross_product(sK12,sK13)),empty_set) ),
inference(instantiation,[status(thm)],[21]) ).
fof(p11,plain,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
cnf(16,plain,
( ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ),
inference(cnf,[status(esa)],[p11]) ).
cnf(l61,plain,
( ~ empty(empty_set)
| ~ ilf_type(empty_set,set_type)
| ~ ilf_type(sK5(empty_set,cross_product(sK12,sK13)),set_type)
| ~ member(sK5(empty_set,cross_product(sK12,sK13)),empty_set) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(l49,plain,
( ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK13,set_type)
| ilf_type(cross_product(sK12,sK13),set_type) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l84,plain,
ilf_type(sK13,set_type),
inference(instantiation,[status(thm)],[37]) ).
cnf(l48,plain,
ilf_type(empty_set,set_type),
inference(instantiation,[status(thm)],[37]) ).
cnf(l64,plain,
ilf_type(sK5(empty_set,cross_product(sK12,sK13)),set_type),
inference(instantiation,[status(thm)],[37]) ).
cnf(l389,plain,
ilf_type(empty_set,set_type),
inference(instantiation,[status(thm)],[37]) ).
fof(p5a,plain,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5a) ).
cnf(5,plain,
empty(empty_set),
inference(cnf,[status(esa)],[p5a]) ).
cnf(l62,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[5]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l156,l3,l2,l4,l88,l10,l14,l12,l91,l100,l400,l39,l61,l49,l84,l48,l64,l389,l62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET662+3 : TPTP v9.0.0. Released v2.2.0.
% 0.02/0.09 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.29 % Computer : n018.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Jul 21 22:14:49 EDT 2025
% 0.08/0.29 % CPUTime :
% 0.08/0.29 % launching worker at depth: 3
% 0.08/0.29 % launching worker at depth: 2
% 0.08/0.29 % launching worker at depth: 1
% 0.08/0.29 % launching worker at depth: 4
% 0.08/0.29 % launching worker at depth: 5
% 0.08/0.29 % launching worker at depth: 6
% 0.08/0.29 % launching worker at depth: 7
% 0.08/0.29 % launching worker at depth: 8
% 0.08/0.29 % launching worker at depth: 9
% 0.14/0.31 % launching worker at depth: 10
% 0.14/0.52 % launching worker at depth: 11
% 34.19/4.59 % launching worker at depth: 12
% 248.86/31.60 % SZS status Theorem for theBenchmark
% 248.86/31.60 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------