%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET641+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 : n017.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 244.85s 30.97s
% Output : CNFRefutation 244.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 28 unt; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 182 ( 73 ~; 72 |; 3 &)
% ( 5 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relset_1_3,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',prove_relset_1_3) ).
fof(prove_relset_1_3_negated,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)) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_3]) ).
cnf(40,plain,
ilf_type(sK16,set_type),
inference(cnf,[status(esa)],[prove_relset_1_3_negated]) ).
cnf(l0,plain,
ilf_type(sK16,set_type),
inference(instantiation,[status(thm)],[40]) ).
fof(p12,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/sandbox/benchmark/theBenchmark.p',p12) ).
cnf(26,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(cnf,[status(esa)],[p12]) ).
cnf(l1,plain,
( ~ member(sK16,power_set(cross_product(sK17,sK18)))
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(power_set(cross_product(sK17,sK18)),set_type)
| ilf_type(sK16,member_type(power_set(cross_product(sK17,sK18))))
| empty(power_set(cross_product(sK17,sK18))) ),
inference(instantiation,[status(thm)],[26]) ).
fof(p10,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/sandbox/benchmark/theBenchmark.p',p10) ).
cnf(21,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| member(sK8(X0,X1),X0) ),
inference(cnf,[status(esa)],[p10]) ).
cnf(l134,plain,
( ~ ilf_type(sK16,set_type)
| ~ ilf_type(cross_product(sK17,sK18),set_type)
| member(sK16,power_set(cross_product(sK17,sK18)))
| member(sK8(sK16,cross_product(sK17,sK18)),sK16) ),
inference(instantiation,[status(thm)],[21]) ).
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/sandbox/benchmark/theBenchmark.p',p7) ).
cnf(16,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(l75,plain,
( ~ ilf_type(cross_product(sK17,sK18),set_type)
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(sK16,member_type(power_set(cross_product(sK17,sK18))))
| ilf_type(sK16,subset_type(cross_product(sK17,sK18))) ),
inference(instantiation,[status(thm)],[16]) ).
fof(p4,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',p4) ).
cnf(9,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(cross_product(X0,X1),set_type) ),
inference(cnf,[status(esa)],[p4]) ).
cnf(l76,plain,
( ~ ilf_type(sK17,set_type)
| ~ ilf_type(sK18,set_type)
| ilf_type(cross_product(sK17,sK18),set_type) ),
inference(instantiation,[status(thm)],[9]) ).
fof(p1,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/sandbox/benchmark/theBenchmark.p',p1) ).
cnf(0,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)],[p1]) ).
cnf(l603,plain,
( ~ ilf_type(sK17,set_type)
| ~ ilf_type(sK18,set_type)
| ~ ilf_type(sK16,subset_type(cross_product(sK17,sK18)))
| ilf_type(sK16,relation_type(sK17,sK18)) ),
inference(instantiation,[status(thm)],[0]) ).
fof(p18,plain,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
cnf(39,plain,
ilf_type(X0,set_type),
inference(cnf,[status(esa)],[p18]) ).
cnf(l84,plain,
ilf_type(sK18,set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l142,plain,
( ~ ilf_type(sK17,set_type)
| ~ ilf_type(sK18,set_type)
| ilf_type(cross_product(sK17,sK18),set_type) ),
inference(instantiation,[status(thm)],[9]) ).
fof(p5,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
cnf(10,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[p5]) ).
cnf(l138,plain,
( ~ member(sK8(sK16,cross_product(sK17,sK18)),sK16)
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(cross_product(sK17,sK18),set_type)
| ~ ilf_type(sK8(sK16,cross_product(sK17,sK18)),set_type)
| ~ subset(sK16,cross_product(sK17,sK18))
| member(sK8(sK16,cross_product(sK17,sK18)),cross_product(sK17,sK18)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l608,plain,
ilf_type(sK17,set_type),
inference(instantiation,[status(thm)],[39]) ).
fof(p14,plain,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
cnf(28,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ empty(X1) ),
inference(cnf,[status(esa)],[p14]) ).
cnf(l202,plain,
( ~ member(cross_product(sK17,sK18),power_set(cross_product(sK17,sK18)))
| ~ ilf_type(power_set(cross_product(sK17,sK18)),set_type)
| ~ ilf_type(cross_product(sK17,sK18),set_type)
| ~ empty(power_set(cross_product(sK17,sK18))) ),
inference(instantiation,[status(thm)],[28]) ).
fof(p11,plain,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
cnf(24,plain,
( ~ ilf_type(X0,set_type)
| ilf_type(power_set(X0),set_type) ),
inference(cnf,[status(esa)],[p11]) ).
cnf(l69,plain,
( ~ ilf_type(cross_product(sK17,sK18),set_type)
| ilf_type(power_set(cross_product(sK17,sK18)),set_type) ),
inference(instantiation,[status(thm)],[24]) ).
cnf(20,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| ilf_type(sK8(X0,X1),set_type) ),
inference(cnf,[status(esa)],[p10]) ).
cnf(l140,plain,
( ~ ilf_type(sK16,set_type)
| ~ ilf_type(cross_product(sK17,sK18),set_type)
| member(sK16,power_set(cross_product(sK17,sK18)))
| ilf_type(sK8(sK16,cross_product(sK17,sK18)),set_type) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(44,plain,
~ ilf_type(sK16,relation_type(sK17,sK18)),
inference(cnf,[status(esa)],[prove_relset_1_3_negated]) ).
cnf(l834,plain,
~ ilf_type(sK16,relation_type(sK17,sK18)),
inference(instantiation,[status(thm)],[44]) ).
cnf(43,plain,
subset(sK16,cross_product(sK17,sK18)),
inference(cnf,[status(esa)],[prove_relset_1_3_negated]) ).
cnf(l948,plain,
subset(sK16,cross_product(sK17,sK18)),
inference(instantiation,[status(thm)],[43]) ).
cnf(l70,plain,
ilf_type(cross_product(sK17,sK18),set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l731,plain,
ilf_type(cross_product(sK17,sK18),set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l863,plain,
ilf_type(cross_product(sK17,sK18),set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l203,plain,
ilf_type(power_set(cross_product(sK17,sK18)),set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(22,plain,
( ~ member(sK8(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(cnf,[status(esa)],[p10]) ).
cnf(l898,plain,
( ~ member(sK8(sK16,cross_product(sK17,sK18)),cross_product(sK17,sK18))
| ~ ilf_type(sK16,set_type)
| ~ ilf_type(cross_product(sK17,sK18),set_type)
| member(sK16,power_set(cross_product(sK17,sK18))) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(42,plain,
ilf_type(sK18,set_type),
inference(cnf,[status(esa)],[prove_relset_1_3_negated]) ).
cnf(l210,plain,
ilf_type(sK18,set_type),
inference(instantiation,[status(thm)],[42]) ).
cnf(l94,plain,
ilf_type(sK17,set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l550,plain,
( ~ ilf_type(cross_product(sK17,sK18),set_type)
| ~ ilf_type(cross_product(sK17,sK18),set_type)
| member(cross_product(sK17,sK18),power_set(cross_product(sK17,sK18)))
| member(sK8(cross_product(sK17,sK18),cross_product(sK17,sK18)),cross_product(sK17,sK18)) ),
inference(instantiation,[status(thm)],[21]) ).
cnf(l208,plain,
( ~ ilf_type(sK17,set_type)
| ~ ilf_type(sK18,set_type)
| ilf_type(cross_product(sK17,sK18),set_type) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l554,plain,
( ~ ilf_type(sK17,set_type)
| ~ ilf_type(sK18,set_type)
| ilf_type(cross_product(sK17,sK18),set_type) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l990,plain,
ilf_type(cross_product(sK17,sK18),set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l565,plain,
ilf_type(cross_product(sK17,sK18),set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l551,plain,
( ~ member(sK8(cross_product(sK17,sK18),cross_product(sK17,sK18)),cross_product(sK17,sK18))
| ~ ilf_type(cross_product(sK17,sK18),set_type)
| ~ ilf_type(cross_product(sK17,sK18),set_type)
| member(cross_product(sK17,sK18),power_set(cross_product(sK17,sK18))) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(l217,plain,
ilf_type(sK17,set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l212,plain,
ilf_type(sK18,set_type),
inference(instantiation,[status(thm)],[42]) ).
cnf(l214,plain,
ilf_type(sK17,set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l606,plain,
ilf_type(sK18,set_type),
inference(instantiation,[status(thm)],[42]) ).
cnf(l569,plain,
ilf_type(sK17,set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l568,plain,
ilf_type(sK18,set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l553,plain,
ilf_type(cross_product(sK17,sK18),set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(l699,plain,
ilf_type(cross_product(sK17,sK18),set_type),
inference(instantiation,[status(thm)],[39]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l134,l75,l76,l603,l84,l142,l138,l608,l202,l69,l140,l834,l948,l70,l731,l863,l203,l898,l210,l94,l550,l208,l554,l990,l565,l551,l217,l212,l214,l606,l569,l568,l553,l699]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07 % Problem : SET641+3 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.08 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.26 % Computer : n017.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Jul 21 22:11:04 EDT 2025
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % launching worker at depth: 5
% 0.07/0.27 % launching worker at depth: 6
% 0.07/0.27 % launching worker at depth: 2
% 0.07/0.27 % launching worker at depth: 1
% 0.07/0.27 % launching worker at depth: 4
% 0.07/0.27 % launching worker at depth: 3
% 0.07/0.27 % launching worker at depth: 7
% 0.07/0.27 % launching worker at depth: 8
% 0.07/0.27 % launching worker at depth: 9
% 0.07/0.28 % launching worker at depth: 10
% 0.11/0.49 % launching worker at depth: 11
% 23.86/3.29 % launching worker at depth: 12
% 244.85/30.97 % SZS status Theorem for theBenchmark
% 244.85/30.97 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------