%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET679+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 : 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 03:32:30 PM UTC 2025
% Result : Theorem 34.14s 4.62s
% Output : CNFRefutation 34.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 18 unt; 0 def)
% Number of atoms : 72 ( 3 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 70 ( 31 ~; 26 |; 2 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relset_1_46,plain,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> not_equal(identity_relation_of(B),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_46) ).
fof(prove_relset_1_46_negated,plain,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> not_equal(identity_relation_of(B),empty_set) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_46]) ).
cnf(47,plain,
~ empty(sK12),
inference(cnf,[status(esa)],[prove_relset_1_46_negated]) ).
cnf(l0,plain,
~ empty(sK12),
inference(instantiation,[status(thm)],[47]) ).
fof(p8,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',p8) ).
cnf(19,plain,
( ~ ilf_type(X0,set_type)
| ilf_type(sK2(X0),set_type)
| empty(X0) ),
inference(cnf,[status(esa)],[p8]) ).
cnf(l1,plain,
( ~ ilf_type(sK12,set_type)
| ilf_type(sK2(sK12),set_type)
| empty(sK12) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(48,plain,
ilf_type(sK12,set_type),
inference(cnf,[status(esa)],[prove_relset_1_46_negated]) ).
cnf(l2,plain,
ilf_type(sK12,set_type),
inference(instantiation,[status(thm)],[48]) ).
fof(p1,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
cnf(0,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
inference(cnf,[status(esa)],[p1]) ).
cnf(l5,plain,
( ~ member(sK2(sK12),sK12)
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK2(sK12),set_type)
| member(ordered_pair(sK2(sK12),sK2(sK12)),identity_relation_of(sK12)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(20,plain,
( ~ ilf_type(X0,set_type)
| member(sK2(X0),X0)
| empty(X0) ),
inference(cnf,[status(esa)],[p8]) ).
cnf(l25,plain,
( ~ ilf_type(sK12,set_type)
| member(sK2(sK12),sK12)
| empty(sK12) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(l19,plain,
ilf_type(sK12,set_type),
inference(instantiation,[status(thm)],[48]) ).
cnf(l26,plain,
ilf_type(sK12,set_type),
inference(instantiation,[status(thm)],[48]) ).
fof(p7,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( not_equal(B,C)
<=> B != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
cnf(17,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1
| not_equal(X0,X1) ),
inference(cnf,[status(esa)],[p7]) ).
cnf(l120,plain,
( ~ ilf_type(identity_relation_of(sK12),set_type)
| ~ ilf_type(empty_set,set_type)
| identity_relation_of(sK12) = empty_set
| not_equal(identity_relation_of(sK12),empty_set) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(18,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ empty(X1) ),
inference(cnf,[status(esa)],[p8]) ).
cnf(l112,plain,
( ~ member(ordered_pair(sK2(sK12),sK2(sK12)),empty_set)
| ~ ilf_type(empty_set,set_type)
| ~ ilf_type(ordered_pair(sK2(sK12),sK2(sK12)),set_type)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[18]) ).
fof(p3a,plain,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3a) ).
cnf(3,plain,
empty(empty_set),
inference(cnf,[status(esa)],[p3a]) ).
cnf(l140,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[3]) ).
fof(p22,plain,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
cnf(46,plain,
ilf_type(X0,set_type),
inference(cnf,[status(esa)],[p22]) ).
cnf(l117,plain,
ilf_type(empty_set,set_type),
inference(instantiation,[status(thm)],[46]) ).
cnf(49,plain,
~ not_equal(identity_relation_of(sK12),empty_set),
inference(cnf,[status(esa)],[prove_relset_1_46_negated]) ).
cnf(l137,plain,
~ not_equal(identity_relation_of(sK12),empty_set),
inference(instantiation,[status(thm)],[49]) ).
cnf(l134,plain,
ilf_type(empty_set,set_type),
inference(instantiation,[status(thm)],[46]) ).
cnf(l135,plain,
ilf_type(identity_relation_of(sK12),set_type),
inference(instantiation,[status(thm)],[46]) ).
cnf(l114,plain,
ilf_type(ordered_pair(sK2(sK12),sK2(sK12)),set_type),
inference(instantiation,[status(thm)],[46]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l5,l25,l19,l26,l120,l112,l140,l117,l137,l134,l135,l114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET679+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/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 22:18:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 9
% 0.18/0.38 % launching worker at depth: 10
% 2.59/0.66 % launching worker at depth: 11
% 34.14/4.62 % SZS status Theorem for theBenchmark
% 34.14/4.62 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------