%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU325+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n028.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 03:45:12 PM UTC 2025
% Result : Theorem 25.32s 3.51s
% Output : CNFRefutation 25.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 23 unt; 0 def)
% Number of atoms : 124 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 47 ~; 37 |; 14 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 49 ( 2 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_tops_2,plain,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( is_a_cover_of_carrier(A,B)
& B = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tops_2) ).
fof(t5_tops_2_negated,plain,
~ ! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( is_a_cover_of_carrier(A,B)
& B = empty_set ) ) ),
inference(negate_conjecture,[status(cth)],[t5_tops_2]) ).
cnf(86,plain,
~ empty_carrier(sK13),
inference(cnf,[status(esa)],[t5_tops_2_negated]) ).
cnf(l0,plain,
~ empty_carrier(sK13),
inference(instantiation,[status(thm)],[86]) ).
fof(fc2_pre_topc,plain,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
cnf(57,plain,
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf,[status(esa)],[fc2_pre_topc]) ).
cnf(l1,plain,
( ~ empty(cast_as_carrier_subset(sK13))
| ~ one_sorted_str(sK13)
| empty_carrier(sK13) ),
inference(instantiation,[status(thm)],[57]) ).
cnf(87,plain,
one_sorted_str(sK13),
inference(cnf,[status(esa)],[t5_tops_2_negated]) ).
cnf(l3,plain,
one_sorted_str(sK13),
inference(instantiation,[status(thm)],[87]) ).
fof(t2_subset,plain,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
cnf(81,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf,[status(esa)],[t2_subset]) ).
cnf(l2,plain,
( ~ element(sK7(the_carrier(sK13)),cast_as_carrier_subset(sK13))
| in(sK7(the_carrier(sK13)),cast_as_carrier_subset(sK13))
| empty(cast_as_carrier_subset(sK13)) ),
inference(instantiation,[status(thm)],[81]) ).
fof(t4_subset,plain,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
cnf(84,plain,
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| element(X0,X2) ),
inference(cnf,[status(esa)],[t4_subset]) ).
cnf(l4,plain,
( ~ in(sK7(the_carrier(sK13)),the_carrier(sK13))
| ~ element(the_carrier(sK13),powerset(cast_as_carrier_subset(sK13)))
| element(sK7(the_carrier(sK13)),cast_as_carrier_subset(sK13)) ),
inference(instantiation,[status(thm)],[84]) ).
cnf(l31,plain,
( ~ element(sK7(the_carrier(sK13)),the_carrier(sK13))
| in(sK7(the_carrier(sK13)),the_carrier(sK13))
| empty(the_carrier(sK13)) ),
inference(instantiation,[status(thm)],[81]) ).
fof(existence_m1_subset_1,plain,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
cnf(54,plain,
element(sK7(X0),X0),
inference(cnf,[status(esa)],[existence_m1_subset_1]) ).
cnf(l45,plain,
element(sK7(the_carrier(sK13)),the_carrier(sK13)),
inference(instantiation,[status(thm)],[54]) ).
fof(d3_pre_topc,plain,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
cnf(40,plain,
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(cnf,[status(esa)],[d3_pre_topc]) ).
cnf(l6,plain,
( ~ one_sorted_str(sK13)
| cast_as_carrier_subset(sK13) = the_carrier(sK13) ),
inference(instantiation,[status(thm)],[40]) ).
fof(fc1_struct_0,plain,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(the_carrier(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
cnf(55,plain,
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf,[status(esa)],[fc1_struct_0]) ).
cnf(l37,plain,
( ~ empty(the_carrier(sK13))
| ~ one_sorted_str(sK13)
| empty_carrier(sK13) ),
inference(instantiation,[status(thm)],[55]) ).
fof(t3_subset,plain,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
cnf(83,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf,[status(esa)],[t3_subset]) ).
cnf(l71,plain,
( ~ subset(cast_as_carrier_subset(sK13),cast_as_carrier_subset(sK13))
| element(cast_as_carrier_subset(sK13),powerset(cast_as_carrier_subset(sK13))) ),
inference(instantiation,[status(thm)],[83]) ).
cnf(l47,plain,
one_sorted_str(sK13),
inference(instantiation,[status(thm)],[87]) ).
fof(d4_tarski,plain,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
cnf(42,plain,
( ~ in(X0,X1)
| X1 != union(X2)
| in(sK1(X2,X1,X0),X2) ),
inference(cnf,[status(esa)],[d4_tarski]) ).
cnf(l87,plain,
( ~ in(sK7(the_carrier(sK13)),union(sK14))
| union(sK14) != union(empty_set)
| in(sK1(empty_set,union(sK14),sK7(the_carrier(sK13))),empty_set) ),
inference(instantiation,[status(thm)],[42]) ).
cnf(l7,plain,
one_sorted_str(sK13),
inference(instantiation,[status(thm)],[87]) ).
fof(d8_pre_topc,plain,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( is_a_cover_of_carrier(A,B)
<=> cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_pre_topc) ).
cnf(49,plain,
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| ~ is_a_cover_of_carrier(X1,X0)
| cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X0) ),
inference(cnf,[status(esa)],[d8_pre_topc]) ).
cnf(l91,plain,
( ~ element(sK14,powerset(powerset(the_carrier(sK13))))
| ~ one_sorted_str(sK13)
| ~ is_a_cover_of_carrier(sK13,sK14)
| cast_as_carrier_subset(sK13) = union_of_subsets(the_carrier(sK13),sK14) ),
inference(instantiation,[status(thm)],[49]) ).
cnf(l100,plain,
one_sorted_str(sK13),
inference(instantiation,[status(thm)],[87]) ).
fof(t7_boole,plain,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
cnf(92,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf,[status(esa)],[t7_boole]) ).
cnf(l88,plain,
( ~ in(sK1(empty_set,union(sK14),sK7(the_carrier(sK13))),empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[92]) ).
fof(redefinition_k5_setfam_1,plain,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
cnf(78,plain,
( ~ element(X0,powerset(powerset(X1)))
| union_of_subsets(X1,X0) = union(X0) ),
inference(cnf,[status(esa)],[redefinition_k5_setfam_1]) ).
cnf(l105,plain,
( ~ element(sK14,powerset(powerset(the_carrier(sK13))))
| union_of_subsets(the_carrier(sK13),sK14) = union(sK14) ),
inference(instantiation,[status(thm)],[78]) ).
cnf(88,plain,
element(sK14,powerset(powerset(the_carrier(sK13)))),
inference(cnf,[status(esa)],[t5_tops_2_negated]) ).
cnf(l108,plain,
element(sK14,powerset(powerset(the_carrier(sK13)))),
inference(instantiation,[status(thm)],[88]) ).
cnf(l96,plain,
element(sK14,powerset(powerset(the_carrier(sK13)))),
inference(instantiation,[status(thm)],[88]) ).
fof(fc6_membered,plain,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
cnf(58,plain,
empty(empty_set),
inference(cnf,[status(esa)],[fc6_membered]) ).
cnf(l92,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[58]) ).
cnf(90,plain,
sK14 = empty_set,
inference(cnf,[status(esa)],[t5_tops_2_negated]) ).
cnf(l94,plain,
sK14 = empty_set,
inference(instantiation,[status(thm)],[90]) ).
fof(reflexivity_r1_tarski,plain,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
cnf(79,plain,
subset(X0,X0),
inference(cnf,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(l72,plain,
subset(cast_as_carrier_subset(sK13),cast_as_carrier_subset(sK13)),
inference(instantiation,[status(thm)],[79]) ).
cnf(89,plain,
is_a_cover_of_carrier(sK13,sK14),
inference(cnf,[status(esa)],[t5_tops_2_negated]) ).
cnf(l103,plain,
is_a_cover_of_carrier(sK13,sK14),
inference(instantiation,[status(thm)],[89]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l2,l4,l31,l45,l6,l37,l71,l47,l87,l7,l91,l100,l88,l105,l108,l96,l92,l94,l72,l103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU325+1 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n028.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 : Tue Jul 22 00:50:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.36 % launching worker at depth: 10
% 0.19/0.48 % launching worker at depth: 11
% 12.64/1.94 % launching worker at depth: 12
% 25.32/3.51 % SZS status Theorem for theBenchmark
% 25.32/3.51 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------