%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU325+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.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 : Tue May 5 05:11:29 PM UTC 2026
% Result : Theorem 3.85s 3.19s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 18 unt; 0 def)
% Number of atoms : 134 ( 30 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 130 ( 49 ~; 32 |; 34 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 10 sgn 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_finset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(dt_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t5_tops_2,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( is_a_cover_of_carrier(X1,X2)
& X2 = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tops_2) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc2_pre_topc,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(d8_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( is_a_cover_of_carrier(X1,X2)
<=> cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_pre_topc) ).
fof(c_0_11,plain,
! [X2999] :
( ~ empty(X2999)
| X2999 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_12,plain,
! [X2185] :
( element(esk130_1(X2185),powerset(X2185))
& empty(esk130_1(X2185))
& relation(esk130_1(X2185))
& function(esk130_1(X2185))
& one_to_one(esk130_1(X2185))
& epsilon_transitive(esk130_1(X2185))
& epsilon_connected(esk130_1(X2185))
& ordinal(esk130_1(X2185))
& natural(esk130_1(X2185))
& finite(esk130_1(X2185)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
cnf(c_0_13,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
empty(esk130_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X2227,X2228] :
( ~ element(X2228,powerset(powerset(X2227)))
| union_of_subsets(X2227,X2228) = union(X2228) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
cnf(c_0_16,plain,
element(esk130_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
esk130_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,plain,
! [X1962,X1963] :
( ~ element(X1963,powerset(powerset(X1962)))
| element(union_of_subsets(X1962,X1963),powerset(X1962)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
cnf(c_0_19,plain,
( union_of_subsets(X2,X1) = union(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,plain,
! [X2976,X2977,X2978] :
( ~ in(X2976,X2977)
| ~ element(X2977,powerset(X2978))
| ~ empty(X2978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_22,plain,
( element(union_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
union_of_subsets(X1,empty_set) = union(empty_set),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_24,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_25,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
element(union(empty_set),powerset(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_23]) ).
fof(c_0_27,plain,
! [X1652,X1653,X1654] :
( ( X1652 != empty_set
| ~ in(X1653,X1652) )
& ( in(esk41_1(X1654),X1654)
| X1654 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])]) ).
cnf(c_0_28,plain,
( ~ empty(X1)
| ~ in(X2,union(empty_set)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( in(esk41_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_30,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( is_a_cover_of_carrier(X1,X2)
& X2 = empty_set ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t5_tops_2])]) ).
cnf(c_0_31,plain,
( union(empty_set) = empty_set
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
fof(c_0_33,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_pre_topc]) ).
fof(c_0_34,plain,
! [X1739] :
( ~ one_sorted_str(X1739)
| cast_as_carrier_subset(X1739) = the_carrier(X1739) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
fof(c_0_35,negated_conjecture,
( ~ empty_carrier(esk340_0)
& one_sorted_str(esk340_0)
& element(esk341_0,powerset(powerset(the_carrier(esk340_0))))
& is_a_cover_of_carrier(esk340_0,esk341_0)
& esk341_0 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
fof(c_0_36,plain,
! [X1891,X1892] :
( ( ~ is_a_cover_of_carrier(X1891,X1892)
| cast_as_carrier_subset(X1891) = union_of_subsets(the_carrier(X1891),X1892)
| ~ element(X1892,powerset(powerset(the_carrier(X1891))))
| ~ one_sorted_str(X1891) )
& ( cast_as_carrier_subset(X1891) != union_of_subsets(the_carrier(X1891),X1892)
| is_a_cover_of_carrier(X1891,X1892)
| ~ element(X1892,powerset(powerset(the_carrier(X1891))))
| ~ one_sorted_str(X1891) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_pre_topc])])])]) ).
cnf(c_0_37,plain,
union(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_38,plain,
! [X2037] :
( empty_carrier(X2037)
| ~ one_sorted_str(X2037)
| ~ empty(cast_as_carrier_subset(X2037)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_39,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
one_sorted_str(esk340_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
( cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2)
| ~ is_a_cover_of_carrier(X1,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
union_of_subsets(X1,empty_set) = empty_set,
inference(rw,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
is_a_cover_of_carrier(esk340_0,esk341_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,negated_conjecture,
esk341_0 = empty_set,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(cast_as_carrier_subset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,negated_conjecture,
cast_as_carrier_subset(esk340_0) = the_carrier(esk340_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
~ empty_carrier(esk340_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,plain,
( cast_as_carrier_subset(X1) = empty_set
| ~ is_a_cover_of_carrier(X1,empty_set)
| ~ one_sorted_str(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_20]),c_0_42]) ).
cnf(c_0_49,negated_conjecture,
is_a_cover_of_carrier(esk340_0,empty_set),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
~ empty(the_carrier(esk340_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_40])]),c_0_47]) ).
cnf(c_0_51,negated_conjecture,
the_carrier(esk340_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_46]),c_0_40])]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU325+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:57:26 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 3.85/3.19 % Version : CSE_E---1.7
% 3.85/3.19 % Problem : theBenchmark.p
% 3.85/3.19 % SZS status Theorem for theBenchmark.p
% 3.85/3.19 % SZS output start CNFRefutation
% See solution above
% 3.85/3.19 % Total time : 2.537s
%------------------------------------------------------------------------------