%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU325+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 22 unt; 0 def)
% Number of atoms : 162 ( 36 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 168 ( 70 ~; 55 |; 26 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 9 sgn 46 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(fc6_membered,axiom,
( 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/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
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/sandbox2/benchmark/theBenchmark.p',t5_tops_2) ).
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/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(c_0_12,plain,
! [X154] :
( ~ empty(X154)
| X154 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_13,plain,
! [X132] :
( element(esk8_1(X132),powerset(X132))
& empty(esk8_1(X132)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_14,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
empty(esk8_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X149,X150,X151] :
( ~ in(X149,X150)
| ~ element(X150,powerset(X151))
| ~ empty(X151) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_17,plain,
element(esk8_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
esk8_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,plain,
( ~ epred1_0
<=> ! [X1] : ~ empty(X1) ),
introduced(definition) ).
fof(c_0_20,plain,
( ~ epred2_0
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(definition) ).
cnf(c_0_21,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( epred1_0
| ~ empty(X1) ),
inference(split_equiv,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]) ).
fof(c_0_25,plain,
! [X107,X108,X109,X111,X112,X113,X114,X116] :
( ( in(X109,esk1_3(X107,X108,X109))
| ~ in(X109,X108)
| X108 != union(X107) )
& ( in(esk1_3(X107,X108,X109),X107)
| ~ in(X109,X108)
| X108 != union(X107) )
& ( ~ in(X111,X112)
| ~ in(X112,X107)
| in(X111,X108)
| X108 != union(X107) )
& ( ~ in(esk2_2(X113,X114),X114)
| ~ in(esk2_2(X113,X114),X116)
| ~ in(X116,X113)
| X114 = union(X113) )
& ( in(esk2_2(X113,X114),esk3_2(X113,X114))
| in(esk2_2(X113,X114),X114)
| X114 = union(X113) )
& ( in(esk3_2(X113,X114),X113)
| in(esk2_2(X113,X114),X114)
| X114 = union(X113) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_tarski])])])])])]) ).
cnf(c_0_26,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_19]),c_0_20]) ).
cnf(c_0_27,plain,
epred1_0,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X142,X143] :
( ~ element(X142,X143)
| empty(X143)
| in(X142,X143) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_29,plain,
! [X124] : element(esk5_1(X124),X124),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_30,plain,
( epred2_0
| ~ in(X1,empty_set) ),
inference(split_equiv,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
( in(esk1_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
~ epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_33,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( X1 != union(empty_set)
| ~ in(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,plain,
( empty(X1)
| in(esk5_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
( empty(X1)
| X1 != union(empty_set) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_38,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_39,plain,
empty(union(empty_set)),
inference(er,[status(thm)],[c_0_37]) ).
fof(c_0_40,plain,
! [X137,X138] :
( ~ element(X138,powerset(powerset(X137)))
| union_of_subsets(X137,X138) = union(X138) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
fof(c_0_41,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])]) ).
fof(c_0_42,plain,
! [X126] :
( empty_carrier(X126)
| ~ one_sorted_str(X126)
| ~ empty(the_carrier(X126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).
cnf(c_0_43,plain,
union(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_14,c_0_39]) ).
cnf(c_0_44,plain,
( union_of_subsets(X2,X1) = union(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_45,negated_conjecture,
( ~ empty_carrier(esk11_0)
& one_sorted_str(esk11_0)
& element(esk12_0,powerset(powerset(the_carrier(esk11_0))))
& is_a_cover_of_carrier(esk11_0,esk12_0)
& esk12_0 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
cnf(c_0_46,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,plain,
( empty(X1)
| X1 != empty_set ),
inference(rw,[status(thm)],[c_0_37,c_0_43]) ).
fof(c_0_48,plain,
! [X118,X119] :
( ( ~ is_a_cover_of_carrier(X118,X119)
| cast_as_carrier_subset(X118) = union_of_subsets(the_carrier(X118),X119)
| ~ element(X119,powerset(powerset(the_carrier(X118))))
| ~ one_sorted_str(X118) )
& ( cast_as_carrier_subset(X118) != union_of_subsets(the_carrier(X118),X119)
| is_a_cover_of_carrier(X118,X119)
| ~ element(X119,powerset(powerset(the_carrier(X118))))
| ~ one_sorted_str(X118) ) ),
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_49,plain,
union_of_subsets(X1,empty_set) = union(empty_set),
inference(spm,[status(thm)],[c_0_44,c_0_22]) ).
cnf(c_0_50,negated_conjecture,
~ empty_carrier(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
( empty_carrier(X1)
| the_carrier(X1) != empty_set
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
one_sorted_str(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_53,plain,
! [X106] :
( ~ one_sorted_str(X106)
| cast_as_carrier_subset(X106) = the_carrier(X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
cnf(c_0_54,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_48]) ).
cnf(c_0_55,plain,
union_of_subsets(X1,empty_set) = empty_set,
inference(rw,[status(thm)],[c_0_49,c_0_43]) ).
cnf(c_0_56,negated_conjecture,
is_a_cover_of_carrier(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,negated_conjecture,
esk12_0 = empty_set,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_58,negated_conjecture,
the_carrier(esk11_0) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_59,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,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_54,c_0_22]),c_0_55]) ).
cnf(c_0_61,negated_conjecture,
is_a_cover_of_carrier(esk11_0,empty_set),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
cast_as_carrier_subset(esk11_0) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_52])]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_52])]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU325+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:57:47 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Theorem for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.369s
%------------------------------------------------------------------------------