%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU315+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 : 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 : Tue May 5 05:11:27 PM UTC 2026
% Result : Theorem 121.57s 74.15s
% Output : CNFRefutation 122.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 115 ( 30 unt; 0 def)
% Number of atoms : 400 ( 33 equ)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 498 ( 213 ~; 226 |; 40 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 147 ( 7 sgn 41 !; 7 ?)
% 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(s3_subset_1__e1_40__pre_topc,conjecture,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> ? [X3] :
( element(X3,powerset(powerset(the_carrier(X1))))
& ! [X4] :
( element(X4,powerset(the_carrier(X1)))
=> ( in(X4,X3)
<=> ? [X5] :
( element(X5,powerset(the_carrier(X1)))
& X5 = X4
& closed_subset(X5,X1)
& subset(X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(l71_subset_1,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(s1_xboole_0__e1_40__pre_topc__1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(the_carrier(X1)))
& ? [X5] :
( element(X5,powerset(the_carrier(X1)))
& X5 = X4
& closed_subset(X5,X1)
& subset(X2,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_10,plain,
! [X127] :
( ~ empty(X127)
| X127 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_11,plain,
! [X101] :
( element(esk7_1(X101),powerset(X101))
& empty(esk7_1(X101)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> ? [X3] :
( element(X3,powerset(powerset(the_carrier(X1))))
& ! [X4] :
( element(X4,powerset(the_carrier(X1)))
=> ( in(X4,X3)
<=> ? [X5] :
( element(X5,powerset(the_carrier(X1)))
& X5 = X4
& closed_subset(X5,X1)
& subset(X2,X4) ) ) ) ) ),
inference(assume_negation,[status(cth)],[s3_subset_1__e1_40__pre_topc]) ).
cnf(c_0_13,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
empty(esk7_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_16,plain,
! [X128,X129] :
( ~ in(X128,X129)
| ~ empty(X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_17,plain,
! [X122,X123] :
( ( in(esk12_2(X122,X123),X122)
| element(X122,powerset(X123)) )
& ( ~ in(esk12_2(X122,X123),X123)
| element(X122,powerset(X123)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l71_subset_1])])])]) ).
fof(c_0_18,negated_conjecture,
! [X70,X72] :
( topological_space(esk1_0)
& top_str(esk1_0)
& element(esk2_0,powerset(the_carrier(esk1_0)))
& ( element(esk3_1(X70),powerset(the_carrier(esk1_0)))
| ~ element(X70,powerset(powerset(the_carrier(esk1_0)))) )
& ( ~ in(esk3_1(X70),X70)
| ~ element(X72,powerset(the_carrier(esk1_0)))
| X72 != esk3_1(X70)
| ~ closed_subset(X72,esk1_0)
| ~ subset(esk2_0,esk3_1(X70))
| ~ element(X70,powerset(powerset(the_carrier(esk1_0)))) )
& ( element(esk4_1(X70),powerset(the_carrier(esk1_0)))
| in(esk3_1(X70),X70)
| ~ element(X70,powerset(powerset(the_carrier(esk1_0)))) )
& ( esk4_1(X70) = esk3_1(X70)
| in(esk3_1(X70),X70)
| ~ element(X70,powerset(powerset(the_carrier(esk1_0)))) )
& ( closed_subset(esk4_1(X70),esk1_0)
| in(esk3_1(X70),X70)
| ~ element(X70,powerset(powerset(the_carrier(esk1_0)))) )
& ( subset(esk2_0,esk3_1(X70))
| in(esk3_1(X70),X70)
| ~ element(X70,powerset(powerset(the_carrier(esk1_0)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
cnf(c_0_19,plain,
element(esk7_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
esk7_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_21,plain,
! [X118,X119] :
( ( ~ element(X119,X118)
| in(X119,X118)
| empty(X118) )
& ( ~ in(X119,X118)
| element(X119,X118)
| empty(X118) )
& ( ~ element(X119,X118)
| empty(X119)
| ~ empty(X118) )
& ( ~ empty(X119)
| element(X119,X118)
| ~ empty(X118) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_22,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( in(esk12_2(X1,X2),X1)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( esk4_1(X1) = esk3_1(X1)
| in(esk3_1(X1),X1)
| ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_26,plain,
! [X111,X112,X114,X116,X117] :
( ( in(X114,powerset(the_carrier(X111)))
| ~ in(X114,esk9_2(X111,X112))
| ~ topological_space(X111)
| ~ top_str(X111)
| ~ element(X112,powerset(the_carrier(X111))) )
& ( element(esk10_3(X111,X112,X114),powerset(the_carrier(X111)))
| ~ in(X114,esk9_2(X111,X112))
| ~ topological_space(X111)
| ~ top_str(X111)
| ~ element(X112,powerset(the_carrier(X111))) )
& ( esk10_3(X111,X112,X114) = X114
| ~ in(X114,esk9_2(X111,X112))
| ~ topological_space(X111)
| ~ top_str(X111)
| ~ element(X112,powerset(the_carrier(X111))) )
& ( closed_subset(esk10_3(X111,X112,X114),X111)
| ~ in(X114,esk9_2(X111,X112))
| ~ topological_space(X111)
| ~ top_str(X111)
| ~ element(X112,powerset(the_carrier(X111))) )
& ( subset(X112,X114)
| ~ in(X114,esk9_2(X111,X112))
| ~ topological_space(X111)
| ~ top_str(X111)
| ~ element(X112,powerset(the_carrier(X111))) )
& ( ~ in(X116,powerset(the_carrier(X111)))
| ~ element(X117,powerset(the_carrier(X111)))
| X117 != X116
| ~ closed_subset(X117,X111)
| ~ subset(X112,X116)
| in(X116,esk9_2(X111,X112))
| ~ topological_space(X111)
| ~ top_str(X111)
| ~ element(X112,powerset(the_carrier(X111))) ) ),
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)],[s1_xboole_0__e1_40__pre_topc__1])])])])])]) ).
cnf(c_0_27,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( element(esk4_1(X1),powerset(the_carrier(esk1_0)))
| in(esk3_1(X1),X1)
| ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( element(X1,powerset(X2))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( esk4_1(empty_set) = esk3_1(empty_set)
| in(esk3_1(empty_set),empty_set) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_32,negated_conjecture,
( closed_subset(esk4_1(X1),esk1_0)
| in(esk3_1(X1),X1)
| ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,plain,
( in(X1,esk9_2(X2,X4))
| ~ in(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| X3 != X1
| ~ closed_subset(X3,X2)
| ~ subset(X4,X1)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X4,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(csr,[status(thm)],[c_0_27,c_0_22]) ).
fof(c_0_35,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(esk3_1(X1),X1)
| ~ element(X2,powerset(the_carrier(esk1_0)))
| X2 != esk3_1(X1)
| ~ closed_subset(X2,esk1_0)
| ~ subset(esk2_0,esk3_1(X1))
| ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_37,negated_conjecture,
( element(esk4_1(X1),powerset(the_carrier(esk1_0)))
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22]) ).
cnf(c_0_38,negated_conjecture,
esk4_1(empty_set) = esk3_1(empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_30]),c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
( closed_subset(esk4_1(X1),esk1_0)
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_29]),c_0_22]) ).
cnf(c_0_40,plain,
( in(X1,esk9_2(X2,X3))
| ~ subset(X3,X1)
| ~ closed_subset(X1,X2)
| ~ in(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ topological_space(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_34]) ).
fof(c_0_41,plain,
! [X110] : ~ empty(powerset(X110)),
inference(variable_rename,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( X1 != esk3_1(empty_set)
| ~ subset(esk2_0,esk3_1(empty_set))
| ~ closed_subset(X1,esk1_0)
| ~ in(esk3_1(empty_set),empty_set)
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_43,negated_conjecture,
element(esk3_1(empty_set),powerset(the_carrier(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31])]) ).
cnf(c_0_44,negated_conjecture,
closed_subset(esk3_1(empty_set),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_38]),c_0_31])]) ).
cnf(c_0_45,negated_conjecture,
( subset(esk2_0,esk3_1(X1))
| in(esk3_1(X1),X1)
| ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,plain,
( ~ empty(esk9_2(X1,X2))
| ~ subset(X2,X3)
| ~ closed_subset(X3,X1)
| ~ in(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_40]) ).
cnf(c_0_47,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_48,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( ~ subset(esk2_0,esk3_1(empty_set))
| ~ in(esk3_1(empty_set),empty_set) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_50,negated_conjecture,
( subset(esk2_0,esk3_1(X1))
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_29]),c_0_22]) ).
cnf(c_0_51,plain,
( in(X1,powerset(the_carrier(X2)))
| ~ in(X1,esk9_2(X2,X3))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_52,plain,
( ~ empty(esk9_2(X1,X2))
| ~ subset(X2,X3)
| ~ closed_subset(X3,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
element(esk2_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_54,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_55,negated_conjecture,
topological_space(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_56,negated_conjecture,
( subset(esk2_0,esk3_1(empty_set))
| in(esk3_1(empty_set),empty_set) ),
inference(spm,[status(thm)],[c_0_45,c_0_25]) ).
cnf(c_0_57,negated_conjecture,
~ in(esk3_1(empty_set),empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_31])]) ).
cnf(c_0_58,plain,
( empty(esk9_2(X1,X2))
| in(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X3,esk9_2(X1,X2))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_47]) ).
cnf(c_0_59,negated_conjecture,
( ~ empty(esk9_2(esk1_0,esk2_0))
| ~ subset(esk2_0,X1)
| ~ closed_subset(X1,esk1_0)
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55])]) ).
cnf(c_0_60,negated_conjecture,
subset(esk2_0,esk3_1(empty_set)),
inference(sr,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,plain,
( element(X1,powerset(X2))
| ~ in(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_62,plain,
( in(esk12_2(esk9_2(X1,X2),X3),powerset(the_carrier(X1)))
| element(esk9_2(X1,X2),powerset(X3))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_23]) ).
cnf(c_0_63,negated_conjecture,
( empty(esk9_2(esk1_0,esk2_0))
| in(X1,powerset(the_carrier(esk1_0)))
| ~ element(X1,esk9_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_53]),c_0_54]),c_0_55])]) ).
cnf(c_0_64,negated_conjecture,
~ empty(esk9_2(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_43]),c_0_60]),c_0_44])]) ).
cnf(c_0_65,plain,
( element(esk9_2(X1,X2),powerset(powerset(the_carrier(X1))))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
( element(X1,powerset(powerset(the_carrier(esk1_0))))
| ~ element(esk12_2(X1,powerset(the_carrier(esk1_0))),esk9_2(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_63]),c_0_64]) ).
cnf(c_0_67,plain,
( element(esk12_2(X1,X2),X1)
| element(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_23]) ).
cnf(c_0_68,plain,
( subset(X1,X2)
| ~ in(X2,esk9_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_69,negated_conjecture,
( subset(esk2_0,esk3_1(esk9_2(esk1_0,X1)))
| in(esk3_1(esk9_2(esk1_0,X1)),esk9_2(esk1_0,X1))
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_65]),c_0_54]),c_0_55])]) ).
cnf(c_0_70,negated_conjecture,
element(esk9_2(esk1_0,esk2_0),powerset(powerset(the_carrier(esk1_0)))),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
( subset(esk2_0,esk3_1(esk9_2(esk1_0,X1)))
| subset(X1,esk3_1(esk9_2(esk1_0,X1)))
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_54]),c_0_55])]) ).
cnf(c_0_72,negated_conjecture,
( esk4_1(esk9_2(esk1_0,esk2_0)) = esk3_1(esk9_2(esk1_0,esk2_0))
| in(esk3_1(esk9_2(esk1_0,esk2_0)),esk9_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_70]) ).
cnf(c_0_73,plain,
( element(X1,esk9_2(X2,X3))
| ~ subset(X3,X1)
| ~ closed_subset(X1,X2)
| ~ in(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ topological_space(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_74,negated_conjecture,
( closed_subset(esk4_1(esk9_2(esk1_0,X1)),esk1_0)
| in(esk3_1(esk9_2(esk1_0,X1)),esk9_2(esk1_0,X1))
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_65]),c_0_54]),c_0_55])]) ).
cnf(c_0_75,plain,
( esk10_3(X1,X2,X3) = X3
| ~ in(X3,esk9_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_76,negated_conjecture,
( closed_subset(esk4_1(esk9_2(esk1_0,esk2_0)),esk1_0)
| in(esk3_1(esk9_2(esk1_0,esk2_0)),esk9_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_70]) ).
cnf(c_0_77,negated_conjecture,
( X1 != esk3_1(esk9_2(esk1_0,X2))
| ~ subset(esk2_0,esk3_1(esk9_2(esk1_0,X2)))
| ~ closed_subset(X1,esk1_0)
| ~ in(esk3_1(esk9_2(esk1_0,X2)),esk9_2(esk1_0,X2))
| ~ element(X1,powerset(the_carrier(esk1_0)))
| ~ element(X2,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_65]),c_0_54]),c_0_55])]) ).
cnf(c_0_78,negated_conjecture,
subset(esk2_0,esk3_1(esk9_2(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_71,c_0_53]) ).
cnf(c_0_79,negated_conjecture,
( esk4_1(esk9_2(esk1_0,esk2_0)) = esk3_1(esk9_2(esk1_0,esk2_0))
| in(esk3_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_72]),c_0_53]),c_0_54]),c_0_55])]) ).
cnf(c_0_80,negated_conjecture,
( element(esk3_1(X1),powerset(the_carrier(esk1_0)))
| ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_81,plain,
( element(X1,esk9_2(X2,X3))
| ~ subset(X3,X1)
| ~ closed_subset(X1,X2)
| ~ element(X3,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ topological_space(X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_47]),c_0_48]) ).
cnf(c_0_82,negated_conjecture,
( empty(esk9_2(esk1_0,esk2_0))
| element(X1,powerset(the_carrier(esk1_0)))
| ~ element(X1,esk9_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_63]) ).
cnf(c_0_83,negated_conjecture,
( closed_subset(esk4_1(esk9_2(esk1_0,X1)),esk1_0)
| element(esk3_1(esk9_2(esk1_0,X1)),esk9_2(esk1_0,X1))
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_34,c_0_74]) ).
cnf(c_0_84,plain,
( closed_subset(esk10_3(X1,X2,X3),X1)
| ~ in(X3,esk9_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_85,negated_conjecture,
( esk10_3(esk1_0,esk2_0,esk3_1(esk9_2(esk1_0,esk2_0))) = esk3_1(esk9_2(esk1_0,esk2_0))
| closed_subset(esk4_1(esk9_2(esk1_0,esk2_0)),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_53]),c_0_54]),c_0_55])]) ).
cnf(c_0_86,negated_conjecture,
( esk4_1(esk9_2(esk1_0,esk2_0)) = esk3_1(esk9_2(esk1_0,esk2_0))
| X1 != esk3_1(esk9_2(esk1_0,esk2_0))
| ~ closed_subset(X1,esk1_0)
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_72]),c_0_78]),c_0_53])]) ).
cnf(c_0_87,negated_conjecture,
( esk4_1(esk9_2(esk1_0,esk2_0)) = esk3_1(esk9_2(esk1_0,esk2_0))
| element(esk3_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_34,c_0_79]) ).
cnf(c_0_88,negated_conjecture,
( in(esk3_1(esk9_2(esk1_0,esk2_0)),esk9_2(esk1_0,esk2_0))
| element(esk4_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_28,c_0_70]) ).
cnf(c_0_89,negated_conjecture,
( empty(esk9_2(esk1_0,esk3_1(X1)))
| in(X2,powerset(the_carrier(esk1_0)))
| ~ element(X1,powerset(powerset(the_carrier(esk1_0))))
| ~ element(X2,esk9_2(esk1_0,esk3_1(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_80]),c_0_54]),c_0_55])]) ).
cnf(c_0_90,negated_conjecture,
( element(X1,esk9_2(esk1_0,esk3_1(X2)))
| ~ subset(esk3_1(X2),X1)
| ~ closed_subset(X1,esk1_0)
| ~ element(X2,powerset(powerset(the_carrier(esk1_0))))
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_80]),c_0_54]),c_0_55])]) ).
cnf(c_0_91,negated_conjecture,
( ~ empty(esk9_2(esk1_0,esk3_1(X1)))
| ~ subset(esk3_1(X1),X2)
| ~ closed_subset(X2,esk1_0)
| ~ element(X1,powerset(powerset(the_carrier(esk1_0))))
| ~ element(X2,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_80]),c_0_54]),c_0_55])]) ).
cnf(c_0_92,negated_conjecture,
( closed_subset(esk4_1(esk9_2(esk1_0,esk2_0)),esk1_0)
| X1 != esk3_1(esk9_2(esk1_0,esk2_0))
| ~ closed_subset(X1,esk1_0)
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_76]),c_0_78]),c_0_53])]) ).
cnf(c_0_93,negated_conjecture,
( closed_subset(esk4_1(esk9_2(esk1_0,esk2_0)),esk1_0)
| element(esk3_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_53])]),c_0_39]) ).
cnf(c_0_94,negated_conjecture,
( closed_subset(esk4_1(esk9_2(esk1_0,esk2_0)),esk1_0)
| closed_subset(esk3_1(esk9_2(esk1_0,esk2_0)),esk1_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_53]),c_0_54]),c_0_55])]),c_0_76]) ).
cnf(c_0_95,negated_conjecture,
( esk10_3(esk1_0,esk2_0,esk3_1(esk9_2(esk1_0,esk2_0))) = esk3_1(esk9_2(esk1_0,esk2_0))
| esk4_1(esk9_2(esk1_0,esk2_0)) = esk3_1(esk9_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_72]),c_0_53]),c_0_54]),c_0_55])]) ).
cnf(c_0_96,negated_conjecture,
( esk4_1(esk9_2(esk1_0,esk2_0)) = esk3_1(esk9_2(esk1_0,esk2_0))
| ~ closed_subset(esk3_1(esk9_2(esk1_0,esk2_0)),esk1_0) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_97,negated_conjecture,
( in(esk3_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0)))
| element(esk4_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_88]),c_0_53]),c_0_54]),c_0_55])]) ).
cnf(c_0_98,negated_conjecture,
( empty(esk9_2(esk1_0,esk3_1(esk9_2(esk1_0,esk2_0))))
| in(X1,powerset(the_carrier(esk1_0)))
| ~ element(X1,esk9_2(esk1_0,esk3_1(esk9_2(esk1_0,esk2_0)))) ),
inference(spm,[status(thm)],[c_0_89,c_0_70]) ).
cnf(c_0_99,negated_conjecture,
( element(X1,esk9_2(esk1_0,esk3_1(esk9_2(esk1_0,esk2_0))))
| ~ subset(esk3_1(esk9_2(esk1_0,esk2_0)),X1)
| ~ closed_subset(X1,esk1_0)
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_90,c_0_70]) ).
cnf(c_0_100,negated_conjecture,
( ~ empty(esk9_2(esk1_0,esk3_1(esk9_2(esk1_0,esk2_0))))
| ~ subset(esk3_1(esk9_2(esk1_0,esk2_0)),X1)
| ~ closed_subset(X1,esk1_0)
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_91,c_0_70]) ).
fof(c_0_101,plain,
! [X104] : subset(X104,X104),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_102,negated_conjecture,
closed_subset(esk4_1(esk9_2(esk1_0,esk2_0)),esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_103,negated_conjecture,
esk4_1(esk9_2(esk1_0,esk2_0)) = esk3_1(esk9_2(esk1_0,esk2_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_95]),c_0_53]),c_0_54]),c_0_55])]),c_0_72]),c_0_96]) ).
cnf(c_0_104,negated_conjecture,
( element(esk4_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0)))
| element(esk3_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_34,c_0_97]) ).
cnf(c_0_105,negated_conjecture,
( in(X1,powerset(the_carrier(esk1_0)))
| ~ subset(esk3_1(esk9_2(esk1_0,esk2_0)),X1)
| ~ closed_subset(X1,esk1_0)
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_106,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_107,negated_conjecture,
closed_subset(esk3_1(esk9_2(esk1_0,esk2_0)),esk1_0),
inference(rw,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,negated_conjecture,
element(esk3_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_103])]) ).
cnf(c_0_109,negated_conjecture,
( X1 != esk3_1(esk9_2(esk1_0,esk2_0))
| ~ closed_subset(X1,esk1_0)
| ~ in(esk3_1(esk9_2(esk1_0,esk2_0)),esk9_2(esk1_0,esk2_0))
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_70]),c_0_78])]) ).
cnf(c_0_110,negated_conjecture,
in(esk3_1(esk9_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_108])]) ).
cnf(c_0_111,negated_conjecture,
( X1 != esk3_1(esk9_2(esk1_0,esk2_0))
| ~ closed_subset(X1,esk1_0)
| ~ element(esk3_1(esk9_2(esk1_0,esk2_0)),esk9_2(esk1_0,esk2_0))
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_47]),c_0_64]) ).
cnf(c_0_112,negated_conjecture,
( element(esk3_1(esk9_2(esk1_0,esk2_0)),esk9_2(esk1_0,X1))
| ~ subset(X1,esk3_1(esk9_2(esk1_0,esk2_0)))
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_110]),c_0_107]),c_0_54]),c_0_55])]) ).
cnf(c_0_113,negated_conjecture,
( X1 != esk3_1(esk9_2(esk1_0,esk2_0))
| ~ closed_subset(X1,esk1_0)
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_78]),c_0_53])]) ).
cnf(c_0_114,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_108]),c_0_107])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU315+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n028.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:57:16 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 121.57/74.15 % Version : CSE_E---1.7
% 121.57/74.15 % Problem : theBenchmark.p
% 121.57/74.15 % SZS status Theorem for theBenchmark.p
% 121.57/74.15 % SZS output start CNFRefutation
% See solution above
% 122.05/74.65 % Total time : 47.670s
%------------------------------------------------------------------------------