%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU311+1 : 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 : n006.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 05:11:26 PM UTC 2026
% Result : Theorem 3.17s 2.98s
% Output : CNFRefutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 161 ( 61 ~; 60 |; 22 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 1 sgn 28 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_xboole_0__e2_37_1_1__pre_topc__1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(the_carrier(X1)))
& in(set_difference(cast_as_carrier_subset(X1),X4),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(l71_subset_1,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(s3_subset_1__e2_37_1_1__pre_topc,conjecture,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ? [X3] :
( element(X3,powerset(powerset(the_carrier(X1))))
& ! [X4] :
( element(X4,powerset(the_carrier(X1)))
=> ( in(X4,X3)
<=> in(set_difference(cast_as_carrier_subset(X1),X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__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/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(c_0_5,plain,
! [X127,X128,X130,X131] :
( ( in(X130,powerset(the_carrier(X127)))
| ~ in(X130,esk8_2(X127,X128))
| ~ topological_space(X127)
| ~ top_str(X127)
| ~ element(X128,powerset(powerset(the_carrier(X127)))) )
& ( in(set_difference(cast_as_carrier_subset(X127),X130),X128)
| ~ in(X130,esk8_2(X127,X128))
| ~ topological_space(X127)
| ~ top_str(X127)
| ~ element(X128,powerset(powerset(the_carrier(X127)))) )
& ( ~ in(X131,powerset(the_carrier(X127)))
| ~ in(set_difference(cast_as_carrier_subset(X127),X131),X128)
| in(X131,esk8_2(X127,X128))
| ~ topological_space(X127)
| ~ top_str(X127)
| ~ element(X128,powerset(powerset(the_carrier(X127)))) ) ),
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__e2_37_1_1__pre_topc__1])])])])])]) ).
fof(c_0_6,plain,
! [X136,X137] :
( ( in(esk10_2(X136,X137),X136)
| element(X136,powerset(X137)) )
& ( ~ in(esk10_2(X136,X137),X137)
| element(X136,powerset(X137)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l71_subset_1])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ? [X3] :
( element(X3,powerset(powerset(the_carrier(X1))))
& ! [X4] :
( element(X4,powerset(the_carrier(X1)))
=> ( in(X4,X3)
<=> in(set_difference(cast_as_carrier_subset(X1),X4),X2) ) ) ) ),
inference(assume_negation,[status(cth)],[s3_subset_1__e2_37_1_1__pre_topc]) ).
cnf(c_0_8,plain,
( in(X1,powerset(the_carrier(X2)))
| ~ in(X1,esk8_2(X2,X3))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(esk10_2(X1,X2),X1)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
! [X77] :
( topological_space(esk1_0)
& top_str(esk1_0)
& element(esk2_0,powerset(powerset(the_carrier(esk1_0))))
& ( element(esk3_1(X77),powerset(the_carrier(esk1_0)))
| ~ element(X77,powerset(powerset(the_carrier(esk1_0)))) )
& ( ~ in(esk3_1(X77),X77)
| ~ in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X77)),esk2_0)
| ~ element(X77,powerset(powerset(the_carrier(esk1_0)))) )
& ( in(esk3_1(X77),X77)
| in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X77)),esk2_0)
| ~ element(X77,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_7])])])])]) ).
cnf(c_0_11,plain,
( in(esk10_2(esk8_2(X1,X2),X3),powerset(the_carrier(X1)))
| element(esk8_2(X1,X2),powerset(X3))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
element(esk2_0,powerset(powerset(the_carrier(esk1_0)))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
topological_space(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( element(X1,powerset(X2))
| ~ in(esk10_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( in(esk10_2(esk8_2(esk1_0,esk2_0),X1),powerset(the_carrier(esk1_0)))
| element(esk8_2(esk1_0,esk2_0),powerset(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_17,negated_conjecture,
( in(esk3_1(X1),X1)
| in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X1)),esk2_0)
| ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
element(esk8_2(esk1_0,esk2_0),powerset(powerset(the_carrier(esk1_0)))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_19,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_20,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(esk3_1(X1),X1)
| ~ in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X1)),esk2_0)
| ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,plain,
( in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| ~ in(X2,esk8_2(X1,X3))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,plain,
( in(X1,esk8_2(X2,X3))
| ~ in(X1,powerset(the_carrier(X2)))
| ~ in(set_difference(cast_as_carrier_subset(X2),X1),X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_24,negated_conjecture,
( in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(esk8_2(esk1_0,esk2_0))),esk2_0)
| in(esk3_1(esk8_2(esk1_0,esk2_0)),esk8_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_25,plain,
! [X132,X133] :
( ( ~ element(X133,X132)
| in(X133,X132)
| empty(X132) )
& ( ~ in(X133,X132)
| element(X133,X132)
| empty(X132) )
& ( ~ element(X133,X132)
| empty(X133)
| ~ empty(X132) )
& ( ~ empty(X133)
| element(X133,X132)
| ~ empty(X132) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_26,plain,
! [X126] : ~ empty(powerset(X126)),
inference(variable_rename,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(esk3_1(X1),esk8_2(esk1_0,esk2_0))
| ~ in(esk3_1(X1),X1)
| ~ element(X1,powerset(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_21,c_0_22]),c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_28,negated_conjecture,
( in(esk3_1(esk8_2(esk1_0,esk2_0)),esk8_2(esk1_0,esk2_0))
| ~ in(esk3_1(esk8_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_23,c_0_24]),c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_29,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,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_10]) ).
cnf(c_0_31,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk3_1(esk8_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_27,c_0_28]),c_0_18])]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( in(esk3_1(X1),powerset(the_carrier(esk1_0)))
| ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU311+1 : 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
% 0.13/0.32 % Computer : n006.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:56:31 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 3.17/2.98 % Version : CSE_E---1.7
% 3.17/2.98 % Problem : theBenchmark.p
% 3.17/2.98 % SZS status Theorem for theBenchmark.p
% 3.17/2.98 % SZS output start CNFRefutation
% See solution above
% 3.17/2.99 % Total time : 2.372s
%------------------------------------------------------------------------------