%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU354+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 : n014.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 05:11:35 PM UTC 2026
% Result : Theorem 4.36s 3.16s
% Output : CNFRefutation 4.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 46 ( 18 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 13 |; 3 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 24 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_tex_2,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
fof(d2_tex_2,axiom,
! [X1,X2] :
( element(X2,X1)
=> ( proper_element(X2,X1)
<=> X2 != union(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
fof(dt_k2_subset_1,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(d4_subset_1,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(t99_zfmisc_1,lemma,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
inference(assume_negation,[status(cth)],[t5_tex_2]) ).
fof(c_0_6,plain,
! [X2175,X2176] :
( ( ~ proper_element(X2176,X2175)
| X2176 != union(X2175)
| ~ element(X2176,X2175) )
& ( X2176 = union(X2175)
| proper_element(X2176,X2175)
| ~ element(X2176,X2175) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_tex_2])])]) ).
fof(c_0_7,plain,
! [X2469] : element(cast_to_subset(X2469),powerset(X2469)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(c_0_8,plain,
! [X2280] : cast_to_subset(X2280) = X2280,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(c_0_9,negated_conjecture,
( element(esk440_0,powerset(esk439_0))
& ( ~ proper_element(esk440_0,powerset(esk439_0))
| esk440_0 = esk439_0 )
& ( proper_element(esk440_0,powerset(esk439_0))
| esk440_0 != esk439_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_10,lemma,
! [X3915] : union(powerset(X3915)) = X3915,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
cnf(c_0_11,plain,
( ~ proper_element(X1,X2)
| X1 != union(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( X1 = union(X2)
| proper_element(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
element(esk440_0,powerset(esk439_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( esk440_0 = esk439_0
| ~ proper_element(esk440_0,powerset(esk439_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( ~ proper_element(union(X1),X1)
| ~ element(union(X1),X1) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( proper_element(esk440_0,powerset(esk439_0))
| esk440_0 != esk439_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
esk439_0 = esk440_0,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]) ).
cnf(c_0_22,lemma,
~ proper_element(X1,powerset(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_19])]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21])]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU354+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
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:59:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.36/3.16 % Version : CSE_E---1.7
% 4.36/3.16 % Problem : theBenchmark.p
% 4.36/3.16 % SZS status Theorem for theBenchmark.p
% 4.36/3.16 % SZS output start CNFRefutation
% See solution above
% 4.36/3.17 % Total time : 2.591s
%------------------------------------------------------------------------------