%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU354+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 : n029.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 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 43 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 40 ( 18 ~; 10 |; 6 &)
% ( 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 : 22 ( 0 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rc2_tex_2,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& ~ proper_element(X2,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
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(t99_zfmisc_1,axiom,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(c_0_4,plain,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& ~ proper_element(X2,powerset(X1)) ),
inference(fof_simplification,[status(thm)],[rc2_tex_2]) ).
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,
! [X98,X99] :
( ( ~ proper_element(X99,X98)
| X99 != union(X98)
| ~ element(X99,X98) )
& ( X99 = union(X98)
| proper_element(X99,X98)
| ~ element(X99,X98) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_tex_2])])]) ).
fof(c_0_7,plain,
! [X111] :
( element(esk5_1(X111),powerset(X111))
& ~ proper_element(esk5_1(X111),powerset(X111)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_4])]) ).
fof(c_0_8,plain,
! [X136] : union(powerset(X136)) = X136,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
fof(c_0_9,negated_conjecture,
( element(esk7_0,powerset(esk6_0))
& ( ~ proper_element(esk7_0,powerset(esk6_0))
| esk7_0 = esk6_0 )
& ( proper_element(esk7_0,powerset(esk6_0))
| esk7_0 != esk6_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_10,plain,
( X1 = union(X2)
| proper_element(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
element(esk5_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
~ proper_element(esk5_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
element(esk7_0,powerset(esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( esk7_0 = esk6_0
| ~ proper_element(esk7_0,powerset(esk6_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
esk5_1(X1) = X1,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( proper_element(esk7_0,powerset(esk6_0))
| esk7_0 != esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
esk6_0 = esk7_0,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_12]),c_0_15]) ).
cnf(c_0_19,plain,
~ proper_element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU354+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
% 0.16/0.32 % Computer : n029.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:59:59 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------