%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU430+2 : TPTP v9.2.1. Released v3.4.0.
% 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 : n016.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 05:12:18 PM UTC 2026
% Result : Theorem 5.07s 4.43s
% Output : CNFRefutation 5.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 6 unt; 0 def)
% Number of atoms : 61 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 28 ~; 21 |; 10 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t30_relset_2,conjecture,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( k5_setfam_1(X1,X2) = k1_xboole_0
<=> ! [X3] :
( r2_hidden(X3,X2)
=> X3 = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_2) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> k5_setfam_1(X1,X2) = k3_tarski(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+8.ax',redefinition_k5_setfam_1) ).
fof(t91_orders_1,axiom,
! [X1] :
( ~ ( ? [X2] :
( X2 != k1_xboole_0
& r2_hidden(X2,X1) )
& k3_tarski(X1) = k1_xboole_0 )
& ~ ( k3_tarski(X1) != k1_xboole_0
& ! [X2] :
~ ( X2 != k1_xboole_0
& r2_hidden(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+59.ax',t91_orders_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( k5_setfam_1(X1,X2) = k1_xboole_0
<=> ! [X3] :
( r2_hidden(X3,X2)
=> X3 = k1_xboole_0 ) ) ),
inference(assume_negation,[status(cth)],[t30_relset_2]) ).
fof(c_0_4,plain,
! [X1387,X1388] :
( ~ m1_subset_1(X1388,k1_zfmisc_1(k1_zfmisc_1(X1387)))
| k5_setfam_1(X1387,X1388) = k3_tarski(X1388) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
fof(c_0_5,negated_conjecture,
! [X1325] :
( m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
& ( r2_hidden(esk3_0,esk2_0)
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
& ( esk3_0 != k1_xboole_0
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
& ( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| ~ r2_hidden(X1325,esk2_0)
| X1325 = k1_xboole_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_3])])])])]) ).
cnf(c_0_6,plain,
( k5_setfam_1(X2,X1) = k3_tarski(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X1574,X1575,X1576] :
( ( X1575 = k1_xboole_0
| ~ r2_hidden(X1575,X1574)
| k3_tarski(X1574) != k1_xboole_0 )
& ( esk37_1(X1576) != k1_xboole_0
| k3_tarski(X1576) = k1_xboole_0 )
& ( r2_hidden(esk37_1(X1576),X1576)
| k3_tarski(X1576) = k1_xboole_0 ) ),
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)],[t91_orders_1])])])])])]) ).
cnf(c_0_9,negated_conjecture,
( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| X1 = k1_xboole_0
| ~ r2_hidden(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
k5_setfam_1(esk1_0,esk2_0) = k3_tarski(esk2_0),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
( X1 = k1_xboole_0
| ~ r2_hidden(X1,X2)
| k3_tarski(X2) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( X1 = k1_xboole_0
| ~ r2_hidden(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_14,plain,
( r2_hidden(esk37_1(X1),X1)
| k3_tarski(X1) = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( k3_tarski(X1) = k1_xboole_0
| esk37_1(X1) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
( esk3_0 != k1_xboole_0
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| k3_tarski(esk2_0) != k1_xboole_0 ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_18,negated_conjecture,
k3_tarski(esk2_0) = k1_xboole_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( k3_tarski(esk2_0) != k1_xboole_0
| esk3_0 != k1_xboole_0 ),
inference(rw,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_20,negated_conjecture,
r2_hidden(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
esk3_0 != k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_18])]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_20]),c_0_18])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU430+2 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n016.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 03:12:52 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 5.07/4.43 % Version : CSE_E---1.7
% 5.07/4.43 % Problem : theBenchmark.p
% 5.07/4.43 % SZS status Theorem for theBenchmark.p
% 5.07/4.43 % SZS output start CNFRefutation
% See solution above
% 5.07/4.44 % Total time : 3.712s
%------------------------------------------------------------------------------