%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU146+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 : n024.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 05:10:46 PM UTC 2026
% Result : Theorem 1.12s 1.62s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 85 ( 31 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 78 ( 27 ~; 37 |; 7 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(l4_zfmisc_1,conjecture,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(t3_xboole_1,axiom,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(l2_zfmisc_1,axiom,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(c_0_8,plain,
! [X29,X30,X31] :
( ~ subset(X29,X30)
| in(X31,X29)
| subset(X29,set_difference(X30,singleton(X31))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(c_0_9,plain,
! [X36] : subset(X36,X36),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_10,plain,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X38,X39] :
( ( set_difference(X38,X39) != empty_set
| subset(X38,X39) )
& ( ~ subset(X38,X39)
| set_difference(X38,X39) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
inference(assume_negation,[status(cth)],[l4_zfmisc_1]) ).
cnf(c_0_14,plain,
( subset(X1,set_difference(X1,singleton(X2)))
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,negated_conjecture,
( ( esk1_0 != empty_set
| ~ subset(esk1_0,singleton(esk2_0)) )
& ( esk1_0 != singleton(esk2_0)
| ~ subset(esk1_0,singleton(esk2_0)) )
& ( subset(esk1_0,singleton(esk2_0))
| esk1_0 = empty_set
| esk1_0 = singleton(esk2_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_17,plain,
! [X40] :
( ~ subset(X40,empty_set)
| X40 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(c_0_18,plain,
! [X25,X26] :
( ( subset(X25,X26)
| X25 != X26 )
& ( subset(X26,X25)
| X25 != X26 )
& ( ~ subset(X25,X26)
| ~ subset(X26,X25)
| X25 = X26 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(c_0_19,plain,
! [X27,X28] :
( ( ~ subset(singleton(X27),X28)
| in(X27,X28) )
& ( ~ in(X27,X28)
| subset(singleton(X27),X28) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
cnf(c_0_20,plain,
( subset(X1,empty_set)
| in(X2,X1)
| ~ subset(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( subset(esk1_0,singleton(esk2_0))
| esk1_0 = empty_set
| esk1_0 = singleton(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( singleton(esk2_0) = esk1_0
| esk1_0 = empty_set
| in(esk2_0,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( singleton(esk2_0) = esk1_0
| esk1_0 = empty_set
| ~ subset(singleton(esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( esk1_0 != singleton(esk2_0)
| ~ subset(esk1_0,singleton(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,negated_conjecture,
( singleton(esk2_0) = esk1_0
| esk1_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
fof(c_0_29,plain,
! [X37] : subset(empty_set,X37),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_30,negated_conjecture,
( esk1_0 != empty_set
| ~ subset(esk1_0,singleton(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,negated_conjecture,
esk1_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_11])]) ).
cnf(c_0_32,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU146+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.06 % 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
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 21:46:41 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.12/1.62 % Version : CSE_E---1.7
% 1.12/1.62 % Problem : theBenchmark.p
% 1.12/1.62 % SZS status Theorem for theBenchmark.p
% 1.12/1.62 % SZS output start CNFRefutation
% See solution above
% 1.12/1.62 % Total time : 1.370s
%------------------------------------------------------------------------------