%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU162+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 : n021.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 05:10:52 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 4 unt; 0 def)
% Number of atoms : 52 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 48 ( 22 ~; 17 |; 3 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t65_zfmisc_1,conjecture,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(l28_zfmisc_1,axiom,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(t83_xboole_1,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(l25_zfmisc_1,axiom,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t65_zfmisc_1])]) ).
fof(c_0_6,plain,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
( ( set_difference(esk1_0,singleton(esk2_0)) != esk1_0
| in(esk2_0,esk1_0) )
& ( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
| ~ in(esk2_0,esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X25,X26] :
( ( ~ disjoint(X25,X26)
| set_difference(X25,X26) = X25 )
& ( set_difference(X25,X26) != X25
| disjoint(X25,X26) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(c_0_9,plain,
! [X21,X22] :
( ~ disjoint(X21,X22)
| disjoint(X22,X21) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(c_0_10,plain,
! [X19,X20] :
( in(X19,X20)
| disjoint(singleton(X19),X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
cnf(c_0_11,negated_conjecture,
( in(esk2_0,esk1_0)
| set_difference(esk1_0,singleton(esk2_0)) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
| ~ in(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( in(esk2_0,esk1_0)
| ~ disjoint(esk1_0,singleton(esk2_0)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
( disjoint(X1,singleton(X2))
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( disjoint(esk1_0,singleton(esk2_0))
| ~ in(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
in(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_21,plain,
! [X17,X18] :
( ~ disjoint(singleton(X17),X18)
| ~ in(X17,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l25_zfmisc_1])]) ).
cnf(c_0_22,negated_conjecture,
disjoint(esk1_0,singleton(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_23,plain,
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
disjoint(singleton(esk2_0),esk1_0),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU162+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n021.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 02:47:10 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % 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
%------------------------------------------------------------------------------