%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU120+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 05:10:40 PM UTC 2026
% Result : Theorem 1.10s 1.62s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 4 unt; 0 def)
% Number of atoms : 46 ( 12 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 55 ( 27 ~; 14 |; 11 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 3 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t4_xboole_0,conjecture,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t4_xboole_0])]) ).
fof(c_0_4,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_5,negated_conjecture,
! [X39] :
( ( in(esk6_0,set_intersection2(esk4_0,esk5_0))
| ~ disjoint(esk4_0,esk5_0) )
& ( disjoint(esk4_0,esk5_0)
| ~ disjoint(esk4_0,esk5_0) )
& ( in(esk6_0,set_intersection2(esk4_0,esk5_0))
| ~ in(X39,set_intersection2(esk4_0,esk5_0)) )
& ( disjoint(esk4_0,esk5_0)
| ~ in(X39,set_intersection2(esk4_0,esk5_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])])])])]) ).
fof(c_0_6,plain,
! [X26,X27,X28] :
( ( X26 != empty_set
| ~ in(X27,X26) )
& ( in(esk1_1(X28),X28)
| X28 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
fof(c_0_7,plain,
! [X30,X31] :
( ( ~ disjoint(X30,X31)
| set_intersection2(X30,X31) = empty_set )
& ( set_intersection2(X30,X31) != empty_set
| disjoint(X30,X31) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_8,negated_conjecture,
( disjoint(esk4_0,esk5_0)
| ~ in(X1,set_intersection2(esk4_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( in(esk6_0,set_intersection2(esk4_0,esk5_0))
| ~ disjoint(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
set_intersection2(esk4_0,esk5_0) = empty_set,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_14,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
~ disjoint(esk4_0,esk5_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU120+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Mon May 4 21:43:56 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.26 % start to proof: theBenchmark
% 1.10/1.62 % Version : CSE_E---1.7
% 1.10/1.62 % Problem : theBenchmark.p
% 1.10/1.62 % SZS status Theorem for theBenchmark.p
% 1.10/1.62 % SZS output start CNFRefutation
% See solution above
% 1.10/1.62 % Total time : 1.361s
%------------------------------------------------------------------------------