%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU245+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 : n002.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 05:11:14 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 91 ( 13 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 106 ( 42 ~; 46 |; 11 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 55 ( 5 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d6_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
fof(t16_wellord1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(c_0_3,plain,
! [X72,X73,X74,X75,X76,X77,X78,X79] :
( ( in(X75,X72)
| ~ in(X75,X74)
| X74 != set_intersection2(X72,X73) )
& ( in(X75,X73)
| ~ in(X75,X74)
| X74 != set_intersection2(X72,X73) )
& ( ~ in(X76,X72)
| ~ in(X76,X73)
| in(X76,X74)
| X74 != set_intersection2(X72,X73) )
& ( ~ in(esk10_3(X77,X78,X79),X79)
| ~ in(esk10_3(X77,X78,X79),X77)
| ~ in(esk10_3(X77,X78,X79),X78)
| X79 = set_intersection2(X77,X78) )
& ( in(esk10_3(X77,X78,X79),X77)
| in(esk10_3(X77,X78,X79),X79)
| X79 = set_intersection2(X77,X78) )
& ( in(esk10_3(X77,X78,X79),X78)
| in(esk10_3(X77,X78,X79),X79)
| X79 = set_intersection2(X77,X78) ) ),
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)],[d3_xboole_0])])])])])]) ).
cnf(c_0_4,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_5,plain,
! [X67,X68] :
( ~ relation(X67)
| relation_restriction(X67,X68) = set_intersection2(X67,cartesian_product2(X68,X68)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_wellord1])])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
inference(assume_negation,[status(cth)],[t16_wellord1]) ).
cnf(c_0_7,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,negated_conjecture,
( relation(esk9_0)
& ( ~ in(esk7_0,relation_restriction(esk9_0,esk8_0))
| ~ in(esk7_0,esk9_0)
| ~ in(esk7_0,cartesian_product2(esk8_0,esk8_0)) )
& ( in(esk7_0,esk9_0)
| in(esk7_0,relation_restriction(esk9_0,esk8_0)) )
& ( in(esk7_0,cartesian_product2(esk8_0,esk8_0))
| in(esk7_0,relation_restriction(esk9_0,esk8_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_11,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( in(X1,X2)
| ~ in(X1,relation_restriction(X2,X3))
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( in(esk7_0,esk9_0)
| in(esk7_0,relation_restriction(esk9_0,esk8_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( in(X1,relation_restriction(X2,X3))
| ~ in(X1,cartesian_product2(X3,X3))
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( in(esk7_0,cartesian_product2(esk8_0,esk8_0))
| in(esk7_0,relation_restriction(esk9_0,esk8_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(esk7_0,relation_restriction(esk9_0,esk8_0))
| ~ in(esk7_0,esk9_0)
| ~ in(esk7_0,cartesian_product2(esk8_0,esk8_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
in(esk7_0,esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_20,negated_conjecture,
( in(esk7_0,relation_restriction(esk9_0,esk8_0))
| in(esk7_0,relation_restriction(X1,esk8_0))
| ~ in(esk7_0,X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(esk7_0,relation_restriction(esk9_0,esk8_0))
| ~ in(esk7_0,cartesian_product2(esk8_0,esk8_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_23,negated_conjecture,
in(esk7_0,relation_restriction(esk9_0,esk8_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19]),c_0_14])]) ).
cnf(c_0_24,plain,
( in(X1,cartesian_product2(X2,X2))
| ~ in(X1,relation_restriction(X3,X2))
| ~ relation(X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_9]) ).
cnf(c_0_25,negated_conjecture,
~ in(esk7_0,cartesian_product2(esk8_0,esk8_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_14])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU245+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
% 0.15/0.32 % Computer : n002.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:52:16 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------