%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU056+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n015.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 05:10:34 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 52 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 17 ~; 12 |; 10 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t125_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( disjoint(X1,X2)
& one_to_one(X3) )
=> disjoint(relation_image(X3,X1),relation_image(X3,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).
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(t121_funct_1,axiom,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( one_to_one(X3)
=> relation_image(X3,set_intersection2(X1,X2)) = set_intersection2(relation_image(X3,X1),relation_image(X3,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).
fof(t149_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_image(X1,empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( disjoint(X1,X2)
& one_to_one(X3) )
=> disjoint(relation_image(X3,X1),relation_image(X3,X2)) ) ),
inference(assume_negation,[status(cth)],[t125_funct_1]) ).
fof(c_0_5,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& disjoint(esk12_0,esk13_0)
& one_to_one(esk14_0)
& ~ disjoint(relation_image(esk14_0,esk12_0),relation_image(esk14_0,esk13_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X68,X69] :
( ( ~ disjoint(X68,X69)
| set_intersection2(X68,X69) = empty_set )
& ( set_intersection2(X68,X69) != empty_set
| disjoint(X68,X69) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_7,negated_conjecture,
~ disjoint(relation_image(esk14_0,esk12_0),relation_image(esk14_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X91,X92,X93] :
( ~ relation(X93)
| ~ function(X93)
| ~ one_to_one(X93)
| relation_image(X93,set_intersection2(X91,X92)) = set_intersection2(relation_image(X93,X91),relation_image(X93,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t121_funct_1])]) ).
cnf(c_0_10,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
disjoint(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
set_intersection2(relation_image(esk14_0,esk12_0),relation_image(esk14_0,esk13_0)) != empty_set,
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( relation_image(X1,set_intersection2(X2,X3)) = set_intersection2(relation_image(X1,X2),relation_image(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
set_intersection2(esk12_0,esk13_0) = empty_set,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
one_to_one(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_18,plain,
! [X97] :
( ~ relation(X97)
| relation_image(X97,empty_set) = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t149_relat_1])]) ).
cnf(c_0_19,negated_conjecture,
relation_image(esk14_0,empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_20,plain,
( relation_image(X1,empty_set) = empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU056+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:42:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------