%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU009+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 : 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 05:10:29 PM UTC 2026
% Result : Theorem 1.58s 1.81s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 122 ( 15 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 156 ( 63 ~; 63 |; 20 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t40_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_1) ).
fof(t21_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t40_funct_1]) ).
fof(c_0_6,plain,
! [X93,X94,X95] :
( ( in(X93,relation_dom(X95))
| ~ in(X93,relation_dom(relation_composition(X95,X94)))
| ~ relation(X95)
| ~ function(X95)
| ~ relation(X94)
| ~ function(X94) )
& ( in(apply(X95,X93),relation_dom(X94))
| ~ in(X93,relation_dom(relation_composition(X95,X94)))
| ~ relation(X95)
| ~ function(X95)
| ~ relation(X94)
| ~ function(X94) )
& ( ~ in(X93,relation_dom(X95))
| ~ in(apply(X95,X93),relation_dom(X94))
| in(X93,relation_dom(relation_composition(X95,X94)))
| ~ relation(X95)
| ~ function(X95)
| ~ relation(X94)
| ~ function(X94) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).
fof(c_0_7,negated_conjecture,
( relation(esk13_0)
& function(esk13_0)
& ( ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| ~ in(esk12_0,relation_dom(esk13_0))
| ~ in(apply(esk13_0,esk12_0),esk11_0) )
& ( in(esk12_0,relation_dom(esk13_0))
| in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) )
& ( in(apply(esk13_0,esk12_0),esk11_0)
| in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,plain,
! [X67] : relation(identity_relation(X67)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_9,plain,
! [X75] :
( relation(identity_relation(X75))
& function(identity_relation(X75)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_10,plain,
! [X98,X99,X100] :
( ( relation_dom(X99) = X98
| X99 != identity_relation(X98)
| ~ relation(X99)
| ~ function(X99) )
& ( ~ in(X100,X98)
| apply(X99,X100) = X100
| X99 != identity_relation(X98)
| ~ relation(X99)
| ~ function(X99) )
& ( in(esk10_2(X98,X99),X98)
| relation_dom(X99) != X98
| X99 = identity_relation(X98)
| ~ relation(X99)
| ~ function(X99) )
& ( apply(X99,esk10_2(X98,X99)) != esk10_2(X98,X99)
| relation_dom(X99) != X98
| X99 = identity_relation(X98)
| ~ relation(X99)
| ~ function(X99) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
cnf(c_0_11,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,X3)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( in(esk12_0,relation_dom(esk13_0))
| in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| ~ in(esk12_0,relation_dom(esk13_0))
| ~ in(apply(esk13_0,esk12_0),esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
in(esk12_0,relation_dom(esk13_0)),
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_11,c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_20,plain,
( in(apply(X1,X2),relation_dom(X3))
| ~ in(X2,relation_dom(relation_composition(X1,X3)))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( in(apply(esk13_0,esk12_0),esk11_0)
| in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_13]),c_0_15])]) ).
cnf(c_0_23,plain,
( in(X1,relation_dom(relation_composition(X2,X3)))
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),relation_dom(X3))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| ~ in(apply(esk13_0,esk12_0),esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_25,negated_conjecture,
in(apply(esk13_0,esk12_0),esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_26,plain,
( in(X1,relation_dom(relation_composition(X2,identity_relation(X3))))
| ~ relation(X2)
| ~ function(X2)
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_13]),c_0_15])]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_14]),c_0_16]),c_0_19])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU009+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
% 0.14/0.33 % Computer : n002.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:41:01 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.58/1.81 % Version : CSE_E---1.7
% 1.58/1.81 % Problem : theBenchmark.p
% 1.58/1.81 % SZS status Theorem for theBenchmark.p
% 1.58/1.81 % SZS output start CNFRefutation
% See solution above
% 1.58/1.81 % Total time : 1.371s
%------------------------------------------------------------------------------