%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU215+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.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 05:11:05 PM UTC 2026
% Result : Theorem 1.80s 1.88s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 160 ( 23 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 207 ( 79 ~; 75 |; 29 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(t23_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(t22_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(t21_funct_1,lemma,
! [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/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(c_0_6,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
inference(assume_negation,[status(cth)],[t23_funct_1]) ).
fof(c_0_8,plain,
! [X646,X647,X648] :
( ( X648 != apply(X646,X647)
| in(ordered_pair(X647,X648),X646)
| ~ in(X647,relation_dom(X646))
| ~ relation(X646)
| ~ function(X646) )
& ( ~ in(ordered_pair(X647,X648),X646)
| X648 = apply(X646,X647)
| ~ in(X647,relation_dom(X646))
| ~ relation(X646)
| ~ function(X646) )
& ( X648 != apply(X646,X647)
| X648 = empty_set
| in(X647,relation_dom(X646))
| ~ relation(X646)
| ~ function(X646) )
& ( X648 != empty_set
| X648 = apply(X646,X647)
| in(X647,relation_dom(X646))
| ~ relation(X646)
| ~ function(X646) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,negated_conjecture,
( relation(esk66_0)
& function(esk66_0)
& relation(esk67_0)
& function(esk67_0)
& in(esk65_0,relation_dom(esk66_0))
& apply(relation_composition(esk66_0,esk67_0),esk65_0) != apply(esk67_0,apply(esk66_0,esk65_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_10,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,lemma,
! [X908,X909,X910] :
( ~ relation(X909)
| ~ function(X909)
| ~ relation(X910)
| ~ function(X910)
| ~ in(X908,relation_dom(relation_composition(X910,X909)))
| apply(relation_composition(X910,X909),X908) = apply(X909,apply(X910,X908)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])]) ).
cnf(c_0_12,negated_conjecture,
apply(relation_composition(esk66_0,esk67_0),esk65_0) != apply(esk67_0,apply(esk66_0,esk65_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( apply(X1,X2) = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk67_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
function(esk67_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,lemma,
( apply(relation_composition(X2,X1),X3) = apply(X1,apply(X2,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
relation(esk66_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
function(esk66_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_19,lemma,
! [X904,X905,X906] :
( ( in(X904,relation_dom(X906))
| ~ in(X904,relation_dom(relation_composition(X906,X905)))
| ~ relation(X906)
| ~ function(X906)
| ~ relation(X905)
| ~ function(X905) )
& ( in(apply(X906,X904),relation_dom(X905))
| ~ in(X904,relation_dom(relation_composition(X906,X905)))
| ~ relation(X906)
| ~ function(X906)
| ~ relation(X905)
| ~ function(X905) )
& ( ~ in(X904,relation_dom(X906))
| ~ in(apply(X906,X904),relation_dom(X905))
| in(X904,relation_dom(relation_composition(X906,X905)))
| ~ relation(X906)
| ~ function(X906)
| ~ relation(X905)
| ~ function(X905) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).
cnf(c_0_20,negated_conjecture,
( in(apply(esk66_0,esk65_0),relation_dom(esk67_0))
| apply(relation_composition(esk66_0,esk67_0),esk65_0) != empty_set ),
inference(cn,[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])]) ).
cnf(c_0_21,negated_conjecture,
~ in(esk65_0,relation_dom(relation_composition(esk66_0,esk67_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_12,c_0_16]),c_0_17]),c_0_14]),c_0_18]),c_0_15])]) ).
cnf(c_0_22,lemma,
( 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_19]) ).
cnf(c_0_23,negated_conjecture,
( in(apply(esk66_0,esk65_0),relation_dom(esk67_0))
| ~ relation(relation_composition(esk66_0,esk67_0))
| ~ function(relation_composition(esk66_0,esk67_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
in(esk65_0,relation_dom(esk66_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_25,plain,
! [X749,X750] :
( ( relation(relation_composition(X749,X750))
| ~ relation(X749)
| ~ function(X749)
| ~ relation(X750)
| ~ function(X750) )
& ( function(relation_composition(X749,X750))
| ~ relation(X749)
| ~ function(X749)
| ~ relation(X750)
| ~ function(X750) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
cnf(c_0_26,lemma,
( ~ relation(relation_composition(esk66_0,esk67_0))
| ~ function(relation_composition(esk66_0,esk67_0)) ),
inference(sr,[status(thm)],[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_22,c_0_23]),c_0_14]),c_0_17]),c_0_15]),c_0_18]),c_0_24])]),c_0_21]) ).
cnf(c_0_27,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_28,plain,
! [X729,X730] :
( ~ relation(X729)
| ~ relation(X730)
| relation(relation_composition(X729,X730)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
cnf(c_0_29,lemma,
~ relation(relation_composition(esk66_0,esk67_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_26,c_0_27]),c_0_14]),c_0_17]),c_0_15]),c_0_18])]) ).
cnf(c_0_30,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_14]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU215+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n026.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 02:50:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.80/1.88 % Version : CSE_E---1.7
% 1.80/1.88 % Problem : theBenchmark.p
% 1.80/1.88 % SZS status Theorem for theBenchmark.p
% 1.80/1.88 % SZS output start CNFRefutation
% See solution above
% 1.80/1.88 % Total time : 1.373s
%------------------------------------------------------------------------------