%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU215+3 : TPTP v9.2.1. Released v3.2.0.
% 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 : n025.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 05:11:06 PM UTC 2026
% Result : Theorem 113.34s 71.71s
% Output : CNFRefutation 113.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 181 ( 33 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 229 ( 85 ~; 91 |; 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 : 63 ( 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(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(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/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(t22_funct_1,axiom,
! [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(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,plain,
! [X77,X78,X79] :
( ( X79 != apply(X77,X78)
| in(ordered_pair(X78,X79),X77)
| ~ in(X78,relation_dom(X77))
| ~ relation(X77)
| ~ function(X77) )
& ( ~ in(ordered_pair(X78,X79),X77)
| X79 = apply(X77,X78)
| ~ in(X78,relation_dom(X77))
| ~ relation(X77)
| ~ function(X77) )
& ( X79 != apply(X77,X78)
| X79 = empty_set
| in(X78,relation_dom(X77))
| ~ relation(X77)
| ~ function(X77) )
& ( X79 != empty_set
| X79 = apply(X77,X78)
| in(X78,relation_dom(X77))
| ~ relation(X77)
| ~ function(X77) ) ),
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_8,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]) ).
cnf(c_0_9,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,negated_conjecture,
( relation(esk11_0)
& function(esk11_0)
& relation(esk12_0)
& function(esk12_0)
& in(esk10_0,relation_dom(esk11_0))
& apply(relation_composition(esk11_0,esk12_0),esk10_0) != apply(esk12_0,apply(esk11_0,esk10_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X82,X83] :
( ~ relation(X82)
| ~ relation(X83)
| relation(relation_composition(X82,X83)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
fof(c_0_12,plain,
! [X113,X114,X115] :
( ( in(X113,relation_dom(X115))
| ~ in(X113,relation_dom(relation_composition(X115,X114)))
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) )
& ( in(apply(X115,X113),relation_dom(X114))
| ~ in(X113,relation_dom(relation_composition(X115,X114)))
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) )
& ( ~ in(X113,relation_dom(X115))
| ~ in(apply(X115,X113),relation_dom(X114))
| in(X113,relation_dom(relation_composition(X115,X114)))
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) ) ),
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_13,plain,
( apply(X1,X2) = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X88,X89] :
( ( relation(relation_composition(X88,X89))
| ~ relation(X88)
| ~ function(X88)
| ~ relation(X89)
| ~ function(X89) )
& ( function(relation_composition(X88,X89))
| ~ relation(X88)
| ~ function(X88)
| ~ relation(X89)
| ~ function(X89) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
cnf(c_0_18,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_12]) ).
cnf(c_0_19,negated_conjecture,
( apply(esk12_0,X1) = empty_set
| in(X1,relation_dom(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_20,plain,
( apply(relation_composition(X1,X2),X3) = empty_set
| in(X3,relation_dom(relation_composition(X1,X2)))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(relation_composition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_21,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X116,X117,X118] :
( ~ relation(X117)
| ~ function(X117)
| ~ relation(X118)
| ~ function(X118)
| ~ in(X116,relation_dom(relation_composition(X118,X117)))
| apply(relation_composition(X118,X117),X116) = apply(X117,apply(X118,X116)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])]) ).
cnf(c_0_23,negated_conjecture,
( apply(esk12_0,apply(X1,X2)) = empty_set
| in(X2,relation_dom(relation_composition(X1,esk12_0)))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_14]),c_0_15])]) ).
cnf(c_0_24,negated_conjecture,
in(esk10_0,relation_dom(esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
function(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,plain,
( apply(relation_composition(X1,X2),X3) = empty_set
| in(X3,relation_dom(relation_composition(X1,X2)))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( 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_22]) ).
cnf(c_0_29,negated_conjecture,
( apply(esk12_0,apply(esk11_0,esk10_0)) = empty_set
| in(esk10_0,relation_dom(relation_composition(esk11_0,esk12_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_30,negated_conjecture,
apply(relation_composition(esk11_0,esk12_0),esk10_0) != apply(esk12_0,apply(esk11_0,esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,negated_conjecture,
( apply(relation_composition(X1,esk12_0),X2) = empty_set
| in(X2,relation_dom(relation_composition(X1,esk12_0)))
| ~ relation(X1)
| ~ function(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_14]),c_0_15])]) ).
cnf(c_0_32,negated_conjecture,
apply(esk12_0,apply(esk11_0,esk10_0)) = empty_set,
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(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]),c_0_14]),c_0_26]),c_0_15])]),c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( apply(relation_composition(esk11_0,esk12_0),X1) = empty_set
| in(X1,relation_dom(relation_composition(esk11_0,esk12_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_26])]) ).
cnf(c_0_34,negated_conjecture,
apply(relation_composition(esk11_0,esk12_0),esk10_0) != empty_set,
inference(rw,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( apply(relation_composition(esk11_0,esk12_0),X1) = apply(esk12_0,apply(esk11_0,X1))
| apply(relation_composition(esk11_0,esk12_0),X1) = 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_28,c_0_33]),c_0_25]),c_0_14]),c_0_26]),c_0_15])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_32])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU215+3 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.17/0.33 % Computer : n025.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 02:50:13 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 113.34/71.71 % Version : CSE_E---1.7
% 113.34/71.71 % Problem : theBenchmark.p
% 113.34/71.71 % SZS status Theorem for theBenchmark.p
% 113.34/71.71 % SZS output start CNFRefutation
% See solution above
% 113.85/72.25 % Total time : 49.787s
%------------------------------------------------------------------------------