%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU225+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 : n017.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 05:11:08 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 170 ( 37 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 228 ( 92 ~; 89 |; 25 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 59 ( 4 sgn 37 !; 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/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(t72_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(t68_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(fc4_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(l82_funct_1,axiom,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,relation_dom(X3))
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_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,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
inference(assume_negation,[status(cth)],[t72_funct_1]) ).
fof(c_0_8,plain,
! [X75,X76,X77] :
( ( X77 != apply(X75,X76)
| in(ordered_pair(X76,X77),X75)
| ~ in(X76,relation_dom(X75))
| ~ relation(X75)
| ~ function(X75) )
& ( ~ in(ordered_pair(X76,X77),X75)
| X77 = apply(X75,X76)
| ~ in(X76,relation_dom(X75))
| ~ relation(X75)
| ~ function(X75) )
& ( X77 != apply(X75,X76)
| X77 = empty_set
| in(X76,relation_dom(X75))
| ~ relation(X75)
| ~ function(X75) )
& ( X77 != empty_set
| X77 = apply(X75,X76)
| in(X76,relation_dom(X75))
| ~ relation(X75)
| ~ function(X75) ) ),
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(esk13_0)
& function(esk13_0)
& in(esk12_0,esk11_0)
& apply(relation_dom_restriction(esk13_0,esk11_0),esk12_0) != apply(esk13_0,esk12_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,plain,
! [X114,X115,X116,X117] :
( ( relation_dom(X115) = set_intersection2(relation_dom(X116),X114)
| X115 != relation_dom_restriction(X116,X114)
| ~ relation(X116)
| ~ function(X116)
| ~ relation(X115)
| ~ function(X115) )
& ( ~ in(X117,relation_dom(X115))
| apply(X115,X117) = apply(X116,X117)
| X115 != relation_dom_restriction(X116,X114)
| ~ relation(X116)
| ~ function(X116)
| ~ relation(X115)
| ~ function(X115) )
& ( in(esk10_3(X114,X115,X116),relation_dom(X115))
| relation_dom(X115) != set_intersection2(relation_dom(X116),X114)
| X115 = relation_dom_restriction(X116,X114)
| ~ relation(X116)
| ~ function(X116)
| ~ relation(X115)
| ~ function(X115) )
& ( apply(X115,esk10_3(X114,X115,X116)) != apply(X116,esk10_3(X114,X115,X116))
| relation_dom(X115) != set_intersection2(relation_dom(X116),X114)
| X115 = relation_dom_restriction(X116,X114)
| ~ relation(X116)
| ~ function(X116)
| ~ relation(X115)
| ~ function(X115) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).
fof(c_0_12,plain,
! [X93,X94] :
( ( relation(relation_dom_restriction(X93,X94))
| ~ relation(X93)
| ~ function(X93) )
& ( function(relation_dom_restriction(X93,X94))
| ~ relation(X93)
| ~ function(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(c_0_13,plain,
! [X80,X81] :
( ~ relation(X80)
| relation(relation_dom_restriction(X80,X81)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(c_0_14,plain,
! [X98,X99,X100] :
( ( in(X99,relation_dom(X100))
| ~ in(X99,relation_dom(relation_dom_restriction(X100,X98)))
| ~ relation(X100)
| ~ function(X100) )
& ( in(X99,X98)
| ~ in(X99,relation_dom(relation_dom_restriction(X100,X98)))
| ~ relation(X100)
| ~ function(X100) )
& ( ~ in(X99,relation_dom(X100))
| ~ in(X99,X98)
| in(X99,relation_dom(relation_dom_restriction(X100,X98)))
| ~ relation(X100)
| ~ function(X100) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l82_funct_1])])]) ).
cnf(c_0_15,negated_conjecture,
apply(relation_dom_restriction(esk13_0,esk11_0),esk12_0) != apply(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,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_17,plain,
( apply(X2,X1) = apply(X3,X1)
| ~ in(X1,relation_dom(X2))
| X2 != relation_dom_restriction(X3,X4)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( in(esk12_0,relation_dom(relation_dom_restriction(esk13_0,esk11_0)))
| apply(esk13_0,esk12_0) != empty_set
| ~ relation(relation_dom_restriction(esk13_0,esk11_0))
| ~ function(relation_dom_restriction(esk13_0,esk11_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,plain,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18]),c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( in(esk12_0,relation_dom(esk13_0))
| apply(esk13_0,esk12_0) != empty_set
| ~ relation(relation_dom_restriction(esk13_0,esk11_0))
| ~ function(relation_dom_restriction(esk13_0,esk11_0)) ),
inference(cn,[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_23])]) ).
cnf(c_0_26,negated_conjecture,
~ in(esk12_0,relation_dom(relation_dom_restriction(esk13_0,esk11_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_24]),c_0_22]),c_0_23])]) ).
cnf(c_0_27,plain,
( in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,negated_conjecture,
in(esk12_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,negated_conjecture,
( in(esk12_0,relation_dom(esk13_0))
| apply(esk13_0,esk12_0) != empty_set
| ~ relation(relation_dom_restriction(esk13_0,esk11_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_22]),c_0_23])]) ).
cnf(c_0_30,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(spm,[status(thm)],[c_0_26,c_0_27]),c_0_22]),c_0_23]),c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
( in(esk12_0,relation_dom(esk13_0))
| ~ relation(relation_dom_restriction(esk13_0,esk11_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_22]),c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
~ relation(relation_dom_restriction(esk13_0,esk11_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_19]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU225+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 : n017.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 02:48:42 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------