%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU225+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 : n024.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 05:11:09 PM UTC 2026
% Result : Theorem 1.19s 1.67s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 162 ( 39 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 216 ( 85 ~; 84 |; 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 : 62 ( 3 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/sandbox2/benchmark/theBenchmark.p',d4_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_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/sandbox2/benchmark/theBenchmark.p',t72_funct_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/sandbox2/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,plain,
! [X143,X144,X145,X146] :
( ( relation_dom(X144) = set_intersection2(relation_dom(X145),X143)
| X144 != relation_dom_restriction(X145,X143)
| ~ relation(X145)
| ~ function(X145)
| ~ relation(X144)
| ~ function(X144) )
& ( ~ in(X146,relation_dom(X144))
| apply(X144,X146) = apply(X145,X146)
| X144 != relation_dom_restriction(X145,X143)
| ~ relation(X145)
| ~ function(X145)
| ~ relation(X144)
| ~ function(X144) )
& ( in(esk12_3(X143,X144,X145),relation_dom(X144))
| relation_dom(X144) != set_intersection2(relation_dom(X145),X143)
| X144 = relation_dom_restriction(X145,X143)
| ~ relation(X145)
| ~ function(X145)
| ~ relation(X144)
| ~ function(X144) )
& ( apply(X144,esk12_3(X143,X144,X145)) != apply(X145,esk12_3(X143,X144,X145))
| relation_dom(X144) != set_intersection2(relation_dom(X145),X143)
| X144 = relation_dom_restriction(X145,X143)
| ~ relation(X145)
| ~ function(X145)
| ~ relation(X144)
| ~ function(X144) ) ),
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_8,plain,
! [X109,X110] :
( ( relation(relation_dom_restriction(X109,X110))
| ~ relation(X109)
| ~ function(X109) )
& ( function(relation_dom_restriction(X109,X110))
| ~ relation(X109)
| ~ function(X109) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(c_0_9,plain,
! [X95,X96] :
( ~ relation(X95)
| relation(relation_dom_restriction(X95,X96)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(c_0_10,plain,
! [X90,X91,X92] :
( ( X92 != apply(X90,X91)
| in(ordered_pair(X91,X92),X90)
| ~ in(X91,relation_dom(X90))
| ~ relation(X90)
| ~ function(X90) )
& ( ~ in(ordered_pair(X91,X92),X90)
| X92 = apply(X90,X91)
| ~ in(X91,relation_dom(X90))
| ~ relation(X90)
| ~ function(X90) )
& ( X92 != apply(X90,X91)
| X92 = empty_set
| in(X91,relation_dom(X90))
| ~ relation(X90)
| ~ function(X90) )
& ( X92 != empty_set
| X92 = apply(X90,X91)
| in(X91,relation_dom(X90))
| ~ relation(X90)
| ~ function(X90) ) ),
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_11,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]) ).
cnf(c_0_12,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_7]) ).
cnf(c_0_13,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
( relation(esk15_0)
& function(esk15_0)
& in(esk14_0,esk13_0)
& apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) != apply(esk15_0,esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_17,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_12]),c_0_13]),c_0_14]) ).
cnf(c_0_18,plain,
( apply(X1,X2) = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X114,X115,X116] :
( ( in(X115,relation_dom(X116))
| ~ in(X115,relation_dom(relation_dom_restriction(X116,X114)))
| ~ relation(X116)
| ~ function(X116) )
& ( in(X115,X114)
| ~ in(X115,relation_dom(relation_dom_restriction(X116,X114)))
| ~ relation(X116)
| ~ function(X116) )
& ( ~ in(X115,relation_dom(X116))
| ~ in(X115,X114)
| in(X115,relation_dom(relation_dom_restriction(X116,X114)))
| ~ relation(X116)
| ~ function(X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l82_funct_1])])]) ).
cnf(c_0_20,negated_conjecture,
apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) != apply(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| apply(relation_dom_restriction(X1,X2),X3) = empty_set
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13]),c_0_14]) ).
cnf(c_0_22,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,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_19]) ).
cnf(c_0_25,negated_conjecture,
apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) = empty_set,
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,plain,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
in(esk14_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,negated_conjecture,
apply(esk15_0,esk14_0) != empty_set,
inference(rw,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk14_0,relation_dom(esk15_0)),
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_25,c_0_26]),c_0_22]),c_0_23]),c_0_27])]),c_0_28]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_18]),c_0_22]),c_0_23])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU225+3 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.09 % 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
% 0.06/0.28 % Computer : n024.cluster.edu
% 0.06/0.28 % Model : x86_64 x86_64
% 0.06/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.28 % Memory : 8042.1875MB
% 0.06/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.28 % CPULimit : 300
% 0.06/0.28 % WCLimit : 300
% 0.06/0.28 % DateTime : Mon May 4 21:49:57 EDT 2026
% 0.06/0.28 % CPUTime :
% 0.06/0.28 % start to proof: theBenchmark
% 1.19/1.67 % Version : CSE_E---1.7
% 1.19/1.67 % Problem : theBenchmark.p
% 1.19/1.67 % SZS status Theorem for theBenchmark.p
% 1.19/1.67 % SZS output start CNFRefutation
% See solution above
% 1.19/1.67 % Total time : 1.361s
%------------------------------------------------------------------------------