%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU225+2 : 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 : n005.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 1.82s 1.93s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 119 ( 25 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 145 ( 56 ~; 50 |; 19 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 ( 2 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/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(t70_funct_1,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_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(t86_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_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,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,
! [X688,X689,X690] :
( ( X690 != apply(X688,X689)
| in(ordered_pair(X689,X690),X688)
| ~ in(X689,relation_dom(X688))
| ~ relation(X688)
| ~ function(X688) )
& ( ~ in(ordered_pair(X689,X690),X688)
| X690 = apply(X688,X689)
| ~ in(X689,relation_dom(X688))
| ~ relation(X688)
| ~ function(X688) )
& ( X690 != apply(X688,X689)
| X690 = empty_set
| in(X689,relation_dom(X688))
| ~ relation(X688)
| ~ function(X688) )
& ( X690 != empty_set
| X690 = apply(X688,X689)
| in(X689,relation_dom(X688))
| ~ relation(X688)
| ~ function(X688) ) ),
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(esk82_0)
& function(esk82_0)
& in(esk81_0,esk80_0)
& apply(relation_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,lemma,
! [X1108,X1109,X1110] :
( ~ relation(X1110)
| ~ function(X1110)
| ~ in(X1109,relation_dom(relation_dom_restriction(X1110,X1108)))
| apply(relation_dom_restriction(X1110,X1108),X1109) = apply(X1110,X1109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t70_funct_1])]) ).
cnf(c_0_11,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]) ).
cnf(c_0_12,negated_conjecture,
apply(relation_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,lemma,
( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
function(esk82_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_11]) ).
cnf(c_0_17,negated_conjecture,
~ in(esk81_0,relation_dom(relation_dom_restriction(esk82_0,esk80_0))),
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])]) ).
fof(c_0_18,plain,
! [X819,X820] :
( ( relation(relation_dom_restriction(X819,X820))
| ~ relation(X819)
| ~ function(X819) )
& ( function(relation_dom_restriction(X819,X820))
| ~ relation(X819)
| ~ function(X819) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
cnf(c_0_19,negated_conjecture,
( apply(esk82_0,esk81_0) != empty_set
| ~ relation(relation_dom_restriction(esk82_0,esk80_0))
| ~ function(relation_dom_restriction(esk82_0,esk80_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X788,X789] :
( ~ relation(X788)
| relation(relation_dom_restriction(X788,X789)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(c_0_22,lemma,
! [X1125,X1126,X1127] :
( ( in(X1125,X1126)
| ~ in(X1125,relation_dom(relation_dom_restriction(X1127,X1126)))
| ~ relation(X1127) )
& ( in(X1125,relation_dom(X1127))
| ~ in(X1125,relation_dom(relation_dom_restriction(X1127,X1126)))
| ~ relation(X1127) )
& ( ~ in(X1125,X1126)
| ~ in(X1125,relation_dom(X1127))
| in(X1125,relation_dom(relation_dom_restriction(X1127,X1126)))
| ~ relation(X1127) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t86_relat_1])])]) ).
cnf(c_0_23,negated_conjecture,
( apply(esk82_0,esk81_0) != empty_set
| ~ relation(relation_dom_restriction(esk82_0,esk80_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14]),c_0_15])]) ).
cnf(c_0_24,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,lemma,
( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
| ~ in(X1,X2)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
in(esk81_0,esk80_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
apply(esk82_0,esk81_0) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14])]) ).
cnf(c_0_28,lemma,
~ in(esk81_0,relation_dom(esk82_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_25]),c_0_14]),c_0_26])]) ).
cnf(c_0_29,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_27,c_0_16]),c_0_14]),c_0_15])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU225+2 : 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 : n005.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 02:50:00 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.82/1.93 % Version : CSE_E---1.7
% 1.82/1.93 % Problem : theBenchmark.p
% 1.82/1.93 % SZS status Theorem for theBenchmark.p
% 1.82/1.93 % SZS output start CNFRefutation
% See solution above
% 1.82/1.94 % Total time : 1.424s
%------------------------------------------------------------------------------