%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU223+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 : n023.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 1.52s 1.82s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 82 ( 19 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 106 ( 42 ~; 40 |; 14 &)
% ( 1 <=>; 9 =>; 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 3 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t70_funct_1,conjecture,
! [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/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
fof(t68_funct_1,lemma,
! [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(c_0_4,negated_conjecture,
~ ! [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) ) ),
inference(assume_negation,[status(cth)],[t70_funct_1]) ).
fof(c_0_5,lemma,
! [X1090,X1091,X1092,X1093] :
( ( relation_dom(X1091) = set_intersection2(relation_dom(X1092),X1090)
| X1091 != relation_dom_restriction(X1092,X1090)
| ~ relation(X1092)
| ~ function(X1092)
| ~ relation(X1091)
| ~ function(X1091) )
& ( ~ in(X1093,relation_dom(X1091))
| apply(X1091,X1093) = apply(X1092,X1093)
| X1091 != relation_dom_restriction(X1092,X1090)
| ~ relation(X1092)
| ~ function(X1092)
| ~ relation(X1091)
| ~ function(X1091) )
& ( in(esk79_3(X1090,X1091,X1092),relation_dom(X1091))
| relation_dom(X1091) != set_intersection2(relation_dom(X1092),X1090)
| X1091 = relation_dom_restriction(X1092,X1090)
| ~ relation(X1092)
| ~ function(X1092)
| ~ relation(X1091)
| ~ function(X1091) )
& ( apply(X1091,esk79_3(X1090,X1091,X1092)) != apply(X1092,esk79_3(X1090,X1091,X1092))
| relation_dom(X1091) != set_intersection2(relation_dom(X1092),X1090)
| X1091 = relation_dom_restriction(X1092,X1090)
| ~ relation(X1092)
| ~ function(X1092)
| ~ relation(X1091)
| ~ function(X1091) ) ),
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_6,plain,
! [X813,X814] :
( ( relation(relation_dom_restriction(X813,X814))
| ~ relation(X813)
| ~ function(X813) )
& ( function(relation_dom_restriction(X813,X814))
| ~ relation(X813)
| ~ function(X813) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(c_0_7,plain,
! [X782,X783] :
( ~ relation(X782)
| relation(relation_dom_restriction(X782,X783)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(c_0_8,negated_conjecture,
( relation(esk82_0)
& function(esk82_0)
& in(esk81_0,relation_dom(relation_dom_restriction(esk82_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_4])])]) ).
cnf(c_0_9,lemma,
( 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_5]) ).
cnf(c_0_10,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
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_8]) ).
cnf(c_0_13,lemma,
( 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_9]),c_0_10]),c_0_11]) ).
cnf(c_0_14,negated_conjecture,
relation(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
function(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
in(esk81_0,relation_dom(relation_dom_restriction(esk82_0,esk80_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[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]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SEU223+2 : TPTP v9.2.1. Released v3.3.0.
% 0.10/0.13 % 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
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:50:09 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.52/1.82 % Version : CSE_E---1.7
% 1.52/1.82 % Problem : theBenchmark.p
% 1.52/1.82 % SZS status Theorem for theBenchmark.p
% 1.52/1.82 % SZS output start CNFRefutation
% See solution above
% 1.52/1.83 % Total time : 1.423s
%------------------------------------------------------------------------------