%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU037+1 : 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 : n011.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 05:10:32 PM UTC 2026
% Result : Theorem 1.23s 1.72s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 99 ( 26 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 124 ( 51 ~; 49 |; 14 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 46 ( 3 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t71_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_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(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
inference(assume_negation,[status(cth)],[t71_funct_1]) ).
fof(c_0_6,plain,
! [X113,X114,X115,X116] :
( ( relation_dom(X114) = set_intersection2(relation_dom(X115),X113)
| X114 != relation_dom_restriction(X115,X113)
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) )
& ( ~ in(X116,relation_dom(X114))
| apply(X114,X116) = apply(X115,X116)
| X114 != relation_dom_restriction(X115,X113)
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) )
& ( in(esk12_3(X113,X114,X115),relation_dom(X114))
| relation_dom(X114) != set_intersection2(relation_dom(X115),X113)
| X114 = relation_dom_restriction(X115,X113)
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) )
& ( apply(X114,esk12_3(X113,X114,X115)) != apply(X115,esk12_3(X113,X114,X115))
| relation_dom(X114) != set_intersection2(relation_dom(X115),X113)
| X114 = relation_dom_restriction(X115,X113)
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) ) ),
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_7,plain,
! [X82,X83] :
( ( relation(relation_dom_restriction(X82,X83))
| ~ relation(X82)
| ~ function(X82) )
& ( function(relation_dom_restriction(X82,X83))
| ~ relation(X82)
| ~ function(X82) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(c_0_8,plain,
! [X73,X74] :
( ~ relation(X73)
| relation(relation_dom_restriction(X73,X74)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(c_0_9,negated_conjecture,
( relation(esk15_0)
& function(esk15_0)
& in(esk14_0,set_intersection2(relation_dom(esk15_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_5])])]) ).
fof(c_0_10,plain,
! [X71,X72] : set_intersection2(X71,X72) = set_intersection2(X72,X71),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_11,plain,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| X1 != relation_dom_restriction(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
in(esk14_0,set_intersection2(relation_dom(esk15_0),esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( set_intersection2(relation_dom(X1),X2) = relation_dom(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_11]),c_0_12]),c_0_13]) ).
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_6]) ).
cnf(c_0_18,negated_conjecture,
in(esk14_0,set_intersection2(esk13_0,relation_dom(esk15_0))),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( set_intersection2(X1,relation_dom(X2)) = relation_dom(relation_dom_restriction(X2,X1))
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,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_12]),c_0_13]) ).
cnf(c_0_23,negated_conjecture,
in(esk14_0,relation_dom(relation_dom_restriction(esk15_0,esk13_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_24,negated_conjecture,
apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) != apply(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,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_22,c_0_23]),c_0_20]),c_0_21])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU037+1 : 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
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 5 02:57:02 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % start to proof: theBenchmark
% 1.23/1.72 % Version : CSE_E---1.7
% 1.23/1.72 % Problem : theBenchmark.p
% 1.23/1.72 % SZS status Theorem for theBenchmark.p
% 1.23/1.72 % SZS output start CNFRefutation
% See solution above
% 1.23/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------