%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU212+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 : n006.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 05:11:05 PM UTC 2026
% Result : Theorem 5.99s 4.49s
% Output : CNFRefutation 6.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 145 ( 40 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 168 ( 67 ~; 68 |; 17 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 3 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t8_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
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(t20_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_6,plain,
! [X681,X682] : ordered_pair(X681,X682) = unordered_pair(unordered_pair(X681,X682),singleton(X681)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,lemma,
! [X996] : unordered_pair(X996,X996) = singleton(X996),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
inference(assume_negation,[status(cth)],[t8_funct_1]) ).
fof(c_0_9,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_10,lemma,
! [X888,X889,X890] :
( ( in(X888,relation_dom(X890))
| ~ in(ordered_pair(X888,X889),X890)
| ~ relation(X890) )
& ( in(X889,relation_rng(X890))
| ~ in(ordered_pair(X888,X889),X890)
| ~ relation(X890) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,negated_conjecture,
( relation(esk72_0)
& function(esk72_0)
& ( ~ in(ordered_pair(esk70_0,esk71_0),esk72_0)
| ~ in(esk70_0,relation_dom(esk72_0))
| esk71_0 != apply(esk72_0,esk70_0) )
& ( in(esk70_0,relation_dom(esk72_0))
| in(ordered_pair(esk70_0,esk71_0),esk72_0) )
& ( esk71_0 = apply(esk72_0,esk70_0)
| in(ordered_pair(esk70_0,esk71_0),esk72_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_14,plain,
! [X635,X636,X637] :
( ( X637 != apply(X635,X636)
| in(ordered_pair(X636,X637),X635)
| ~ in(X636,relation_dom(X635))
| ~ relation(X635)
| ~ function(X635) )
& ( ~ in(ordered_pair(X636,X637),X635)
| X637 = apply(X635,X636)
| ~ in(X636,relation_dom(X635))
| ~ relation(X635)
| ~ function(X635) )
& ( X637 != apply(X635,X636)
| X637 = empty_set
| in(X636,relation_dom(X635))
| ~ relation(X635)
| ~ function(X635) )
& ( X637 != empty_set
| X637 = apply(X635,X636)
| in(X636,relation_dom(X635))
| ~ relation(X635)
| ~ function(X635) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_15,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_17,plain,
! [X472,X473] : unordered_pair(X472,X473) = unordered_pair(X473,X472),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_18,negated_conjecture,
( in(esk70_0,relation_dom(esk72_0))
| in(ordered_pair(esk70_0,esk71_0),esk72_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( X2 = apply(X3,X1)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(ordered_pair(esk70_0,esk71_0),esk72_0)
| ~ in(esk70_0,relation_dom(esk72_0))
| esk71_0 != apply(esk72_0,esk70_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( in(esk70_0,relation_dom(esk72_0))
| in(unordered_pair(unordered_pair(esk70_0,esk71_0),unordered_pair(esk70_0,esk70_0)),esk72_0) ),
inference(rw,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_24,plain,
( X2 = apply(X3,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( esk71_0 = apply(esk72_0,esk70_0)
| in(ordered_pair(esk70_0,esk71_0),esk72_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
( esk71_0 != apply(esk72_0,esk70_0)
| ~ in(esk70_0,relation_dom(esk72_0))
| ~ in(unordered_pair(unordered_pair(esk70_0,esk71_0),unordered_pair(esk70_0,esk70_0)),esk72_0) ),
inference(rw,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_27,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( in(unordered_pair(unordered_pair(esk70_0,esk70_0),unordered_pair(esk70_0,esk71_0)),esk72_0)
| in(esk70_0,relation_dom(esk72_0)) ),
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
relation(esk72_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,plain,
( X1 = apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(csr,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_31,negated_conjecture,
( esk71_0 = apply(esk72_0,esk70_0)
| in(unordered_pair(unordered_pair(esk70_0,esk71_0),unordered_pair(esk70_0,esk70_0)),esk72_0) ),
inference(rw,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_32,plain,
( in(ordered_pair(X3,X1),X2)
| X1 != apply(X2,X3)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_33,negated_conjecture,
( apply(esk72_0,esk70_0) != esk71_0
| ~ in(unordered_pair(unordered_pair(esk70_0,esk70_0),unordered_pair(esk70_0,esk71_0)),esk72_0)
| ~ in(esk70_0,relation_dom(esk72_0)) ),
inference(rw,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
in(esk70_0,relation_dom(esk72_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_35,plain,
( X1 = apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X1)),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_36,negated_conjecture,
( apply(esk72_0,esk70_0) = esk71_0
| in(unordered_pair(unordered_pair(esk70_0,esk70_0),unordered_pair(esk70_0,esk71_0)),esk72_0) ),
inference(rw,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_37,negated_conjecture,
function(esk72_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_38,plain,
( in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2)
| X1 != apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_39,negated_conjecture,
( apply(esk72_0,esk70_0) != esk71_0
| ~ in(unordered_pair(unordered_pair(esk70_0,esk70_0),unordered_pair(esk70_0,esk71_0)),esk72_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_40,negated_conjecture,
apply(esk72_0,esk70_0) = esk71_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_29]),c_0_37])]) ).
cnf(c_0_41,plain,
( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,apply(X2,X1))),X2)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_38]),c_0_22]) ).
cnf(c_0_42,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk70_0,esk70_0),unordered_pair(esk70_0,esk71_0)),esk72_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_43,negated_conjecture,
$false,
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_41,c_0_40]),c_0_29]),c_0_37]),c_0_34])]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU212+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:49:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 5.99/4.49 % Version : CSE_E---1.7
% 5.99/4.49 % Problem : theBenchmark.p
% 5.99/4.49 % SZS status Theorem for theBenchmark.p
% 5.99/4.49 % SZS output start CNFRefutation
% See solution above
% 6.08/4.50 % Total time : 3.426s
%------------------------------------------------------------------------------