%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU212+1 : 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 : n014.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 05:11:04 PM UTC 2026
% Result : Theorem 1.17s 1.85s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 138 ( 40 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 169 ( 65 ~; 69 |; 18 &)
% ( 8 <=>; 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 : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 55 ( 2 sgn 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
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(c_0_4,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_5,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_6,plain,
! [X56,X57,X58,X60,X61,X62,X64] :
( ( ~ in(X58,X57)
| in(ordered_pair(X58,esk1_3(X56,X57,X58)),X56)
| X57 != relation_dom(X56)
| ~ relation(X56) )
& ( ~ in(ordered_pair(X60,X61),X56)
| in(X60,X57)
| X57 != relation_dom(X56)
| ~ relation(X56) )
& ( ~ in(esk2_2(X56,X62),X62)
| ~ in(ordered_pair(esk2_2(X56,X62),X64),X56)
| X62 = relation_dom(X56)
| ~ relation(X56) )
& ( in(esk2_2(X56,X62),X62)
| in(ordered_pair(esk2_2(X56,X62),esk3_2(X56,X62)),X56)
| X62 = relation_dom(X56)
| ~ relation(X56) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_relat_1])])])])])]) ).
fof(c_0_7,plain,
! [X66,X67] : ordered_pair(X66,X67) = unordered_pair(unordered_pair(X66,X67),singleton(X66)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,negated_conjecture,
( relation(esk13_0)
& function(esk13_0)
& ( ~ in(ordered_pair(esk11_0,esk12_0),esk13_0)
| ~ in(esk11_0,relation_dom(esk13_0))
| esk12_0 != apply(esk13_0,esk11_0) )
& ( in(esk11_0,relation_dom(esk13_0))
| in(ordered_pair(esk11_0,esk12_0),esk13_0) )
& ( esk12_0 = apply(esk13_0,esk11_0)
| in(ordered_pair(esk11_0,esk12_0),esk13_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_9,plain,
! [X53,X54,X55] :
( ( X55 != apply(X53,X54)
| in(ordered_pair(X54,X55),X53)
| ~ in(X54,relation_dom(X53))
| ~ relation(X53)
| ~ function(X53) )
& ( ~ in(ordered_pair(X54,X55),X53)
| X55 = apply(X53,X54)
| ~ in(X54,relation_dom(X53))
| ~ relation(X53)
| ~ function(X53) )
& ( X55 != apply(X53,X54)
| X55 = empty_set
| in(X54,relation_dom(X53))
| ~ relation(X53)
| ~ function(X53) )
& ( X55 != empty_set
| X55 = apply(X53,X54)
| in(X54,relation_dom(X53))
| ~ relation(X53)
| ~ function(X53) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_10,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( esk12_0 = apply(esk13_0,esk11_0)
| in(ordered_pair(esk11_0,esk12_0),esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,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_9]) ).
cnf(c_0_14,negated_conjecture,
( in(esk11_0,relation_dom(esk13_0))
| in(ordered_pair(esk11_0,esk12_0),esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( in(X1,X4)
| X4 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( esk12_0 = apply(esk13_0,esk11_0)
| in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0) ),
inference(rw,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( X2 = apply(X3,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( in(esk11_0,relation_dom(esk13_0))
| in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0) ),
inference(rw,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(ordered_pair(esk11_0,esk12_0),esk13_0)
| ~ in(esk11_0,relation_dom(esk13_0))
| esk12_0 != apply(esk13_0,esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,negated_conjecture,
( apply(esk13_0,esk11_0) = esk12_0
| in(esk11_0,X1)
| X1 != relation_dom(esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
( apply(esk13_0,esk11_0) = esk12_0
| ~ in(esk11_0,relation_dom(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_17]),c_0_19])]) ).
cnf(c_0_24,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_9]) ).
cnf(c_0_25,negated_conjecture,
( in(esk11_0,relation_dom(esk13_0))
| in(esk11_0,X1)
| X1 != relation_dom(esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_17])]) ).
cnf(c_0_26,negated_conjecture,
( esk12_0 != apply(esk13_0,esk11_0)
| ~ in(esk11_0,relation_dom(esk13_0))
| ~ in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0) ),
inference(rw,[status(thm)],[c_0_21,c_0_11]) ).
cnf(c_0_27,negated_conjecture,
apply(esk13_0,esk11_0) = esk12_0,
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_22]),c_0_23]) ).
cnf(c_0_28,plain,
( in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| X1 != apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_24,c_0_11]) ).
cnf(c_0_29,negated_conjecture,
in(esk11_0,relation_dom(esk13_0)),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0)
| ~ in(esk11_0,relation_dom(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_31,negated_conjecture,
( in(unordered_pair(unordered_pair(esk11_0,X1),singleton(esk11_0)),esk13_0)
| X1 != esk12_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_27]),c_0_17]),c_0_19])]) ).
cnf(c_0_32,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_29])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.17 % Problem : SEU212+1 : TPTP v9.2.1. Released v3.3.0.
% 0.06/0.17 % 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
% 0.14/0.42 % Computer : n014.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8042.1875MB
% 0.14/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Tue May 5 02:48:21 EDT 2026
% 0.14/0.42 % CPUTime :
% 0.18/0.46 % start to proof: theBenchmark
% 1.17/1.85 % Version : CSE_E---1.7
% 1.17/1.85 % Problem : theBenchmark.p
% 1.17/1.85 % SZS status Theorem for theBenchmark.p
% 1.17/1.85 % SZS output start CNFRefutation
% See solution above
% 1.17/1.85 % Total time : 1.384s
%------------------------------------------------------------------------------