%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU239+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 : n010.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 05:11:13 PM UTC 2026
% Result : Theorem 48.16s 28.28s
% Output : CNFRefutation 48.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 95 ( 7 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 103 ( 42 ~; 44 |; 6 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(l1_wellord1,conjecture,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
fof(d1_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
fof(d9_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(c_0_5,plain,
! [X880,X881] : ordered_pair(X880,X881) = unordered_pair(unordered_pair(X880,X881),singleton(X880)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_6,lemma,
! [X1298] : unordered_pair(X1298,X1298) = singleton(X1298),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[l1_wellord1]) ).
fof(c_0_8,plain,
! [X711,X712,X713,X714] :
( ( ~ is_reflexive_in(X711,X712)
| ~ in(X713,X712)
| in(ordered_pair(X713,X713),X711)
| ~ relation(X711) )
& ( in(esk21_2(X711,X714),X714)
| is_reflexive_in(X711,X714)
| ~ relation(X711) )
& ( ~ in(ordered_pair(esk21_2(X711,X714),esk21_2(X711,X714)),X711)
| is_reflexive_in(X711,X714)
| ~ relation(X711) ) ),
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)],[d1_relat_2])])])])])]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
! [X992] :
( relation(esk67_0)
& ( in(esk68_0,relation_field(esk67_0))
| ~ reflexive(esk67_0) )
& ( ~ in(ordered_pair(esk68_0,esk68_0),esk67_0)
| ~ reflexive(esk67_0) )
& ( reflexive(esk67_0)
| ~ in(X992,relation_field(esk67_0))
| in(ordered_pair(X992,X992),esk67_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
cnf(c_0_12,plain,
( is_reflexive_in(X1,X2)
| ~ in(ordered_pair(esk21_2(X1,X2),esk21_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( reflexive(esk67_0)
| in(ordered_pair(X1,X1),esk67_0)
| ~ in(X1,relation_field(esk67_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk21_2(X1,X2),esk21_2(X1,X2)),unordered_pair(esk21_2(X1,X2),esk21_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
( reflexive(esk67_0)
| in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1)),esk67_0)
| ~ in(X1,relation_field(esk67_0)) ),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
relation(esk67_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X920] :
( ( ~ reflexive(X920)
| is_reflexive_in(X920,relation_field(X920))
| ~ relation(X920) )
& ( ~ is_reflexive_in(X920,relation_field(X920))
| reflexive(X920)
| ~ relation(X920) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).
cnf(c_0_19,negated_conjecture,
( reflexive(esk67_0)
| is_reflexive_in(esk67_0,X1)
| ~ in(esk21_2(esk67_0,X1),relation_field(esk67_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_20,plain,
( in(esk21_2(X1,X2),X2)
| is_reflexive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(ordered_pair(esk68_0,esk68_0),esk67_0)
| ~ reflexive(esk67_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( reflexive(esk67_0)
| is_reflexive_in(esk67_0,relation_field(esk67_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17])]) ).
cnf(c_0_24,plain,
( in(ordered_pair(X3,X3),X1)
| ~ is_reflexive_in(X1,X2)
| ~ in(X3,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
( ~ reflexive(esk67_0)
| ~ in(unordered_pair(unordered_pair(esk68_0,esk68_0),unordered_pair(esk68_0,esk68_0)),esk67_0) ),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_26,negated_conjecture,
reflexive(esk67_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17])]) ).
cnf(c_0_27,plain,
( in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X3)),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(rw,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_28,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( in(esk68_0,relation_field(esk67_0))
| ~ reflexive(esk67_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk68_0,esk68_0),unordered_pair(esk68_0,esk68_0)),esk67_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_31,plain,
( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1)),X2)
| ~ reflexive(X2)
| ~ relation(X2)
| ~ in(X1,relation_field(X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
in(esk68_0,relation_field(esk67_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_26])]) ).
cnf(c_0_33,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_30,c_0_31]),c_0_26]),c_0_17]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU239+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.15/0.33 % Computer : n010.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 02:50:51 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 48.16/28.28 % Version : CSE_E---1.7
% 48.16/28.28 % Problem : theBenchmark.p
% 48.16/28.28 % SZS status Theorem for theBenchmark.p
% 48.16/28.28 % SZS output start CNFRefutation
% See solution above
% 48.36/28.46 % Total time : 21.498s
%------------------------------------------------------------------------------