%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU239+1 : 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 : n016.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 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 107 ( 6 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 119 ( 49 ~; 53 |; 6 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 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 : 51 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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,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_6,negated_conjecture,
! [X74] :
( relation(esk3_0)
& ( in(esk4_0,relation_field(esk3_0))
| ~ reflexive(esk3_0) )
& ( ~ in(ordered_pair(esk4_0,esk4_0),esk3_0)
| ~ reflexive(esk3_0) )
& ( reflexive(esk3_0)
| ~ in(X74,relation_field(esk3_0))
| in(ordered_pair(X74,X74),esk3_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_5])])])])]) ).
fof(c_0_7,plain,
! [X59,X60] : ordered_pair(X59,X60) = unordered_pair(unordered_pair(X59,X60),singleton(X59)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,plain,
! [X54,X55,X56,X57] :
( ( ~ is_reflexive_in(X54,X55)
| ~ in(X56,X55)
| in(ordered_pair(X56,X56),X54)
| ~ relation(X54) )
& ( in(esk1_2(X54,X57),X57)
| is_reflexive_in(X54,X57)
| ~ relation(X54) )
& ( ~ in(ordered_pair(esk1_2(X54,X57),esk1_2(X54,X57)),X54)
| is_reflexive_in(X54,X57)
| ~ relation(X54) ) ),
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,negated_conjecture,
( reflexive(esk3_0)
| in(ordered_pair(X1,X1),esk3_0)
| ~ in(X1,relation_field(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X50,X51] : unordered_pair(X50,X51) = unordered_pair(X51,X50),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,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_13,plain,
( is_reflexive_in(X1,X2)
| ~ in(ordered_pair(esk1_2(X1,X2),esk1_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( reflexive(esk3_0)
| in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),esk3_0)
| ~ in(X1,relation_field(esk3_0)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( in(esk1_2(X1,X2),X2)
| is_reflexive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(ordered_pair(esk4_0,esk4_0),esk3_0)
| ~ reflexive(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,plain,
( in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
fof(c_0_20,plain,
! [X62] :
( ( ~ reflexive(X62)
| is_reflexive_in(X62,relation_field(X62))
| ~ relation(X62) )
& ( ~ is_reflexive_in(X62,relation_field(X62))
| reflexive(X62)
| ~ relation(X62) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).
cnf(c_0_21,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2)),singleton(esk1_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( reflexive(esk3_0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),esk3_0)
| ~ in(X1,relation_field(esk3_0)) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( is_reflexive_in(esk3_0,X1)
| in(esk1_2(esk3_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( ~ reflexive(esk3_0)
| ~ in(unordered_pair(unordered_pair(esk4_0,esk4_0),singleton(esk4_0)),esk3_0) ),
inference(rw,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_25,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),X2)
| ~ is_reflexive_in(X2,X3)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_26,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_28,negated_conjecture,
( reflexive(esk3_0)
| is_reflexive_in(esk3_0,relation_field(esk3_0))
| in(unordered_pair(singleton(esk1_2(esk3_0,relation_field(esk3_0))),unordered_pair(esk1_2(esk3_0,relation_field(esk3_0)),esk1_2(esk3_0,relation_field(esk3_0)))),esk3_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( ~ reflexive(esk3_0)
| ~ in(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk4_0)),esk3_0) ),
inference(rw,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_30,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),X2)
| ~ reflexive(X2)
| ~ relation(X2)
| ~ in(X1,relation_field(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( in(esk4_0,relation_field(esk3_0))
| ~ reflexive(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
( reflexive(esk3_0)
| is_reflexive_in(esk3_0,relation_field(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_17])]) ).
cnf(c_0_33,negated_conjecture,
~ reflexive(esk3_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_17])]),c_0_31]) ).
cnf(c_0_34,plain,
( reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_35,negated_conjecture,
is_reflexive_in(esk3_0,relation_field(esk3_0)),
inference(sr,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_17])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU239+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n016.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:51:36 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------