%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU268+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 : n013.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 05:11:18 PM UTC 2026
% Result : Theorem 6.29s 4.57s
% Output : CNFRefutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 20 unt; 0 def)
% Number of atoms : 104 ( 26 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 124 ( 52 ~; 55 |; 10 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 51 ( 3 sgn 25 !; 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(d1_wellord2,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = inclusion_relation(X1)
<=> ( relation_field(X2) = X1
& ! [X3,X4] :
( ( in(X3,X1)
& in(X4,X1) )
=> ( in(ordered_pair(X3,X4),X2)
<=> subset(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).
fof(l1_wellord1,lemma,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(dt_k1_wellord2,axiom,
! [X1] : relation(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_wellord2,conjecture,
! [X1] : reflexive(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
fof(c_0_7,plain,
! [X1105,X1106] : ordered_pair(X1105,X1106) = unordered_pair(unordered_pair(X1105,X1106),singleton(X1105)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,lemma,
! [X1665] : unordered_pair(X1665,X1665) = singleton(X1665),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_9,plain,
! [X926,X927,X928,X929] :
( ( relation_field(X927) = X926
| X927 != inclusion_relation(X926)
| ~ relation(X927) )
& ( ~ in(ordered_pair(X928,X929),X927)
| subset(X928,X929)
| ~ in(X928,X926)
| ~ in(X929,X926)
| X927 != inclusion_relation(X926)
| ~ relation(X927) )
& ( ~ subset(X928,X929)
| in(ordered_pair(X928,X929),X927)
| ~ in(X928,X926)
| ~ in(X929,X926)
| X927 != inclusion_relation(X926)
| ~ relation(X927) )
& ( in(esk29_2(X926,X927),X926)
| relation_field(X927) != X926
| X927 = inclusion_relation(X926)
| ~ relation(X927) )
& ( in(esk30_2(X926,X927),X926)
| relation_field(X927) != X926
| X927 = inclusion_relation(X926)
| ~ relation(X927) )
& ( ~ in(ordered_pair(esk29_2(X926,X927),esk30_2(X926,X927)),X927)
| ~ subset(esk29_2(X926,X927),esk30_2(X926,X927))
| relation_field(X927) != X926
| X927 = inclusion_relation(X926)
| ~ relation(X927) )
& ( in(ordered_pair(esk29_2(X926,X927),esk30_2(X926,X927)),X927)
| subset(esk29_2(X926,X927),esk30_2(X926,X927))
| relation_field(X927) != X926
| X927 = inclusion_relation(X926)
| ~ relation(X927) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_wellord2])])])])]) ).
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]) ).
cnf(c_0_11,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,lemma,
! [X1264,X1265] :
( ( ~ reflexive(X1264)
| ~ in(X1265,relation_field(X1264))
| in(ordered_pair(X1265,X1265),X1264)
| ~ relation(X1264) )
& ( in(esk89_1(X1264),relation_field(X1264))
| reflexive(X1264)
| ~ relation(X1264) )
& ( ~ in(ordered_pair(esk89_1(X1264),esk89_1(X1264)),X1264)
| reflexive(X1264)
| ~ relation(X1264) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l1_wellord1])])])])]) ).
cnf(c_0_13,plain,
( in(ordered_pair(X1,X2),X3)
| ~ subset(X1,X2)
| ~ in(X1,X4)
| ~ in(X2,X4)
| X3 != inclusion_relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_15,plain,
! [X1175] : relation(inclusion_relation(X1175)),
inference(variable_rename,[status(thm)],[dt_k1_wellord2]) ).
cnf(c_0_16,lemma,
( reflexive(X1)
| ~ in(ordered_pair(esk89_1(X1),esk89_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X3 != inclusion_relation(X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
relation(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X1353] : subset(X1353,X1353),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] : reflexive(inclusion_relation(X1)),
inference(assume_negation,[status(cth)],[t2_wellord2]) ).
cnf(c_0_21,plain,
( relation_field(X1) = X2
| X1 != inclusion_relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,lemma,
( reflexive(X1)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk89_1(X1),esk89_1(X1)),unordered_pair(esk89_1(X1),esk89_1(X1))),X1) ),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_23,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),inclusion_relation(X3))
| ~ subset(X1,X2)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18])]) ).
cnf(c_0_24,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,negated_conjecture,
~ reflexive(inclusion_relation(esk120_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_26,lemma,
( in(esk89_1(X1),relation_field(X1))
| reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,plain,
relation_field(inclusion_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_18])]) ).
cnf(c_0_28,lemma,
( reflexive(inclusion_relation(X1))
| ~ in(esk89_1(inclusion_relation(X1)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]),c_0_24])]) ).
cnf(c_0_29,negated_conjecture,
~ reflexive(inclusion_relation(esk120_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,lemma,
reflexive(inclusion_relation(X1)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_18])]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU268+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 : n013.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 02:52:41 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.29/4.57 % Version : CSE_E---1.7
% 6.29/4.57 % Problem : theBenchmark.p
% 6.29/4.57 % SZS status Theorem for theBenchmark.p
% 6.29/4.57 % SZS output start CNFRefutation
% See solution above
% 6.29/4.58 % Total time : 3.430s
%------------------------------------------------------------------------------