%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU254+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 : n005.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 05:11:16 PM UTC 2026
% Result : Theorem 6.57s 4.50s
% Output : CNFRefutation 6.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 11 unt; 0 def)
% Number of atoms : 179 ( 6 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 196 ( 78 ~; 95 |; 12 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 132 ( 13 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l2_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X4),X1) )
=> in(ordered_pair(X2,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_wellord1) ).
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(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(dt_k2_wellord1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(t24_wellord1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( transitive(X2)
=> transitive(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_wellord1) ).
fof(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(t16_wellord1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(c_0_7,plain,
! [X72,X73,X74,X75] :
( ( ~ transitive(X72)
| ~ in(ordered_pair(X73,X74),X72)
| ~ in(ordered_pair(X74,X75),X72)
| in(ordered_pair(X73,X75),X72)
| ~ relation(X72) )
& ( in(ordered_pair(esk2_1(X72),esk3_1(X72)),X72)
| transitive(X72)
| ~ relation(X72) )
& ( in(ordered_pair(esk3_1(X72),esk4_1(X72)),X72)
| transitive(X72)
| ~ relation(X72) )
& ( ~ in(ordered_pair(esk2_1(X72),esk4_1(X72)),X72)
| transitive(X72)
| ~ relation(X72) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_wellord1])])])])]) ).
fof(c_0_8,plain,
! [X61,X62] : ordered_pair(X61,X62) = unordered_pair(unordered_pair(X61,X62),singleton(X61)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_9,plain,
( in(ordered_pair(esk3_1(X1),esk4_1(X1)),X1)
| transitive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X57,X58] : unordered_pair(X57,X58) = unordered_pair(X58,X57),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( transitive(X1)
| in(unordered_pair(unordered_pair(esk3_1(X1),esk4_1(X1)),singleton(esk3_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X65,X66] :
( ~ relation(X65)
| relation(relation_restriction(X65,X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( transitive(X2)
=> transitive(relation_restriction(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t24_wellord1]) ).
cnf(c_0_16,plain,
( in(ordered_pair(esk2_1(X1),esk3_1(X1)),X1)
| transitive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_17,plain,
! [X84,X85,X86,X87] :
( ( in(X84,X86)
| ~ in(ordered_pair(X84,X85),cartesian_product2(X86,X87)) )
& ( in(X85,X87)
| ~ in(ordered_pair(X84,X85),cartesian_product2(X86,X87)) )
& ( ~ in(X84,X86)
| ~ in(X85,X87)
| in(ordered_pair(X84,X85),cartesian_product2(X86,X87)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
cnf(c_0_18,plain,
( transitive(X1)
| in(unordered_pair(singleton(esk3_1(X1)),unordered_pair(esk3_1(X1),esk4_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,negated_conjecture,
( relation(esk11_0)
& transitive(esk11_0)
& ~ transitive(relation_restriction(esk11_0,esk10_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_21,plain,
( transitive(X1)
| in(unordered_pair(unordered_pair(esk2_1(X1),esk3_1(X1)),singleton(esk2_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_22,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( in(ordered_pair(X2,X4),X1)
| ~ transitive(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_24,plain,
! [X88,X89,X90] :
( ( in(X88,X90)
| ~ in(X88,relation_restriction(X90,X89))
| ~ relation(X90) )
& ( in(X88,cartesian_product2(X89,X89))
| ~ in(X88,relation_restriction(X90,X89))
| ~ relation(X90) )
& ( ~ in(X88,X90)
| ~ in(X88,cartesian_product2(X89,X89))
| in(X88,relation_restriction(X90,X89))
| ~ relation(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_wellord1])])]) ).
cnf(c_0_25,plain,
( transitive(relation_restriction(X1,X2))
| in(unordered_pair(singleton(esk3_1(relation_restriction(X1,X2))),unordered_pair(esk3_1(relation_restriction(X1,X2)),esk4_1(relation_restriction(X1,X2)))),relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( transitive(X1)
| in(unordered_pair(singleton(esk2_1(X1)),unordered_pair(esk2_1(X1),esk3_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_28,plain,
( transitive(X1)
| ~ in(ordered_pair(esk2_1(X1),esk4_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_29,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_22,c_0_10]) ).
cnf(c_0_30,plain,
( in(unordered_pair(unordered_pair(X2,X4),singleton(X2)),X1)
| ~ relation(X1)
| ~ transitive(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_10]),c_0_10]),c_0_10]) ).
cnf(c_0_31,plain,
( in(X1,X2)
| ~ in(X1,relation_restriction(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(unordered_pair(singleton(esk3_1(relation_restriction(esk11_0,X1))),unordered_pair(esk3_1(relation_restriction(esk11_0,X1)),esk4_1(relation_restriction(esk11_0,X1)))),relation_restriction(esk11_0,X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( transitive(relation_restriction(X1,X2))
| in(unordered_pair(singleton(esk2_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk3_1(relation_restriction(X1,X2)))),relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_34,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_35,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,plain,
( transitive(X1)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk2_1(X1),esk4_1(X1)),singleton(esk2_1(X1))),X1) ),
inference(rw,[status(thm)],[c_0_28,c_0_10]) ).
cnf(c_0_37,plain,
( in(X1,relation_restriction(X2,X3))
| ~ in(X1,X2)
| ~ in(X1,cartesian_product2(X3,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_29,c_0_13]) ).
cnf(c_0_39,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| ~ transitive(X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X2)),X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_40,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(unordered_pair(singleton(esk3_1(relation_restriction(esk11_0,X1))),unordered_pair(esk3_1(relation_restriction(esk11_0,X1)),esk4_1(relation_restriction(esk11_0,X1)))),esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_26])]) ).
cnf(c_0_41,negated_conjecture,
transitive(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_42,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(unordered_pair(singleton(esk2_1(relation_restriction(esk11_0,X1))),unordered_pair(esk2_1(relation_restriction(esk11_0,X1)),esk3_1(relation_restriction(esk11_0,X1)))),relation_restriction(esk11_0,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_43,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_34,c_0_10]) ).
cnf(c_0_44,plain,
( in(X1,cartesian_product2(X2,X2))
| ~ in(X1,relation_restriction(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_45,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_35,c_0_10]) ).
cnf(c_0_46,plain,
( transitive(X1)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk2_1(X1)),unordered_pair(esk2_1(X1),esk4_1(X1))),X1) ),
inference(rw,[status(thm)],[c_0_36,c_0_13]) ).
cnf(c_0_47,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),relation_restriction(X3,X4))
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| ~ in(X2,X4)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(unordered_pair(singleton(X2),unordered_pair(X2,esk4_1(relation_restriction(esk11_0,X1)))),esk11_0)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,esk3_1(relation_restriction(esk11_0,X1)))),esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_26])]) ).
cnf(c_0_49,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(unordered_pair(singleton(esk2_1(relation_restriction(esk11_0,X1))),unordered_pair(esk2_1(relation_restriction(esk11_0,X1)),esk3_1(relation_restriction(esk11_0,X1)))),esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_42]),c_0_26])]) ).
cnf(c_0_50,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_43,c_0_13]) ).
cnf(c_0_51,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(unordered_pair(singleton(esk2_1(relation_restriction(esk11_0,X1))),unordered_pair(esk2_1(relation_restriction(esk11_0,X1)),esk3_1(relation_restriction(esk11_0,X1)))),cartesian_product2(X1,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_42]),c_0_26])]) ).
cnf(c_0_52,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_45,c_0_13]) ).
cnf(c_0_53,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(unordered_pair(singleton(esk3_1(relation_restriction(esk11_0,X1))),unordered_pair(esk3_1(relation_restriction(esk11_0,X1)),esk4_1(relation_restriction(esk11_0,X1)))),cartesian_product2(X1,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_32]),c_0_26])]) ).
cnf(c_0_54,plain,
( transitive(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk2_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk4_1(relation_restriction(X1,X2)))),X1)
| ~ in(esk4_1(relation_restriction(X1,X2)),X2)
| ~ in(esk2_1(relation_restriction(X1,X2)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_19]) ).
cnf(c_0_55,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(unordered_pair(singleton(esk2_1(relation_restriction(esk11_0,X1))),unordered_pair(esk2_1(relation_restriction(esk11_0,X1)),esk4_1(relation_restriction(esk11_0,X1)))),esk11_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(esk2_1(relation_restriction(esk11_0,X1)),X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( transitive(relation_restriction(esk11_0,X1))
| in(esk4_1(relation_restriction(esk11_0,X1)),X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
~ transitive(relation_restriction(esk11_0,esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_59,negated_conjecture,
transitive(relation_restriction(esk11_0,X1)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_26])]),c_0_56]),c_0_57]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU254+1 : 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 : n005.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 02:54:30 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.57/4.50 % Version : CSE_E---1.7
% 6.57/4.50 % Problem : theBenchmark.p
% 6.57/4.50 % SZS status Theorem for theBenchmark.p
% 6.57/4.50 % SZS output start CNFRefutation
% See solution above
% 6.57/4.52 % Total time : 3.368s
%------------------------------------------------------------------------------