%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU241+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 : n027.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 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 10 unt; 0 def)
% Number of atoms : 190 ( 23 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 228 ( 93 ~; 105 |; 17 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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; 3 con; 0-2 aty)
% Number of variables : 95 ( 5 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3_wellord1,conjecture,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
fof(d4_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_antisymmetric_in(X1,X2)
<=> ! [X3,X4] :
( ( in(X3,X2)
& in(X4,X2)
& in(ordered_pair(X3,X4),X1)
& in(ordered_pair(X4,X3),X1) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
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(t30_relat_1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
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(d12_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1) )
=> X2 = X3 ) ) ),
inference(assume_negation,[status(cth)],[l3_wellord1]) ).
fof(c_0_7,plain,
! [X61,X62,X63,X64,X65] :
( ( ~ is_antisymmetric_in(X61,X62)
| ~ in(X63,X62)
| ~ in(X64,X62)
| ~ in(ordered_pair(X63,X64),X61)
| ~ in(ordered_pair(X64,X63),X61)
| X63 = X64
| ~ relation(X61) )
& ( in(esk1_2(X61,X65),X65)
| is_antisymmetric_in(X61,X65)
| ~ relation(X61) )
& ( in(esk2_2(X61,X65),X65)
| is_antisymmetric_in(X61,X65)
| ~ relation(X61) )
& ( in(ordered_pair(esk1_2(X61,X65),esk2_2(X61,X65)),X61)
| is_antisymmetric_in(X61,X65)
| ~ relation(X61) )
& ( in(ordered_pair(esk2_2(X61,X65),esk1_2(X61,X65)),X61)
| is_antisymmetric_in(X61,X65)
| ~ relation(X61) )
& ( esk1_2(X61,X65) != esk2_2(X61,X65)
| is_antisymmetric_in(X61,X65)
| ~ relation(X61) ) ),
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_2])])])])])]) ).
fof(c_0_8,plain,
! [X68,X69] : ordered_pair(X68,X69) = unordered_pair(unordered_pair(X68,X69),singleton(X68)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,negated_conjecture,
! [X83,X84] :
( relation(esk4_0)
& ( in(ordered_pair(esk5_0,esk6_0),esk4_0)
| ~ antisymmetric(esk4_0) )
& ( in(ordered_pair(esk6_0,esk5_0),esk4_0)
| ~ antisymmetric(esk4_0) )
& ( esk5_0 != esk6_0
| ~ antisymmetric(esk4_0) )
& ( antisymmetric(esk4_0)
| ~ in(ordered_pair(X83,X84),esk4_0)
| ~ in(ordered_pair(X84,X83),esk4_0)
| X83 = X84 ) ),
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_6])])])])]) ).
fof(c_0_10,plain,
! [X95,X96,X97] :
( ( in(X95,relation_field(X97))
| ~ in(ordered_pair(X95,X96),X97)
| ~ relation(X97) )
& ( in(X96,relation_field(X97))
| ~ in(ordered_pair(X95,X96),X97)
| ~ relation(X97) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_relat_1])])]) ).
cnf(c_0_11,plain,
( X3 = X4
| ~ is_antisymmetric_in(X1,X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X56,X57] : unordered_pair(X56,X57) = unordered_pair(X57,X56),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_14,negated_conjecture,
( in(ordered_pair(esk5_0,esk6_0),esk4_0)
| ~ antisymmetric(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( in(ordered_pair(esk6_0,esk5_0),esk4_0)
| ~ antisymmetric(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( X3 = X4
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X3,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).
cnf(c_0_19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0)
| ~ antisymmetric(esk4_0) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_21,negated_conjecture,
( in(unordered_pair(unordered_pair(esk6_0,esk5_0),singleton(esk6_0)),esk4_0)
| ~ antisymmetric(esk4_0) ),
inference(rw,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_22,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(rw,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_23,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(rw,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_24,plain,
( in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ is_antisymmetric_in(X3,X4)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| ~ in(X2,X4)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( in(unordered_pair(singleton(esk5_0),unordered_pair(esk5_0,esk6_0)),esk4_0)
| ~ antisymmetric(esk4_0) ),
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_27,negated_conjecture,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( in(unordered_pair(singleton(esk6_0),unordered_pair(esk5_0,esk6_0)),esk4_0)
| ~ antisymmetric(esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_19]),c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( esk5_0 != esk6_0
| ~ antisymmetric(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2) ),
inference(rw,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_31,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) ),
inference(rw,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_32,negated_conjecture,
( antisymmetric(esk4_0)
| X1 = X2
| ~ in(ordered_pair(X1,X2),esk4_0)
| ~ in(ordered_pair(X2,X1),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_24,c_0_12]) ).
cnf(c_0_34,negated_conjecture,
( ~ is_antisymmetric_in(esk4_0,X1)
| ~ antisymmetric(esk4_0)
| ~ in(esk5_0,X1)
| ~ in(esk6_0,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_19])]),c_0_28]),c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( in(esk6_0,relation_field(esk4_0))
| ~ antisymmetric(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_27])]) ).
cnf(c_0_36,negated_conjecture,
( in(esk5_0,relation_field(esk4_0))
| ~ antisymmetric(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_27])]) ).
fof(c_0_37,plain,
! [X60] :
( ( ~ antisymmetric(X60)
| is_antisymmetric_in(X60,relation_field(X60))
| ~ relation(X60) )
& ( ~ is_antisymmetric_in(X60,relation_field(X60))
| antisymmetric(X60)
| ~ relation(X60) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_relat_2])])]) ).
cnf(c_0_38,plain,
( in(ordered_pair(esk2_2(X1,X2),esk1_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_39,negated_conjecture,
( X1 = X2
| antisymmetric(esk4_0)
| ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),esk4_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_12]),c_0_12]) ).
cnf(c_0_40,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_41,negated_conjecture,
( ~ is_antisymmetric_in(esk4_0,relation_field(esk4_0))
| ~ antisymmetric(esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_42,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(unordered_pair(esk2_2(X1,X2),esk1_2(X1,X2)),singleton(esk2_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_38,c_0_12]) ).
cnf(c_0_44,negated_conjecture,
( X1 = X2
| antisymmetric(esk4_0)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),esk4_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_19]),c_0_19]) ).
cnf(c_0_45,negated_conjecture,
( is_antisymmetric_in(esk4_0,X1)
| in(unordered_pair(singleton(esk1_2(esk4_0,X1)),unordered_pair(esk1_2(esk4_0,X1),esk2_2(esk4_0,X1))),esk4_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_27]) ).
cnf(c_0_46,negated_conjecture,
~ antisymmetric(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_27])]) ).
cnf(c_0_47,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(singleton(esk2_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_19]),c_0_19]) ).
cnf(c_0_48,negated_conjecture,
( esk2_2(esk4_0,X1) = esk1_2(esk4_0,X1)
| is_antisymmetric_in(esk4_0,X1)
| ~ in(unordered_pair(singleton(esk2_2(esk4_0,X1)),unordered_pair(esk1_2(esk4_0,X1),esk2_2(esk4_0,X1))),esk4_0) ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_19]) ).
cnf(c_0_49,negated_conjecture,
( is_antisymmetric_in(esk4_0,X1)
| in(unordered_pair(singleton(esk2_2(esk4_0,X1)),unordered_pair(esk1_2(esk4_0,X1),esk2_2(esk4_0,X1))),esk4_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_27]) ).
cnf(c_0_50,plain,
( is_antisymmetric_in(X1,X2)
| esk1_2(X1,X2) != esk2_2(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_51,negated_conjecture,
( esk2_2(esk4_0,X1) = esk1_2(esk4_0,X1)
| is_antisymmetric_in(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
( antisymmetric(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_53,negated_conjecture,
is_antisymmetric_in(esk4_0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_27])]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_27])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU241+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 : n027.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
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 02:51:20 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.368s
%------------------------------------------------------------------------------