%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU255+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 : n022.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 1.54s 1.80s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 116 ( 14 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 122 ( 46 ~; 57 |; 9 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 2 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_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(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(dt_k2_wellord1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(t25_wellord1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
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/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(c_0_6,plain,
! [X66,X67,X68] :
( ( ~ antisymmetric(X66)
| ~ in(ordered_pair(X67,X68),X66)
| ~ in(ordered_pair(X68,X67),X66)
| X67 = X68
| ~ relation(X66) )
& ( in(ordered_pair(esk2_1(X66),esk3_1(X66)),X66)
| antisymmetric(X66)
| ~ relation(X66) )
& ( in(ordered_pair(esk3_1(X66),esk2_1(X66)),X66)
| antisymmetric(X66)
| ~ relation(X66) )
& ( esk2_1(X66) != esk3_1(X66)
| antisymmetric(X66)
| ~ relation(X66) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_wellord1])])])])]) ).
fof(c_0_7,plain,
! [X55,X56] : ordered_pair(X55,X56) = unordered_pair(unordered_pair(X55,X56),singleton(X55)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_8,plain,
( in(ordered_pair(esk2_1(X1),esk3_1(X1)),X1)
| antisymmetric(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X51,X52] : unordered_pair(X51,X52) = unordered_pair(X52,X51),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_11,plain,
( in(ordered_pair(esk3_1(X1),esk2_1(X1)),X1)
| antisymmetric(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( antisymmetric(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_8,c_0_9]) ).
cnf(c_0_13,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X59,X60] :
( ~ relation(X59)
| relation(relation_restriction(X59,X60)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t25_wellord1]) ).
cnf(c_0_16,plain,
( antisymmetric(X1)
| in(unordered_pair(unordered_pair(esk3_1(X1),esk2_1(X1)),singleton(esk3_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_17,plain,
( antisymmetric(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_12,c_0_13]) ).
cnf(c_0_18,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,negated_conjecture,
( relation(esk10_0)
& antisymmetric(esk10_0)
& ~ antisymmetric(relation_restriction(esk10_0,esk9_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_20,plain,
( antisymmetric(X1)
| in(unordered_pair(singleton(esk3_1(X1)),unordered_pair(esk2_1(X1),esk3_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_13]),c_0_13]) ).
cnf(c_0_21,plain,
( X2 = X3
| ~ antisymmetric(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_22,plain,
! [X76,X77,X78] :
( ( in(X76,X78)
| ~ in(X76,relation_restriction(X78,X77))
| ~ relation(X78) )
& ( in(X76,cartesian_product2(X77,X77))
| ~ in(X76,relation_restriction(X78,X77))
| ~ relation(X78) )
& ( ~ in(X76,X78)
| ~ in(X76,cartesian_product2(X77,X77))
| in(X76,relation_restriction(X78,X77))
| ~ relation(X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_wellord1])])]) ).
cnf(c_0_23,plain,
( antisymmetric(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_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( antisymmetric(relation_restriction(X1,X2))
| in(unordered_pair(singleton(esk3_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_20,c_0_18]) ).
cnf(c_0_26,plain,
( X2 = X3
| ~ relation(X1)
| ~ antisymmetric(X1)
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_9]),c_0_9]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| ~ in(X1,relation_restriction(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( antisymmetric(relation_restriction(esk10_0,X1))
| in(unordered_pair(singleton(esk2_1(relation_restriction(esk10_0,X1))),unordered_pair(esk2_1(relation_restriction(esk10_0,X1)),esk3_1(relation_restriction(esk10_0,X1)))),relation_restriction(esk10_0,X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( antisymmetric(relation_restriction(esk10_0,X1))
| in(unordered_pair(singleton(esk3_1(relation_restriction(esk10_0,X1))),unordered_pair(esk2_1(relation_restriction(esk10_0,X1)),esk3_1(relation_restriction(esk10_0,X1)))),relation_restriction(esk10_0,X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ antisymmetric(X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_13]),c_0_13]) ).
cnf(c_0_31,negated_conjecture,
( antisymmetric(relation_restriction(esk10_0,X1))
| in(unordered_pair(singleton(esk2_1(relation_restriction(esk10_0,X1))),unordered_pair(esk2_1(relation_restriction(esk10_0,X1)),esk3_1(relation_restriction(esk10_0,X1)))),esk10_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24])]) ).
cnf(c_0_32,negated_conjecture,
antisymmetric(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,negated_conjecture,
( antisymmetric(relation_restriction(esk10_0,X1))
| in(unordered_pair(singleton(esk3_1(relation_restriction(esk10_0,X1))),unordered_pair(esk2_1(relation_restriction(esk10_0,X1)),esk3_1(relation_restriction(esk10_0,X1)))),esk10_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_24])]) ).
cnf(c_0_34,plain,
( antisymmetric(X1)
| esk2_1(X1) != esk3_1(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_35,negated_conjecture,
( esk3_1(relation_restriction(esk10_0,X1)) = esk2_1(relation_restriction(esk10_0,X1))
| antisymmetric(relation_restriction(esk10_0,X1)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_24])]),c_0_13]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
~ antisymmetric(relation_restriction(esk10_0,esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,negated_conjecture,
( antisymmetric(relation_restriction(esk10_0,X1))
| ~ relation(relation_restriction(esk10_0,X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
~ relation(relation_restriction(esk10_0,esk9_0)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_18]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU255+1 : 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 : n022.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 02:53:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.54/1.80 % Version : CSE_E---1.7
% 1.54/1.80 % Problem : theBenchmark.p
% 1.54/1.80 % SZS status Theorem for theBenchmark.p
% 1.54/1.80 % SZS output start CNFRefutation
% See solution above
% 1.54/1.80 % Total time : 1.371s
%------------------------------------------------------------------------------