%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU257+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 : n015.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 1.22s 1.71s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 5 unt; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 224 ( 102 ~; 94 |; 11 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 7 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_ordering(X1)
<=> ( reflexive(X1)
& transitive(X1)
& antisymmetric(X1)
& connected(X1)
& well_founded_relation(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
fof(t31_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( well_founded_relation(X2)
=> well_founded_relation(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_wellord1) ).
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(t23_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( connected(X2)
=> connected(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_wellord1) ).
fof(t25_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
fof(t24_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( transitive(X2)
=> transitive(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_wellord1) ).
fof(t32_wellord1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( well_ordering(X2)
=> well_ordering(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_wellord1) ).
fof(t22_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> ( reflexive(X2)
=> reflexive(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_wellord1) ).
fof(c_0_8,plain,
! [X26] :
( ( reflexive(X26)
| ~ well_ordering(X26)
| ~ relation(X26) )
& ( transitive(X26)
| ~ well_ordering(X26)
| ~ relation(X26) )
& ( antisymmetric(X26)
| ~ well_ordering(X26)
| ~ relation(X26) )
& ( connected(X26)
| ~ well_ordering(X26)
| ~ relation(X26) )
& ( well_founded_relation(X26)
| ~ well_ordering(X26)
| ~ relation(X26) )
& ( ~ reflexive(X26)
| ~ transitive(X26)
| ~ antisymmetric(X26)
| ~ connected(X26)
| ~ well_founded_relation(X26)
| well_ordering(X26)
| ~ relation(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])]) ).
fof(c_0_9,plain,
! [X40,X41] :
( ~ relation(X41)
| ~ well_founded_relation(X41)
| well_founded_relation(relation_restriction(X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t31_wellord1])]) ).
fof(c_0_10,plain,
! [X29,X30] :
( ~ relation(X29)
| relation(relation_restriction(X29,X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])]) ).
cnf(c_0_11,plain,
( well_ordering(X1)
| ~ reflexive(X1)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ connected(X1)
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( well_founded_relation(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X34,X35] :
( ~ relation(X35)
| ~ connected(X35)
| connected(relation_restriction(X35,X34)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_wellord1])]) ).
cnf(c_0_15,plain,
( well_ordering(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| ~ connected(relation_restriction(X1,X2))
| ~ antisymmetric(relation_restriction(X1,X2))
| ~ transitive(relation_restriction(X1,X2))
| ~ reflexive(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_16,plain,
( connected(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X38,X39] :
( ~ relation(X39)
| ~ antisymmetric(X39)
| antisymmetric(relation_restriction(X39,X38)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_wellord1])]) ).
cnf(c_0_18,plain,
( well_ordering(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(relation_restriction(X1,X2))
| ~ transitive(relation_restriction(X1,X2))
| ~ reflexive(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( antisymmetric(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X36,X37] :
( ~ relation(X37)
| ~ transitive(X37)
| transitive(relation_restriction(X37,X36)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t24_wellord1])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( well_ordering(X2)
=> well_ordering(relation_restriction(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t32_wellord1]) ).
cnf(c_0_22,plain,
( well_ordering(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(relation_restriction(X1,X2))
| ~ reflexive(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( transitive(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X32,X33] :
( ~ relation(X33)
| ~ reflexive(X33)
| reflexive(relation_restriction(X33,X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_wellord1])]) ).
fof(c_0_25,negated_conjecture,
( relation(esk2_0)
& well_ordering(esk2_0)
& ~ well_ordering(relation_restriction(esk2_0,esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_26,plain,
( well_ordering(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( reflexive(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
~ well_ordering(relation_restriction(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
( well_ordering(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( ~ well_founded_relation(esk2_0)
| ~ connected(esk2_0)
| ~ antisymmetric(esk2_0)
| ~ transitive(esk2_0)
| ~ reflexive(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_32,plain,
( well_founded_relation(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33,negated_conjecture,
well_ordering(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,negated_conjecture,
( ~ connected(esk2_0)
| ~ antisymmetric(esk2_0)
| ~ transitive(esk2_0)
| ~ reflexive(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_30])]) ).
cnf(c_0_35,plain,
( connected(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_36,negated_conjecture,
( ~ antisymmetric(esk2_0)
| ~ transitive(esk2_0)
| ~ reflexive(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_33]),c_0_30])]) ).
cnf(c_0_37,plain,
( antisymmetric(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,negated_conjecture,
( ~ transitive(esk2_0)
| ~ reflexive(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33]),c_0_30])]) ).
cnf(c_0_39,plain,
( transitive(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_40,negated_conjecture,
~ reflexive(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_33]),c_0_30])]) ).
cnf(c_0_41,plain,
( reflexive(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_33]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU257+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n015.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 02:52:47 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.22/1.71 % Version : CSE_E---1.7
% 1.22/1.71 % Problem : theBenchmark.p
% 1.22/1.71 % SZS status Theorem for theBenchmark.p
% 1.22/1.71 % SZS output start CNFRefutation
% See solution above
% 1.22/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------