%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM411+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n025.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 04:57:15 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 89 ( 37 ~; 34 |; 10 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 46 ( 4 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t47_ordinal1,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> ! [X3] :
( transfinite_sequence_of(X3,X1)
=> transfinite_sequence_of(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(d8_ordinal1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2)
& transfinite_sequence(X2) )
=> ( transfinite_sequence_of(X2,X1)
<=> subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(dt_m1_ordinal1,axiom,
! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ( relation(X2)
& function(X2)
& transfinite_sequence(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> ! [X3] :
( transfinite_sequence_of(X3,X1)
=> transfinite_sequence_of(X3,X2) ) ),
inference(assume_negation,[status(cth)],[t47_ordinal1]) ).
fof(c_0_6,plain,
! [X98,X99,X100] :
( ~ subset(X98,X99)
| ~ subset(X99,X100)
| subset(X98,X100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(c_0_7,negated_conjecture,
( subset(esk17_0,esk18_0)
& transfinite_sequence_of(esk19_0,esk17_0)
& ~ transfinite_sequence_of(esk19_0,esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_8,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
subset(esk17_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X70,X71] :
( ( ~ transfinite_sequence_of(X71,X70)
| subset(relation_rng(X71),X70)
| ~ relation(X71)
| ~ function(X71)
| ~ transfinite_sequence(X71) )
& ( ~ subset(relation_rng(X71),X70)
| transfinite_sequence_of(X71,X70)
| ~ relation(X71)
| ~ function(X71)
| ~ transfinite_sequence(X71) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])]) ).
fof(c_0_11,plain,
! [X72,X73] :
( ( relation(X73)
| ~ transfinite_sequence_of(X73,X72) )
& ( function(X73)
| ~ transfinite_sequence_of(X73,X72) )
& ( transfinite_sequence(X73)
| ~ transfinite_sequence_of(X73,X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_ordinal1])])]) ).
cnf(c_0_12,negated_conjecture,
( subset(X1,esk18_0)
| ~ subset(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence_of(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( function(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( transfinite_sequence(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( subset(X1,esk18_0)
| ~ subset(X2,esk17_0)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_18,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence_of(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]) ).
fof(c_0_19,plain,
! [X95] : subset(X95,X95),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_20,negated_conjecture,
( subset(X1,esk18_0)
| ~ subset(X1,relation_rng(X2))
| ~ transfinite_sequence_of(X2,esk17_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
( transfinite_sequence_of(X1,X2)
| ~ subset(relation_rng(X1),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( subset(relation_rng(X1),esk18_0)
| ~ transfinite_sequence_of(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
~ transfinite_sequence_of(esk19_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
( transfinite_sequence_of(X1,esk18_0)
| ~ transfinite_sequence_of(X1,esk17_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]),c_0_15]),c_0_16]) ).
cnf(c_0_26,negated_conjecture,
transfinite_sequence_of(esk19_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM411+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n025.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 00:31:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------