%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM412+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n012.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 1.12s 1.61s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 91 ( 36 ~; 33 |; 12 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 3 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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/sandbox/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(t48_ordinal1,conjecture,
! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ! [X3] :
( ordinal(X3)
=> transfinite_sequence_of(tseq_dom_restriction(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_ordinal1) ).
fof(t47_ordinal1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> ! [X3] :
( transfinite_sequence_of(X3,X1)
=> transfinite_sequence_of(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(dt_k2_ordinal1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& transfinite_sequence(X1)
& ordinal(X2) )
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
fof(c_0_5,plain,
! [X80,X81] :
( ( ~ transfinite_sequence_of(X81,X80)
| subset(relation_rng(X81),X80)
| ~ relation(X81)
| ~ function(X81)
| ~ transfinite_sequence(X81) )
& ( ~ subset(relation_rng(X81),X80)
| transfinite_sequence_of(X81,X80)
| ~ relation(X81)
| ~ function(X81)
| ~ transfinite_sequence(X81) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])]) ).
fof(c_0_6,plain,
! [X86,X87] :
( ( relation(X87)
| ~ transfinite_sequence_of(X87,X86) )
& ( function(X87)
| ~ transfinite_sequence_of(X87,X86) )
& ( transfinite_sequence(X87)
| ~ transfinite_sequence_of(X87,X86) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_ordinal1])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ! [X3] :
( ordinal(X3)
=> transfinite_sequence_of(tseq_dom_restriction(X2,X3),X1) ) ),
inference(assume_negation,[status(cth)],[t48_ordinal1]) ).
cnf(c_0_8,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_5]) ).
cnf(c_0_9,plain,
( function(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( transfinite_sequence(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,negated_conjecture,
( transfinite_sequence_of(esk18_0,esk17_0)
& ordinal(esk19_0)
& ~ transfinite_sequence_of(tseq_dom_restriction(esk18_0,esk19_0),esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_13,plain,
! [X122,X123,X124] :
( ~ subset(X122,X123)
| ~ transfinite_sequence_of(X124,X122)
| transfinite_sequence_of(X124,X123) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_ordinal1])])]) ).
cnf(c_0_14,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_8,c_0_9]),c_0_10]),c_0_11]) ).
cnf(c_0_15,negated_conjecture,
transfinite_sequence_of(esk18_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( transfinite_sequence_of(X3,X2)
| ~ subset(X1,X2)
| ~ transfinite_sequence_of(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
subset(relation_rng(esk18_0),esk17_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X82,X83] :
( ~ relation(X82)
| ~ function(X82)
| ~ transfinite_sequence(X82)
| ~ ordinal(X83)
| transfinite_sequence_of(tseq_dom_restriction(X82,X83),relation_rng(X82)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_ordinal1])]) ).
cnf(c_0_19,negated_conjecture,
( transfinite_sequence_of(X1,esk17_0)
| ~ transfinite_sequence_of(X1,relation_rng(esk18_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( transfinite_sequence_of(tseq_dom_restriction(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
transfinite_sequence(esk18_0),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
relation(esk18_0),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
function(esk18_0),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
~ transfinite_sequence_of(tseq_dom_restriction(esk18_0,esk19_0),esk17_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
( transfinite_sequence_of(tseq_dom_restriction(esk18_0,X1),esk17_0)
| ~ ordinal(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
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
% 0.00/0.06 % Problem : NUM412+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 00:31:30 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.12/1.61 % Version : CSE_E---1.7
% 1.12/1.61 % Problem : theBenchmark.p
% 1.12/1.61 % SZS status Theorem for theBenchmark.p
% 1.12/1.61 % SZS output start CNFRefutation
% See solution above
% 1.12/1.61 % Total time : 1.362s
%------------------------------------------------------------------------------