%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM393+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 : n003.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 04:57:14 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 65 ( 24 ~; 26 |; 7 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 25 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t25_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> inclusion_comparable(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_ordinal1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d9_xboole_0,axiom,
! [X1,X2] :
( inclusion_comparable(X1,X2)
<=> ( subset(X1,X2)
| subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> inclusion_comparable(X1,X2) ) ),
inference(assume_negation,[status(cth)],[t25_ordinal1]) ).
fof(c_0_5,plain,
! [X64,X65] :
( ~ ordinal(X64)
| ~ ordinal(X65)
| ordinal_subset(X64,X65)
| ordinal_subset(X65,X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
fof(c_0_6,negated_conjecture,
( ordinal(esk13_0)
& ordinal(esk14_0)
& ~ inclusion_comparable(esk13_0,esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
ordinal(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X66,X67] :
( ( ~ inclusion_comparable(X66,X67)
| subset(X66,X67)
| subset(X67,X66) )
& ( ~ subset(X66,X67)
| inclusion_comparable(X66,X67) )
& ( ~ subset(X67,X66)
| inclusion_comparable(X66,X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_xboole_0])])]) ).
fof(c_0_10,plain,
! [X81,X82] :
( ( ~ ordinal_subset(X81,X82)
| subset(X81,X82)
| ~ ordinal(X81)
| ~ ordinal(X82) )
& ( ~ subset(X81,X82)
| ordinal_subset(X81,X82)
| ~ ordinal(X81)
| ~ ordinal(X82) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_11,negated_conjecture,
( ordinal_subset(X1,esk14_0)
| ordinal_subset(esk14_0,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
ordinal(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
~ inclusion_comparable(esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( inclusion_comparable(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ordinal_subset(esk14_0,esk13_0)
| ordinal_subset(esk13_0,esk14_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
~ subset(esk14_0,esk13_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( inclusion_comparable(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
ordinal_subset(esk13_0,esk14_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12]),c_0_8])]),c_0_17]) ).
cnf(c_0_20,negated_conjecture,
~ subset(esk13_0,esk14_0),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_19]),c_0_8]),c_0_12])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM393+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 : n003.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 00:30:56 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.375s
%------------------------------------------------------------------------------