%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM414+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 : n011.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 04:57:16 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 72 ( 8 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 84 ( 35 ~; 27 |; 14 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 23 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t50_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ proper_subset(X1,X2)
& X1 != X2
& ~ proper_subset(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_ordinal1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ proper_subset(X1,X2)
& X1 != X2
& ~ proper_subset(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t50_ordinal1])]) ).
fof(c_0_5,plain,
! [X71,X72] :
( ~ ordinal(X71)
| ~ ordinal(X72)
| ordinal_subset(X71,X72)
| ordinal_subset(X72,X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
fof(c_0_6,negated_conjecture,
( ordinal(esk16_0)
& ordinal(esk17_0)
& ~ proper_subset(esk16_0,esk17_0)
& esk16_0 != esk17_0
& ~ proper_subset(esk17_0,esk16_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(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X92,X93] :
( ( ~ ordinal_subset(X92,X93)
| subset(X92,X93)
| ~ ordinal(X92)
| ~ ordinal(X93) )
& ( ~ subset(X92,X93)
| ordinal_subset(X92,X93)
| ~ ordinal(X92)
| ~ ordinal(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_10,negated_conjecture,
( ordinal_subset(X1,esk17_0)
| ordinal_subset(esk17_0,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
ordinal(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( ordinal_subset(esk17_0,esk16_0)
| ordinal_subset(esk16_0,esk17_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_14,plain,
! [X73,X74] :
( ( subset(X73,X74)
| ~ proper_subset(X73,X74) )
& ( X73 != X74
| ~ proper_subset(X73,X74) )
& ( ~ subset(X73,X74)
| X73 = X74
| proper_subset(X73,X74) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
cnf(c_0_15,negated_conjecture,
( subset(esk17_0,esk16_0)
| ordinal_subset(esk16_0,esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11]),c_0_8])]) ).
cnf(c_0_16,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( subset(esk17_0,esk16_0)
| subset(esk16_0,esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_15]),c_0_8]),c_0_11])]) ).
cnf(c_0_18,negated_conjecture,
esk16_0 != esk17_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
~ proper_subset(esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
subset(esk16_0,esk17_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]) ).
cnf(c_0_21,negated_conjecture,
~ proper_subset(esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_20]),c_0_18]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM414+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n011.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 00:31:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------