%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM405+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 : n001.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 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 3 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 42 ( 20 ~; 14 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 24 ( 2 sgn 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t37_ordinal1,axiom,
! [X1] :
~ ! [X2] :
( in(X2,X1)
<=> ordinal(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).
fof(s1_xboole_0__e2_43__ordinal1,axiom,
! [X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& ordinal(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).
fof(t38_ordinal1,conjecture,
! [X1] :
~ ! [X2] :
( ordinal(X2)
=> in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_ordinal1) ).
fof(c_0_3,plain,
! [X74] :
( ( ~ in(esk16_1(X74),X74)
| ~ ordinal(esk16_1(X74)) )
& ( in(esk16_1(X74),X74)
| ordinal(esk16_1(X74)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_ordinal1])])]) ).
fof(c_0_4,plain,
! [X66,X68,X69] :
( ( in(X68,X66)
| ~ in(X68,esk15_1(X66)) )
& ( ordinal(X68)
| ~ in(X68,esk15_1(X66)) )
& ( ~ in(X69,X66)
| ~ ordinal(X69)
| in(X69,esk15_1(X66)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[s1_xboole_0__e2_43__ordinal1])])])])])]) ).
cnf(c_0_5,plain,
( ~ in(esk16_1(X1),X1)
| ~ ordinal(esk16_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
( in(X1,esk15_1(X2))
| ~ in(X1,X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( ordinal(X1)
| ~ in(X1,esk15_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( in(esk16_1(X1),X1)
| ordinal(esk16_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
~ ! [X2] :
( ordinal(X2)
=> in(X2,X1) ),
inference(assume_negation,[status(cth)],[t38_ordinal1]) ).
cnf(c_0_10,plain,
( ~ ordinal(esk16_1(esk15_1(X1)))
| ~ in(esk16_1(esk15_1(X1)),X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_11,plain,
ordinal(esk16_1(esk15_1(X1))),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_12,negated_conjecture,
! [X77] :
( ~ ordinal(X77)
| in(X77,esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_13,plain,
~ in(esk16_1(esk15_1(X1)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).
cnf(c_0_14,negated_conjecture,
( in(X1,esk17_0)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM405+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 : n001.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 00:31:48 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % 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
% 1.27/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------