%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% 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 : n024.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 05:34:42 PM UTC 2026
% Result : Theorem 1.09s 1.61s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 36 ( 3 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 9 |; 3 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 5 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_016,conjecture,
? [X6,X8] :
~ ( ord(X6)
=> ( ~ ord(X8)
=> ord(merge(X6,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_016) ).
fof(axiom_009,axiom,
! [X3] : merge(nil,X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
fof(axiom_007,axiom,
! [X4] : ~ leqNat(s(X4),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(axiom_015,axiom,
! [X3,X7,X6] :
( ord(cons(X3,cons(X7,X6)))
<=> ( leqNat(X3,X7)
& ord(cons(X7,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(axiom_013,axiom,
ord(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
fof(c_0_5,negated_conjecture,
~ ? [X6,X8] :
~ ( ord(X6)
=> ( ~ ord(X8)
=> ord(merge(X6,X8)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_016])]) ).
fof(c_0_6,negated_conjecture,
! [X65,X66] :
( ~ ord(X65)
| ord(X66)
| ord(merge(X65,X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
fof(c_0_7,plain,
! [X50] : merge(nil,X50) = X50,
inference(variable_rename,[status(thm)],[axiom_009]) ).
fof(c_0_8,plain,
! [X4] : ~ leqNat(s(X4),z),
inference(fof_simplification,[status(thm)],[axiom_007]) ).
fof(c_0_9,plain,
! [X62,X63,X64] :
( ( leqNat(X62,X63)
| ~ ord(cons(X62,cons(X63,X64))) )
& ( ord(cons(X63,X64))
| ~ ord(cons(X62,cons(X63,X64))) )
& ( ~ leqNat(X62,X63)
| ~ ord(cons(X63,X64))
| ord(cons(X62,cons(X63,X64))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_015])])]) ).
cnf(c_0_10,negated_conjecture,
( ord(X2)
| ord(merge(X1,X2))
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
ord(nil),
inference(split_conjunct,[status(thm)],[axiom_013]) ).
cnf(c_0_12,plain,
merge(nil,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,plain,
! [X47] : ~ leqNat(s(X47),z),
inference(variable_rename,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( leqNat(X1,X2)
| ~ ord(cons(X1,cons(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
ord(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_16,plain,
~ leqNat(s(X1),z),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
leqNat(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_18,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.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 02:55:26 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.09/1.61 % Version : CSE_E---1.7
% 1.09/1.61 % Problem : theBenchmark.p
% 1.09/1.61 % SZS status Theorem for theBenchmark.p
% 1.09/1.61 % SZS output start CNFRefutation
% See solution above
% 1.09/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------