%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n006.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 06:56:35 PM UTC 2026
% Result : Theorem 3.00s 1.71s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 5 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 16 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leqNat > ord > merge > cons > #nlpp > tail > s > proj1S > head > z > nil
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(proj1S,type,
proj1S: $i > $i ).
tff(s,type,
s: $i > $i ).
tff(ord,type,
ord: $i > $o ).
tff(merge,type,
merge: ( $i * $i ) > $i ).
tff(leqNat,type,
leqNat: ( $i * $i ) > $o ).
tff(cons,type,
cons: ( $i * $i ) > $i ).
tff(tail,type,
tail: $i > $i ).
tff(z,type,
z: $i ).
tff(head,type,
head: $i > $i ).
tff(nil,type,
nil: $i ).
tff(f_59,axiom,
ord(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
tff(f_47,axiom,
! [Y] : ( merge(nil,Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
tff(f_76,negated_conjecture,
~ ? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_016) ).
tff(f_67,axiom,
! [Y,Y2,Xs] :
( ord(cons(Y,cons(Y2,Xs)))
<=> ( leqNat(Y,Y2)
& ord(cons(Y2,Xs)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
tff(f_41,axiom,
! [Z] : ~ leqNat(s(Z),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
tff(c_28,plain,
ord(nil),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_20,plain,
! [Y_13] : ( merge(nil,Y_13) = Y_13 ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_71,plain,
! [Xs_40,Ys_41] :
( ord(merge(Xs_40,Ys_41))
| ord(Ys_41)
| ~ ord(Xs_40) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_74,plain,
! [Y_13] :
( ord(Y_13)
| ord(Y_13)
| ~ ord(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_71]) ).
tff(c_76,plain,
! [Y_13] : ord(Y_13),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_74]) ).
tff(c_36,plain,
! [Y_25,Y2_26,Xs_27] :
( leqNat(Y_25,Y2_26)
| ~ ord(cons(Y_25,cons(Y2_26,Xs_27))) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_107,plain,
! [Y_25,Y2_26] : leqNat(Y_25,Y2_26),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_36]) ).
tff(c_14,plain,
! [Z_10] : ~ leqNat(s(Z_10),z),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_115,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_107,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.18/0.34 % Computer : n006.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue May 5 11:15:16 EDT 2026
% 0.18/0.34 % CPUTime :
% 3.00/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.00/1.72
% 3.00/1.72 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------