%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM457+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 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 : Wed Apr 9 07:55:58 PM UTC 2025
% Result : Theorem 4.63s 2.11s
% Output : CNFRefutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 28 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 46 ( 18 ~; 19 |; 3 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ aNaturalNumber0 > sdtpldt0 > sdtasdt0 > #nlpp > xn > xm > sz10 > sz00
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(sz00,type,
sz00: $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff(xm,type,
xm: $i ).
tff(xn,type,
xn: $i ).
tff(f_150,negated_conjecture,
~ ( ( sdtasdt0(xm,xn) = sz00 )
=> ( ( xm = sz00 )
| ( xn = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_144,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__624) ).
tff(f_93,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(f_131,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1,W2] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
tff(c_54,plain,
xn != sz00,
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_52,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_63,plain,
! [W0_32] :
( ( sdtasdt0(W0_32,sz00) = sz00 )
| ~ aNaturalNumber0(W0_32) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_79,plain,
sdtasdt0(xm,sz00) = sz00,
inference(resolution,[status(thm)],[c_52,c_63]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_56,plain,
xm != sz00,
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_50,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_58,plain,
sdtasdt0(xm,xn) = sz00,
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_1047,plain,
! [W0_60,W2_61,W1_62] :
( ( sdtasdt0(W0_60,W2_61) != sdtasdt0(W0_60,W1_62) )
| ( W2_61 = W1_62 )
| ~ aNaturalNumber0(W2_61)
| ~ aNaturalNumber0(W1_62)
| ( sz00 = W0_60 )
| ~ aNaturalNumber0(W0_60) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_1125,plain,
! [W1_62] :
( ( sdtasdt0(xm,W1_62) != sz00 )
| ( xn = W1_62 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(W1_62)
| ( xm = sz00 )
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_58,c_1047]) ).
tff(c_1243,plain,
! [W1_62] :
( ( sdtasdt0(xm,W1_62) != sz00 )
| ( xn = W1_62 )
| ~ aNaturalNumber0(W1_62)
| ( xm = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_50,c_1125]) ).
tff(c_1289,plain,
! [W1_64] :
( ( sdtasdt0(xm,W1_64) != sz00 )
| ( xn = W1_64 )
| ~ aNaturalNumber0(W1_64) ),
inference(negUnitSimplification,[status(thm)],[c_56,c_1243]) ).
tff(c_1307,plain,
( ( sdtasdt0(xm,sz00) != sz00 )
| ( xn = sz00 ) ),
inference(resolution,[status(thm)],[c_4,c_1289]) ).
tff(c_1324,plain,
xn = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_79,c_1307]) ).
tff(c_1326,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_1324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM457+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 12:38:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.63/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.74/2.12
% 4.74/2.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------