%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM423+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/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 : n031.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 07:55:52 PM UTC 2025
% Result : Theorem 18.47s 6.83s
% Output : CNFRefutation 18.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 65 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 26 ~; 25 |; 10 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 16 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aDivisorOf0 > aInteger0 > sdtpldt0 > sdtasdt0 > #nlpp > smndt0 > xq > xa > sz10 > sz00 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(aInteger0,type,
aInteger0: $i > $o ).
tff(xq,type,
xq: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xa,type,
xa: $i ).
tff(sz10,type,
sz10: $i ).
tff(sz00,type,
sz00: $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0,type,
smndt0: $i > $i ).
tff(aDivisorOf0,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(sdteqdtlpzmzozddtrp0,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_159,hypothesis,
( aInteger0(xa)
& aInteger0(xq)
& ( xq != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).
tff(f_30,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
tff(f_109,axiom,
! [W0] :
( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
tff(f_140,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
tff(f_73,axiom,
! [W0] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
tff(f_153,definition,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
tff(f_161,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(c_62,plain,
xq != sz00,
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_66,plain,
aInteger0(xa),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_64,plain,
aInteger0(xq),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_4,plain,
aInteger0(sz00),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_71,plain,
! [W0_42] :
( ( sdtasdt0(W0_42,sz00) = sz00 )
| ~ aInteger0(W0_42) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_88,plain,
sdtasdt0(xq,sz00) = sz00,
inference(resolution,[status(thm)],[c_64,c_71]) ).
tff(c_1231,plain,
! [W1_78,W2_79] :
( aDivisorOf0(W1_78,sdtasdt0(W1_78,W2_79))
| ~ aInteger0(W2_79)
| ( sz00 = W1_78 )
| ~ aInteger0(W1_78)
| ~ aInteger0(sdtasdt0(W1_78,W2_79)) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_1304,plain,
( aDivisorOf0(xq,sz00)
| ~ aInteger0(sz00)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(sdtasdt0(xq,sz00)) ),
inference(superposition,[status(thm),theory(equality)],[c_88,c_1231]) ).
tff(c_1356,plain,
( aDivisorOf0(xq,sz00)
| ( xq = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_88,c_64,c_4,c_1304]) ).
tff(c_1357,plain,
aDivisorOf0(xq,sz00),
inference(negUnitSimplification,[status(thm)],[c_62,c_1356]) ).
tff(c_24,plain,
! [W0_13] :
( ( sdtpldt0(W0_13,smndt0(W0_13)) = sz00 )
| ~ aInteger0(W0_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1697,plain,
! [W0_86,W1_87,W2_88] :
( sdteqdtlpzmzozddtrp0(W0_86,W1_87,W2_88)
| ~ aDivisorOf0(W2_88,sdtpldt0(W0_86,smndt0(W1_87)))
| ( sz00 = W2_88 )
| ~ aInteger0(W2_88)
| ~ aInteger0(W1_87)
| ~ aInteger0(W0_86) ),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_22951,plain,
! [W0_193,W2_194] :
( sdteqdtlpzmzozddtrp0(W0_193,W0_193,W2_194)
| ~ aDivisorOf0(W2_194,sz00)
| ( sz00 = W2_194 )
| ~ aInteger0(W2_194)
| ~ aInteger0(W0_193)
| ~ aInteger0(W0_193)
| ~ aInteger0(W0_193) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_1697]) ).
tff(c_68,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_22957,plain,
( ~ aDivisorOf0(xq,sz00)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[c_22951,c_68]) ).
tff(c_22961,plain,
xq = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_66,c_64,c_1357,c_22957]) ).
tff(c_22963,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62,c_22961]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : NUM423+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.11 % 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
% 0.11/0.31 % Computer : n031.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Apr 8 12:13:22 EDT 2025
% 0.11/0.31 % CPUTime :
% 18.47/6.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.47/6.84
% 18.47/6.84 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------