%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM425+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 : n032.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 5.83s 2.48s
% Output : CNFRefutation 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 71 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 37 ~; 24 |; 11 &)
% ( 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 21 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aDivisorOf0 > aInteger0 > sdtpldt0 > sdtasdt0 > #nlpp > smndt0 > xq > xb > 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(xb,type,
xb: $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_170,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& ( xq != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).
tff(f_171,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__724) ).
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_35,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
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_176,negated_conjecture,
~ ? [W0] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(c_64,plain,
xq != sz00,
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_70,plain,
aInteger0(xa),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_68,plain,
aInteger0(xb),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_66,plain,
aInteger0(xq),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_72,plain,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_4074,plain,
! [W2_109,W0_110,W1_111] :
( aDivisorOf0(W2_109,sdtpldt0(W0_110,smndt0(W1_111)))
| ~ sdteqdtlpzmzozddtrp0(W0_110,W1_111,W2_109)
| ( sz00 = W2_109 )
| ~ aInteger0(W2_109)
| ~ aInteger0(W1_111)
| ~ aInteger0(W0_110) ),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_8,plain,
! [W0_2] :
( aInteger0(smndt0(W0_2))
| ~ aInteger0(W0_2) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_10,plain,
! [W0_3,W1_4] :
( aInteger0(sdtpldt0(W0_3,W1_4))
| ~ aInteger0(W1_4)
| ~ aInteger0(W0_3) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_52,plain,
! [W0_27,W1_33] :
( aInteger0('#skF_1'(W0_27,W1_33))
| ~ aDivisorOf0(W1_33,W0_27)
| ~ aInteger0(W0_27) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_987,plain,
! [W1_77,W0_78] :
( ( sdtasdt0(W1_77,'#skF_1'(W0_78,W1_77)) = W0_78 )
| ~ aDivisorOf0(W1_77,W0_78)
| ~ aInteger0(W0_78) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_74,plain,
! [W0_42] :
( ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,W0_42) )
| ~ aInteger0(W0_42) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_1038,plain,
! [W0_79] :
( ( sdtpldt0(xa,smndt0(xb)) != W0_79 )
| ~ aInteger0('#skF_1'(W0_79,xq))
| ~ aDivisorOf0(xq,W0_79)
| ~ aInteger0(W0_79) ),
inference(superposition,[status(thm),theory(equality)],[c_987,c_74]) ).
tff(c_1043,plain,
! [W0_27] :
( ( sdtpldt0(xa,smndt0(xb)) != W0_27 )
| ~ aDivisorOf0(xq,W0_27)
| ~ aInteger0(W0_27) ),
inference(resolution,[status(thm)],[c_52,c_1038]) ).
tff(c_1320,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(reflexivity,[status(thm),theory(equality)],[c_1043]) ).
tff(c_1989,plain,
~ aInteger0(sdtpldt0(xa,smndt0(xb))),
inference(splitLeft,[status(thm)],[c_1320]) ).
tff(c_2141,plain,
( ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[c_10,c_1989]) ).
tff(c_2144,plain,
~ aInteger0(smndt0(xb)),
inference(demodulation,[status(thm),theory(equality)],[c_70,c_2141]) ).
tff(c_2147,plain,
~ aInteger0(xb),
inference(resolution,[status(thm)],[c_8,c_2144]) ).
tff(c_2151,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_68,c_2147]) ).
tff(c_2152,plain,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))),
inference(splitRight,[status(thm)],[c_1320]) ).
tff(c_4080,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xb)
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[c_4074,c_2152]) ).
tff(c_4108,plain,
xq = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_70,c_68,c_66,c_72,c_4080]) ).
tff(c_4110,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_64,c_4108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM425+1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.09 % 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
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Tue Apr 8 12:14:15 EDT 2025
% 0.08/0.29 % CPUTime :
% 5.83/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.83/2.48
% 5.83/2.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------