%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM849+2 : TPTP v9.0.0. Released v4.1.0.
% 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 : n017.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 07:57:20 PM UTC 2025
% Result : Theorem 4.52s 2.10s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ vplus > vmul > #nlpp > vsucc > vd449 > vd448 > v1 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(vd449,type,
vd449: $i ).
tff(vplus,type,
vplus: ( $i * $i ) > $i ).
tff(vsucc,type,
vsucc: $i > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(v1,type,
v1: $i ).
tff(vmul,type,
vmul: ( $i * $i ) > $i ).
tff(vd448,type,
vd448: $i ).
tff(f_53,axiom,
! [Vd418,Vd419] : ( vmul(Vd418,Vd419) = vmul(Vd419,Vd418) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ass(cond(270,0),0)) ).
tff(f_32,negated_conjecture,
~ ! [Vd454] :
( ( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454)) )
=> ( vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qu(ind(296),imp(296))) ).
tff(f_55,axiom,
! [Vd408,Vd409] : ( vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ass(cond(261,0),0)) ).
tff(f_61,axiom,
! [Vd78,Vd79] : ( vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ass(cond(61,0),0)) ).
tff(f_51,axiom,
! [Vd432,Vd433,Vd434] : ( vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ass(cond(281,0),0)) ).
tff(c_18,plain,
! [Vd419_9,Vd418_8] : ( vmul(Vd419_9,Vd418_8) = vmul(Vd418_8,Vd419_9) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_2,plain,
vmul(vmul(vd448,vd449),vsucc('#skF_1')) != vmul(vd448,vmul(vd449,vsucc('#skF_1'))),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_37,plain,
vmul(vsucc('#skF_1'),vmul(vd448,vd449)) != vmul(vd448,vmul(vd449,vsucc('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_2]) ).
tff(c_506,plain,
! [Vd408_34,Vd409_35] : ( vplus(vmul(Vd408_34,Vd409_35),Vd409_35) = vmul(vsucc(Vd408_34),Vd409_35) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_26,plain,
! [Vd79_15,Vd78_14] : ( vplus(Vd79_15,Vd78_14) = vplus(Vd78_14,Vd79_15) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_523,plain,
! [Vd409_35,Vd408_34] : ( vplus(Vd409_35,vmul(Vd408_34,Vd409_35)) = vmul(vsucc(Vd408_34),Vd409_35) ),
inference(superposition,[status(thm),theory(equality)],[c_506,c_26]) ).
tff(c_4,plain,
vmul(vmul(vd448,vd449),'#skF_1') = vmul(vd448,vmul(vd449,'#skF_1')),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_36,plain,
vmul(vd448,vmul('#skF_1',vd449)) = vmul('#skF_1',vmul(vd448,vd449)),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_18,c_4]) ).
tff(c_891,plain,
! [Vd432_44,Vd433_45,Vd434_46] : ( vplus(vmul(Vd432_44,Vd433_45),vmul(Vd432_44,Vd434_46)) = vmul(Vd432_44,vplus(Vd433_45,Vd434_46)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_2028,plain,
! [Vd434_59] : ( vplus(vmul('#skF_1',vmul(vd448,vd449)),vmul(vd448,Vd434_59)) = vmul(vd448,vplus(vmul('#skF_1',vd449),Vd434_59)) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_891]) ).
tff(c_20,plain,
! [Vd408_10,Vd409_11] : ( vplus(vmul(Vd408_10,Vd409_11),Vd409_11) = vmul(vsucc(Vd408_10),Vd409_11) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_2053,plain,
vmul(vsucc('#skF_1'),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul('#skF_1',vd449),vd449)),
inference(superposition,[status(thm),theory(equality)],[c_2028,c_20]) ).
tff(c_2116,plain,
vmul(vsucc('#skF_1'),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_523,c_26,c_2053]) ).
tff(c_2118,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_37,c_2116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM849+2 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.13 % 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
% 0.13/0.32 % Computer : n017.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Apr 8 15:34:40 EDT 2025
% 0.13/0.32 % CPUTime :
% 4.52/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.52/2.10
% 4.52/2.10 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------