%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM845+1 : 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 : n005.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 07:57:19 PM UTC 2025
% Result : Theorem 49.09s 32.92s
% Output : CNFRefutation 49.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 2 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less > leq > greater > geq > vplus > vmul > #nlpp > vsucc > vskolem2 > vd411 > v1 > #skF_3 > #skF_1 > #skF_2 > #skF_5 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(vplus,type,
vplus: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(less,type,
less: ( $i * $i ) > $o ).
tff(vskolem2,type,
vskolem2: $i > $i ).
tff(vsucc,type,
vsucc: $i > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(vd411,type,
vd411: $i ).
tff(v1,type,
v1: $i ).
tff(geq,type,
geq: ( $i * $i ) > $o ).
tff(vmul,type,
vmul: ( $i * $i ) > $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_258,axiom,
! [Vd68,Vd69] : ( vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ass(cond(52,0),0)) ).
tff(f_256,axiom,
! [Vd78,Vd79] : ( vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ass(cond(61,0),0)) ).
tff(f_31,negated_conjecture,
~ ! [Vd416] :
( ( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416) )
=> ( vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qu(ind(267),imp(267))) ).
tff(f_72,axiom,
! [Vd396,Vd397] :
( ( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) )
& ( vmul(Vd396,v1) = Vd396 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qu(cond(conseq(axiom(3)),32),and(holds(definiens(249),399,0),holds(definiens(249),398,0)))) ).
tff(f_266,axiom,
! [Vd42,Vd43] :
( ( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)) )
& ( vplus(Vd42,v1) = vsucc(Vd42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qu(cond(conseq(axiom(3)),3),and(holds(definiens(29),45,0),holds(definiens(29),44,0)))) ).
tff(f_262,axiom,
! [Vd46,Vd47,Vd48] : ( vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ass(cond(33,0),0)) ).
tff(c_121,plain,
! [Vd68_114,Vd69_115] : ( vplus(vsucc(Vd68_114),Vd69_115) = vsucc(vplus(Vd68_114,Vd69_115)) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_119,plain,
! [Vd79_113,Vd78_112] : ( vplus(Vd79_113,Vd78_112) = vplus(Vd78_112,Vd79_113) ),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_2,plain,
vplus(vmul(vd411,vsucc('#skF_1')),vsucc('#skF_1')) != vmul(vsucc(vd411),vsucc('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_155,plain,
vsucc(vplus('#skF_1',vmul(vd411,vsucc('#skF_1')))) != vmul(vsucc(vd411),vsucc('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_2]) ).
tff(c_2952,plain,
! [Vd396_319,Vd397_320] : ( vplus(vmul(Vd396_319,Vd397_320),Vd396_319) = vmul(Vd396_319,vsucc(Vd397_320)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_3067,plain,
! [Vd396_319,Vd397_320] : ( vplus(Vd396_319,vmul(Vd396_319,Vd397_320)) = vmul(Vd396_319,vsucc(Vd397_320)) ),
inference(superposition,[status(thm),theory(equality)],[c_2952,c_119]) ).
tff(c_127,plain,
! [Vd42_120,Vd43_121] : ( vplus(Vd42_120,vsucc(Vd43_121)) = vsucc(vplus(Vd42_120,Vd43_121)) ),
inference(cnfTransformation,[status(thm)],[f_266]) ).
tff(c_4059,plain,
! [Vd46_371,Vd47_372,Vd48_373] : ( vplus(vplus(Vd46_371,Vd47_372),Vd48_373) = vplus(Vd46_371,vplus(Vd47_372,Vd48_373)) ),
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_4262,plain,
! [Vd79_113,Vd46_371,Vd47_372] : ( vplus(Vd79_113,vplus(Vd46_371,Vd47_372)) = vplus(Vd46_371,vplus(Vd47_372,Vd79_113)) ),
inference(superposition,[status(thm),theory(equality)],[c_119,c_4059]) ).
tff(c_4,plain,
vplus(vmul(vd411,'#skF_1'),'#skF_1') = vmul(vsucc(vd411),'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_4282,plain,
! [Vd48_373] : ( vplus(vmul(vsucc(vd411),'#skF_1'),Vd48_373) = vplus(vmul(vd411,'#skF_1'),vplus('#skF_1',Vd48_373)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_4059]) ).
tff(c_163178,plain,
! [Vd48_1966] : ( vplus(vmul(vsucc(vd411),'#skF_1'),Vd48_1966) = vplus('#skF_1',vplus(Vd48_1966,vmul(vd411,'#skF_1'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4262,c_4282]) ).
tff(c_30,plain,
! [Vd396_10,Vd397_11] : ( vplus(vmul(Vd396_10,Vd397_11),Vd396_10) = vmul(Vd396_10,vsucc(Vd397_11)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_164646,plain,
vplus('#skF_1',vplus(vsucc(vd411),vmul(vd411,'#skF_1'))) = vmul(vsucc(vd411),vsucc('#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_163178,c_30]) ).
tff(c_165037,plain,
vsucc(vplus('#skF_1',vmul(vd411,vsucc('#skF_1')))) = vmul(vsucc(vd411),vsucc('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_3067,c_127,c_121,c_164646]) ).
tff(c_165039,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_155,c_165037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM845+1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 15:33:57 EDT 2025
% 0.13/0.34 % CPUTime :
% 49.09/32.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.09/32.93
% 49.09/32.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------