%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM835+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 : n021.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 07:57:16 PM UTC 2025
% Result : Theorem 4.00s 2.07s
% Output : CNFRefutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 18 ( 6 ~; 11 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 10 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ m > vplus > #nlpp > vsucc > vskolem2 > vskolem3 > vd165 > vd151 > v1 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(m,type,
m: $i > $o ).
tff(vplus,type,
vplus: ( $i * $i ) > $i ).
tff(vskolem2,type,
vskolem2: $i > $i ).
tff(vsucc,type,
vsucc: $i > $i ).
tff(v1,type,
v1: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(vd151,type,
vd151: $i ).
tff(vskolem3,type,
vskolem3: $i ).
tff(vd165,type,
vd165: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_35,negated_conjecture,
~ ( ? [Vd180] : ( vd165 = vplus(vd151,Vd180) )
| ? [Vd170] : ( vd151 = vplus(vd165,Vd170) )
| ( vd151 = vd165 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dis(case_distinction(conseq(110)))) ).
tff(f_126,axiom,
! [Vd151,Vd152] :
( m(Vd152)
<=> ( ( Vd151 = Vd152 )
| ? [Vd155] : ( Vd151 = vplus(Vd152,Vd155) )
| ? [Vd157] : ( Vd152 = vplus(Vd151,Vd157) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def(cond(conseq(105),0),1)) ).
tff(c_2,plain,
vd165 != vd151,
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_44,plain,
! [Vd152_16] : m(Vd152_16),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_38,plain,
! [Vd151_15,Vd152_16] :
( ( vplus(Vd151_15,'#skF_2'(Vd151_15,Vd152_16)) = Vd152_16 )
| ( vplus(Vd152_16,'#skF_1'(Vd151_15,Vd152_16)) = Vd151_15 )
| ( Vd152_16 = Vd151_15 )
| ~ m(Vd152_16) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_749,plain,
! [Vd151_70,Vd152_71] :
( ( vplus(Vd151_70,'#skF_2'(Vd151_70,Vd152_71)) = Vd152_71 )
| ( vplus(Vd152_71,'#skF_1'(Vd151_70,Vd152_71)) = Vd151_70 )
| ( Vd152_71 = Vd151_70 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_38]) ).
tff(c_4,plain,
! [Vd170_2] : ( vplus(vd165,Vd170_2) != vd151 ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_931,plain,
! [Vd151_74] :
( ( vd151 != Vd151_74 )
| ( vplus(Vd151_74,'#skF_2'(Vd151_74,vd165)) = vd165 )
| ( vd165 = Vd151_74 ) ),
inference(superposition,[status(thm),theory(equality)],[c_749,c_4]) ).
tff(c_6,plain,
! [Vd180_1] : ( vplus(vd151,Vd180_1) != vd165 ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_980,plain,
vd165 = vd151,
inference(superposition,[status(thm),theory(equality)],[c_931,c_6]) ).
tff(c_1017,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2,c_980]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM835+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
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 15:32:58 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.00/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.37/2.07
% 4.37/2.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------