%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG089+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n013.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 08:31:30 PM UTC 2025
% Result : Theorem 7.23s 2.71s
% Output : CNFRefutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 42 ( 1 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 40 ( 17 ~; 11 |; 8 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 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 : 29 ( 29 usr; 11 con; 0-4 aty)
% Number of variables : 10 ( 10 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ aElementOf0 > aSet0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > xz > xy > xx > xn > xm > xl > xk > xJ > xI > sz10 > sz00 > #skF_6 > #skF_4 > #skF_8 > #skF_5 > #skF_7 > #skF_9 > #skF_13 > #skF_11 > #skF_3 > #skF_2 > #skF_12 > #skF_1 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff(xl,type,
xl: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(sdtpldt1,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(sz00,type,
sz00: $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(aIdeal0,type,
aIdeal0: $i > $o ).
tff(xI,type,
xI: $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i * $i ) > $i ).
tff(xy,type,
xy: $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xx,type,
xx: $i ).
tff(smndt0,type,
smndt0: $i > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i * $i ) > $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xz,type,
xz: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(xJ,type,
xJ: $i ).
tff(sdtasasdt0,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(xm,type,
xm: $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff(xn,type,
xn: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_208,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
tff(f_218,hypothesis,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& ( xx = sdtpldt0(xk,xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
tff(f_213,hypothesis,
( aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).
tff(f_205,definition,
! [W0] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
tff(f_230,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(c_124,plain,
aIdeal0(xJ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_136,plain,
aElementOf0(xl,xJ),
inference(cnfTransformation,[status(thm)],[f_218]) ).
tff(c_128,plain,
aElement0(xz),
inference(cnfTransformation,[status(thm)],[f_213]) ).
tff(c_3639,plain,
! [W2_216,W1_217,W0_218] :
( aElementOf0(sdtasdt0(W2_216,W1_217),W0_218)
| ~ aElement0(W2_216)
| ~ aElementOf0(W1_217,W0_218)
| ~ aIdeal0(W0_218) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_126,plain,
aIdeal0(xI),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_138,plain,
aElementOf0(xk,xI),
inference(cnfTransformation,[status(thm)],[f_218]) ).
tff(c_1543,plain,
! [W2_173,W1_174,W0_175] :
( aElementOf0(sdtasdt0(W2_173,W1_174),W0_175)
| ~ aElement0(W2_173)
| ~ aElementOf0(W1_174,W0_175)
| ~ aIdeal0(W0_175) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_150,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_151,plain,
~ aElementOf0(sdtasdt0(xz,xk),xI),
inference(splitLeft,[status(thm)],[c_150]) ).
tff(c_1557,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xk,xI)
| ~ aIdeal0(xI) ),
inference(resolution,[status(thm)],[c_1543,c_151]) ).
tff(c_1684,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_126,c_138,c_128,c_1557]) ).
tff(c_1685,plain,
~ aElementOf0(sdtasdt0(xz,xl),xJ),
inference(splitRight,[status(thm)],[c_150]) ).
tff(c_3649,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xl,xJ)
| ~ aIdeal0(xJ) ),
inference(resolution,[status(thm)],[c_3639,c_1685]) ).
tff(c_3811,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_124,c_136,c_128,c_3649]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG089+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 18:53:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.23/2.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.23/2.72
% 7.23/2.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------