%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG091+2 : 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 : 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 08:31:31 PM UTC 2025
% Result : Theorem 7.88s 2.83s
% Output : CNFRefutation 7.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 10 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 37 ( 17 ~; 13 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 15 con; 0-4 aty)
% Number of variables : 12 ( 8 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ aElementOf0 > aSet0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > xz > xy > xx > xn > xm > xl > xk > xJ > xI > sz10 > sz00 > #skF_17 > #skF_6 > #skF_15 > #skF_4 > #skF_8 > #skF_16 > #skF_14 > #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_17',type,
'#skF_17': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff('#skF_15',type,
'#skF_15': $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('#skF_16',type,
'#skF_16': $i ).
tff(xy,type,
xy: $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $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_270,hypothesis,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__994) ).
tff(f_274,hypothesis,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1061) ).
tff(f_273,hypothesis,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1021) ).
tff(f_275,hypothesis,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1098) ).
tff(f_293,negated_conjecture,
~ ( ( ? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sdtpldt0(xx,xy) ) )
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
& ( ? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& ( sdtpldt0(W0,W1) = sdtasdt0(xz,xx) ) )
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(c_172,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_170,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_178,plain,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xx,xy),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_176,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_174,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_180,plain,
sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) = sdtasdt0(xz,xx),
inference(cnfTransformation,[status(thm)],[f_275]) ).
tff(c_188,plain,
! [W0_145,W1_146,W0_147,W1_148] :
( ( sdtpldt0(xx,xy) != sdtpldt0(W0_145,W1_146) )
| ~ aElementOf0(W1_146,xJ)
| ~ aElementOf0(W0_145,xI)
| ( sdtpldt0(W0_147,W1_148) != sdtasdt0(xz,xx) )
| ~ aElementOf0(W1_148,xJ)
| ~ aElementOf0(W0_147,xI) ),
inference(cnfTransformation,[status(thm)],[f_293]) ).
tff(c_283,plain,
! [W0_147,W1_148] :
( ( sdtpldt0(W0_147,W1_148) != sdtasdt0(xz,xx) )
| ~ aElementOf0(W1_148,xJ)
| ~ aElementOf0(W0_147,xI) ),
inference(splitLeft,[status(thm)],[c_188]) ).
tff(c_2965,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(superposition,[status(thm),theory(equality)],[c_180,c_283]) ).
tff(c_2973,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_176,c_174,c_2965]) ).
tff(c_2974,plain,
! [W0_145,W1_146] :
( ( sdtpldt0(xx,xy) != sdtpldt0(W0_145,W1_146) )
| ~ aElementOf0(W1_146,xJ)
| ~ aElementOf0(W0_145,xI) ),
inference(splitRight,[status(thm)],[c_188]) ).
tff(c_4232,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(superposition,[status(thm),theory(equality)],[c_178,c_2974]) ).
tff(c_4240,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_172,c_170,c_4232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG091+2 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % 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
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 18:46:44 EDT 2025
% 0.14/0.35 % CPUTime :
% 7.88/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.88/2.83
% 7.88/2.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------