%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG088+1 : TPTP v9.0.0. Released v2.7.0.
% 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 : n025.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 05:24:08 PM UTC 2025
% Result : Theorem 7.79s 2.78s
% Output : CNFRefutation 8.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 79 ( 68 unt; 0 typ; 0 def)
% Number of atoms : 272 ( 265 equ)
% Maximal formula atoms : 110 ( 3 avg)
% Number of connectives : 220 ( 27 ~; 58 |; 134 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 3 avg)
% Maximal term depth : 3 ( 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 : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ op2 > op1 > #nlpp > j > h > e24 > e23 > e22 > e21 > e20 > e14 > e13 > e12 > e11 > e10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(e21,type,
e21: $i ).
tff(e24,type,
e24: $i ).
tff(e20,type,
e20: $i ).
tff(e13,type,
e13: $i ).
tff(e22,type,
e22: $i ).
tff(op2,type,
op2: ( $i * $i ) > $i ).
tff(op1,type,
op1: ( $i * $i ) > $i ).
tff(e10,type,
e10: $i ).
tff(h,type,
h: $i > $i ).
tff(e23,type,
e23: $i ).
tff(e14,type,
e14: $i ).
tff(e12,type,
e12: $i ).
tff(j,type,
j: $i > $i ).
tff(e11,type,
e11: $i ).
tff(f_83,axiom,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e20 != e24 )
& ( e21 != e22 )
& ( e21 != e23 )
& ( e21 != e24 )
& ( e22 != e23 )
& ( e22 != e24 )
& ( e23 != e24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f_206,axiom,
( ( op1(e10,e10) = e10 )
& ( op1(e10,e11) = e11 )
& ( op1(e10,e12) = e12 )
& ( op1(e10,e13) = e13 )
& ( op1(e10,e14) = e14 )
& ( op1(e11,e10) = e11 )
& ( op1(e11,e11) = e10 )
& ( op1(e11,e12) = e13 )
& ( op1(e11,e13) = e14 )
& ( op1(e11,e14) = e12 )
& ( op1(e12,e10) = e12 )
& ( op1(e12,e11) = e14 )
& ( op1(e12,e12) = e10 )
& ( op1(e12,e13) = e11 )
& ( op1(e12,e14) = e13 )
& ( op1(e13,e10) = e13 )
& ( op1(e13,e11) = e12 )
& ( op1(e13,e12) = e14 )
& ( op1(e13,e13) = e10 )
& ( op1(e13,e14) = e11 )
& ( op1(e14,e10) = e14 )
& ( op1(e14,e11) = e13 )
& ( op1(e14,e12) = e11 )
& ( op1(e14,e13) = e12 )
& ( op1(e14,e14) = e10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f_476,negated_conjecture,
~ ( ( ( ( h(e10) = e20 )
| ( h(e10) = e21 )
| ( h(e10) = e22 )
| ( h(e10) = e23 )
| ( h(e10) = e24 ) )
& ( ( h(e11) = e20 )
| ( h(e11) = e21 )
| ( h(e11) = e22 )
| ( h(e11) = e23 )
| ( h(e11) = e24 ) )
& ( ( h(e12) = e20 )
| ( h(e12) = e21 )
| ( h(e12) = e22 )
| ( h(e12) = e23 )
| ( h(e12) = e24 ) )
& ( ( h(e13) = e20 )
| ( h(e13) = e21 )
| ( h(e13) = e22 )
| ( h(e13) = e23 )
| ( h(e13) = e24 ) )
& ( ( h(e14) = e20 )
| ( h(e14) = e21 )
| ( h(e14) = e22 )
| ( h(e14) = e23 )
| ( h(e14) = e24 ) )
& ( ( j(e20) = e10 )
| ( j(e20) = e11 )
| ( j(e20) = e12 )
| ( j(e20) = e13 )
| ( j(e20) = e14 ) )
& ( ( j(e21) = e10 )
| ( j(e21) = e11 )
| ( j(e21) = e12 )
| ( j(e21) = e13 )
| ( j(e21) = e14 ) )
& ( ( j(e22) = e10 )
| ( j(e22) = e11 )
| ( j(e22) = e12 )
| ( j(e22) = e13 )
| ( j(e22) = e14 ) )
& ( ( j(e23) = e10 )
| ( j(e23) = e11 )
| ( j(e23) = e12 )
| ( j(e23) = e13 )
| ( j(e23) = e14 ) )
& ( ( j(e24) = e10 )
| ( j(e24) = e11 )
| ( j(e24) = e12 )
| ( j(e24) = e13 )
| ( j(e24) = e14 ) ) )
=> ~ ( ( h(op1(e10,e10)) = op2(h(e10),h(e10)) )
& ( h(op1(e10,e11)) = op2(h(e10),h(e11)) )
& ( h(op1(e10,e12)) = op2(h(e10),h(e12)) )
& ( h(op1(e10,e13)) = op2(h(e10),h(e13)) )
& ( h(op1(e10,e14)) = op2(h(e10),h(e14)) )
& ( h(op1(e11,e10)) = op2(h(e11),h(e10)) )
& ( h(op1(e11,e11)) = op2(h(e11),h(e11)) )
& ( h(op1(e11,e12)) = op2(h(e11),h(e12)) )
& ( h(op1(e11,e13)) = op2(h(e11),h(e13)) )
& ( h(op1(e11,e14)) = op2(h(e11),h(e14)) )
& ( h(op1(e12,e10)) = op2(h(e12),h(e10)) )
& ( h(op1(e12,e11)) = op2(h(e12),h(e11)) )
& ( h(op1(e12,e12)) = op2(h(e12),h(e12)) )
& ( h(op1(e12,e13)) = op2(h(e12),h(e13)) )
& ( h(op1(e12,e14)) = op2(h(e12),h(e14)) )
& ( h(op1(e13,e10)) = op2(h(e13),h(e10)) )
& ( h(op1(e13,e11)) = op2(h(e13),h(e11)) )
& ( h(op1(e13,e12)) = op2(h(e13),h(e12)) )
& ( h(op1(e13,e13)) = op2(h(e13),h(e13)) )
& ( h(op1(e13,e14)) = op2(h(e13),h(e14)) )
& ( h(op1(e14,e10)) = op2(h(e14),h(e10)) )
& ( h(op1(e14,e11)) = op2(h(e14),h(e11)) )
& ( h(op1(e14,e12)) = op2(h(e14),h(e12)) )
& ( h(op1(e14,e13)) = op2(h(e14),h(e13)) )
& ( h(op1(e14,e14)) = op2(h(e14),h(e14)) )
& ( j(op2(e20,e20)) = op1(j(e20),j(e20)) )
& ( j(op2(e20,e21)) = op1(j(e20),j(e21)) )
& ( j(op2(e20,e22)) = op1(j(e20),j(e22)) )
& ( j(op2(e20,e23)) = op1(j(e20),j(e23)) )
& ( j(op2(e20,e24)) = op1(j(e20),j(e24)) )
& ( j(op2(e21,e20)) = op1(j(e21),j(e20)) )
& ( j(op2(e21,e21)) = op1(j(e21),j(e21)) )
& ( j(op2(e21,e22)) = op1(j(e21),j(e22)) )
& ( j(op2(e21,e23)) = op1(j(e21),j(e23)) )
& ( j(op2(e21,e24)) = op1(j(e21),j(e24)) )
& ( j(op2(e22,e20)) = op1(j(e22),j(e20)) )
& ( j(op2(e22,e21)) = op1(j(e22),j(e21)) )
& ( j(op2(e22,e22)) = op1(j(e22),j(e22)) )
& ( j(op2(e22,e23)) = op1(j(e22),j(e23)) )
& ( j(op2(e22,e24)) = op1(j(e22),j(e24)) )
& ( j(op2(e23,e20)) = op1(j(e23),j(e20)) )
& ( j(op2(e23,e21)) = op1(j(e23),j(e21)) )
& ( j(op2(e23,e22)) = op1(j(e23),j(e22)) )
& ( j(op2(e23,e23)) = op1(j(e23),j(e23)) )
& ( j(op2(e23,e24)) = op1(j(e23),j(e24)) )
& ( j(op2(e24,e20)) = op1(j(e24),j(e20)) )
& ( j(op2(e24,e21)) = op1(j(e24),j(e21)) )
& ( j(op2(e24,e22)) = op1(j(e24),j(e22)) )
& ( j(op2(e24,e23)) = op1(j(e24),j(e23)) )
& ( j(op2(e24,e24)) = op1(j(e24),j(e24)) )
& ( h(j(e20)) = e20 )
& ( h(j(e21)) = e21 )
& ( h(j(e22)) = e22 )
& ( h(j(e23)) = e23 )
& ( h(j(e24)) = e24 )
& ( j(h(e10)) = e10 )
& ( j(h(e11)) = e11 )
& ( j(h(e12)) = e12 )
& ( j(h(e13)) = e13 )
& ( j(h(e14)) = e14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_255,axiom,
( ( op2(e20,e20) = e20 )
& ( op2(e20,e21) = e21 )
& ( op2(e20,e22) = e22 )
& ( op2(e20,e23) = e23 )
& ( op2(e20,e24) = e24 )
& ( op2(e21,e20) = e21 )
& ( op2(e21,e21) = e22 )
& ( op2(e21,e22) = e23 )
& ( op2(e21,e23) = e24 )
& ( op2(e21,e24) = e20 )
& ( op2(e22,e20) = e22 )
& ( op2(e22,e21) = e24 )
& ( op2(e22,e22) = e21 )
& ( op2(e22,e23) = e20 )
& ( op2(e22,e24) = e23 )
& ( op2(e23,e20) = e23 )
& ( op2(e23,e21) = e20 )
& ( op2(e23,e22) = e24 )
& ( op2(e23,e23) = e21 )
& ( op2(e23,e24) = e22 )
& ( op2(e24,e20) = e24 )
& ( op2(e24,e21) = e23 )
& ( op2(e24,e22) = e20 )
& ( op2(e24,e23) = e22 )
& ( op2(e24,e24) = e21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(f_54,axiom,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e10 != e14 )
& ( e11 != e12 )
& ( e11 != e13 )
& ( e11 != e14 )
& ( e12 != e13 )
& ( e12 != e14 )
& ( e13 != e14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(c_30,plain,
e23 != e21,
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_140,plain,
op1(e10,e10) = e10,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_314,plain,
( ( j(e23) = e14 )
| ( j(e23) = e13 )
| ( j(e23) = e12 )
| ( j(e23) = e11 )
| ( j(e23) = e10 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_1425,plain,
j(e23) = e10,
inference(splitLeft,[status(thm)],[c_314]) ).
tff(c_154,plain,
op2(e23,e23) = e21,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_224,plain,
op1(j(e23),j(e23)) = j(op2(e23,e23)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_349,plain,
op1(j(e23),j(e23)) = j(e21),
inference(demodulation,[status(thm),theory(equality)],[c_154,c_224]) ).
tff(c_1507,plain,
j(e21) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_140,c_1425,c_1425,c_349]) ).
tff(c_208,plain,
h(j(e21)) = e21,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_1508,plain,
h(e10) = e21,
inference(demodulation,[status(thm),theory(equality)],[c_1507,c_208]) ).
tff(c_204,plain,
h(j(e23)) = e23,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_1426,plain,
h(e10) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_1425,c_204]) ).
tff(c_1515,plain,
e23 = e21,
inference(demodulation,[status(thm),theory(equality)],[c_1508,c_1426]) ).
tff(c_1517,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_1515]) ).
tff(c_1519,plain,
j(e23) != e10,
inference(splitRight,[status(thm)],[c_314]) ).
tff(c_318,plain,
( ( j(e21) = e14 )
| ( j(e21) = e13 )
| ( j(e21) = e12 )
| ( j(e21) = e11 )
| ( j(e21) = e10 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_1585,plain,
j(e21) = e10,
inference(splitLeft,[status(thm)],[c_318]) ).
tff(c_178,plain,
op2(e21,e21) = e22,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_248,plain,
op1(j(e21),j(e21)) = j(op2(e21,e21)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_337,plain,
op1(j(e21),j(e21)) = j(e22),
inference(demodulation,[status(thm),theory(equality)],[c_178,c_248]) ).
tff(c_1696,plain,
j(e22) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_140,c_1585,c_1585,c_337]) ).
tff(c_176,plain,
op2(e21,e22) = e23,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_246,plain,
op1(j(e21),j(e22)) = j(op2(e21,e22)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_338,plain,
op1(j(e21),j(e22)) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_176,c_246]) ).
tff(c_1691,plain,
op1(e10,j(e22)) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_1585,c_338]) ).
tff(c_1697,plain,
op1(e10,e10) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_1696,c_1691]) ).
tff(c_1704,plain,
j(e23) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_140,c_1697]) ).
tff(c_1706,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1519,c_1704]) ).
tff(c_1708,plain,
j(e21) != e10,
inference(splitRight,[status(thm)],[c_318]) ).
tff(c_128,plain,
op1(e11,e11) = e10,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_32,plain,
e22 != e21,
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_166,plain,
op2(e22,e22) = e21,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_142,plain,
op2(e24,e24) = e21,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_20,plain,
e11 != e10,
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_328,plain,
( ( h(e11) = e24 )
| ( h(e11) = e23 )
| ( h(e11) = e22 )
| ( h(e11) = e21 )
| ( h(e11) = e20 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_597,plain,
h(e11) = e20,
inference(splitLeft,[status(thm)],[c_328]) ).
tff(c_198,plain,
j(h(e11)) = e11,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_598,plain,
j(e20) = e11,
inference(demodulation,[status(thm),theory(equality)],[c_597,c_198]) ).
tff(c_190,plain,
op2(e20,e20) = e20,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_260,plain,
op1(j(e20),j(e20)) = j(op2(e20,e20)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_331,plain,
op1(j(e20),j(e20)) = j(e20),
inference(demodulation,[status(thm),theory(equality)],[c_190,c_260]) ).
tff(c_894,plain,
e11 = e10,
inference(demodulation,[status(thm),theory(equality)],[c_128,c_598,c_598,c_598,c_331]) ).
tff(c_895,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_894]) ).
tff(c_896,plain,
( ( h(e11) = e21 )
| ( h(e11) = e22 )
| ( h(e11) = e23 )
| ( h(e11) = e24 ) ),
inference(splitRight,[status(thm)],[c_328]) ).
tff(c_1941,plain,
h(e11) = e24,
inference(splitLeft,[status(thm)],[c_896]) ).
tff(c_298,plain,
op2(h(e11),h(e11)) = h(op1(e11,e11)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_362,plain,
op2(h(e11),h(e11)) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_298]) ).
tff(c_1945,plain,
op2(e24,e24) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_1941,c_1941,c_362]) ).
tff(c_1956,plain,
h(e10) = e21,
inference(demodulation,[status(thm),theory(equality)],[c_142,c_1945]) ).
tff(c_200,plain,
j(h(e10)) = e10,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_1972,plain,
j(e21) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_1956,c_200]) ).
tff(c_1974,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1708,c_1972]) ).
tff(c_1975,plain,
( ( h(e11) = e23 )
| ( h(e11) = e22 )
| ( h(e11) = e21 ) ),
inference(splitRight,[status(thm)],[c_896]) ).
tff(c_1977,plain,
h(e11) = e21,
inference(splitLeft,[status(thm)],[c_1975]) ).
tff(c_1982,plain,
op2(e21,e21) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_1977,c_1977,c_362]) ).
tff(c_1993,plain,
h(e10) = e22,
inference(demodulation,[status(thm),theory(equality)],[c_178,c_1982]) ).
tff(c_310,plain,
op2(h(e10),h(e10)) = h(op1(e10,e10)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_356,plain,
op2(h(e10),h(e10)) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_310]) ).
tff(c_2001,plain,
op2(e22,e22) = e22,
inference(demodulation,[status(thm),theory(equality)],[c_1993,c_1993,c_1993,c_356]) ).
tff(c_2010,plain,
e22 = e21,
inference(demodulation,[status(thm),theory(equality)],[c_166,c_2001]) ).
tff(c_2012,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_2010]) ).
tff(c_2013,plain,
( ( h(e11) = e22 )
| ( h(e11) = e23 ) ),
inference(splitRight,[status(thm)],[c_1975]) ).
tff(c_2015,plain,
h(e11) = e23,
inference(splitLeft,[status(thm)],[c_2013]) ).
tff(c_2062,plain,
op2(e23,e23) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_2015,c_2015,c_362]) ).
tff(c_2073,plain,
h(e10) = e21,
inference(demodulation,[status(thm),theory(equality)],[c_154,c_2062]) ).
tff(c_2089,plain,
j(e21) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_2073,c_200]) ).
tff(c_2091,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1708,c_2089]) ).
tff(c_2092,plain,
h(e11) = e22,
inference(splitRight,[status(thm)],[c_2013]) ).
tff(c_2109,plain,
j(e22) = e11,
inference(demodulation,[status(thm),theory(equality)],[c_2092,c_198]) ).
tff(c_236,plain,
op1(j(e22),j(e22)) = j(op2(e22,e22)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_343,plain,
op1(j(e22),j(e22)) = j(e21),
inference(demodulation,[status(thm),theory(equality)],[c_166,c_236]) ).
tff(c_2128,plain,
op1(e11,e11) = j(e21),
inference(demodulation,[status(thm),theory(equality)],[c_2109,c_2109,c_343]) ).
tff(c_2130,plain,
j(e21) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2128]) ).
tff(c_2132,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1708,c_2130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG088+1 : TPTP v9.0.0. Released v2.7.0.
% 0.14/0.13 % 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
% 0.14/0.34 % Computer : n025.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 : Sun Apr 6 06:59:50 EDT 2025
% 0.14/0.35 % CPUTime :
% 7.79/2.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.79/2.79
% 7.79/2.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------