TSTP Solution File: GRP026-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP026-1 : TPTP v8.1.2. Bugfixed v2.0.0.
% 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 : n004.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 : Tue Aug 22 10:39:39 EDT 2023
% Result : Unsatisfiable 9.32s 3.40s
% Output : CNFRefutation 10.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 48
% Syntax : Number of formulae : 275 ( 205 unt; 17 typ; 0 def)
% Number of atoms : 327 ( 165 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 145 ( 76 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-3 aty)
% Number of variables : 67 (; 67 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > group_member > multiply > inverse > #nlpp > identity_for > an_isomorphism > h > g2 > g1 > g > f > d3 > d2 > d1 > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(h,type,
h: $i ).
tff(a,type,
a: $i ).
tff(group_member,type,
group_member: ( $i * $i ) > $o ).
tff(f,type,
f: $i ).
tff(product,type,
product: ( $i * $i * $i * $i ) > $o ).
tff(g2,type,
g2: $i ).
tff(an_isomorphism,type,
an_isomorphism: $i > $i ).
tff(g1,type,
g1: $i ).
tff(b,type,
b: $i ).
tff(d2,type,
d2: $i ).
tff(g,type,
g: $i ).
tff(d1,type,
d1: $i ).
tff(identity_for,type,
identity_for: $i > $i ).
tff(inverse,type,
inverse: ( $i * $i ) > $i ).
tff(multiply,type,
multiply: ( $i * $i * $i ) > $i ).
tff(d3,type,
d3: $i ).
tff(c,type,
c: $i ).
tff(f_163,axiom,
product(g2,h,h,g),
file(unknown,unknown) ).
tff(f_166,axiom,
an_isomorphism(b) = g,
file(unknown,unknown) ).
tff(f_156,axiom,
product(g2,f,g,g),
file(unknown,unknown) ).
tff(f_158,axiom,
product(g2,f,h,h),
file(unknown,unknown) ).
tff(f_167,axiom,
an_isomorphism(c) = h,
file(unknown,unknown) ).
tff(f_155,axiom,
product(g2,f,f,f),
file(unknown,unknown) ).
tff(f_165,axiom,
an_isomorphism(a) = f,
file(unknown,unknown) ).
tff(f_171,axiom,
group_member(d3,g1),
file(unknown,unknown) ).
tff(f_136,axiom,
! [X] :
( ~ group_member(X,g1)
| ( X = a )
| ( X = b )
| ( X = c ) ),
file(unknown,unknown) ).
tff(f_170,axiom,
group_member(d2,g1),
file(unknown,unknown) ).
tff(f_169,axiom,
group_member(d1,g1),
file(unknown,unknown) ).
tff(f_174,axiom,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file(unknown,unknown) ).
tff(f_172,axiom,
product(g1,d1,d2,d3),
file(unknown,unknown) ).
tff(f_146,axiom,
product(g1,a,a,a),
file(unknown,unknown) ).
tff(f_96,axiom,
! [Xg,W,Z,X,Y] :
( ~ product(Xg,X,Y,Z)
| ~ product(Xg,X,Y,W)
| ( W = Z ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
product(g1,a,c,c),
file(unknown,unknown) ).
tff(f_147,axiom,
product(g1,a,b,b),
file(unknown,unknown) ).
tff(f_150,axiom,
product(g1,c,a,c),
file(unknown,unknown) ).
tff(f_159,axiom,
product(g2,h,f,h),
file(unknown,unknown) ).
tff(f_154,axiom,
product(g1,c,c,b),
file(unknown,unknown) ).
tff(f_153,axiom,
product(g1,c,b,a),
file(unknown,unknown) ).
tff(f_152,axiom,
product(g1,b,c,a),
file(unknown,unknown) ).
tff(f_151,axiom,
product(g1,b,b,c),
file(unknown,unknown) ).
tff(f_162,axiom,
product(g2,h,g,f),
file(unknown,unknown) ).
tff(f_157,axiom,
product(g2,g,f,g),
file(unknown,unknown) ).
tff(f_160,axiom,
product(g2,g,g,h),
file(unknown,unknown) ).
tff(f_122,axiom,
group_member(a,g1),
file(unknown,unknown) ).
tff(f_79,axiom,
! [X,Xg,Y] :
( ~ group_member(X,Xg)
| ~ group_member(Y,Xg)
| product(Xg,X,Y,multiply(Xg,X,Y)) ),
file(unknown,unknown) ).
tff(f_161,axiom,
product(g2,g,h,f),
file(unknown,unknown) ).
tff(f_148,axiom,
product(g1,b,a,b),
file(unknown,unknown) ).
tff(f_124,axiom,
group_member(c,g1),
file(unknown,unknown) ).
tff(c_74,plain,
product(g2,h,h,g),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_78,plain,
an_isomorphism(b) = g,
inference(cnfTransformation,[status(thm)],[f_166]) ).
tff(c_60,plain,
product(g2,f,g,g),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_64,plain,
product(g2,f,h,h),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_80,plain,
an_isomorphism(c) = h,
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_58,plain,
product(g2,f,f,f),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_76,plain,
an_isomorphism(a) = f,
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_86,plain,
group_member(d3,g1),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_109,plain,
! [X_50] :
( ( c = X_50 )
| ( b = X_50 )
| ( a = X_50 )
| ~ group_member(X_50,g1) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_146,plain,
( ( d3 = c )
| ( d3 = b )
| ( d3 = a ) ),
inference(resolution,[status(thm)],[c_86,c_109]) ).
tff(c_261,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_146]) ).
tff(c_84,plain,
group_member(d2,g1),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_145,plain,
( ( d2 = c )
| ( d2 = b )
| ( d2 = a ) ),
inference(resolution,[status(thm)],[c_84,c_109]) ).
tff(c_183,plain,
d2 = a,
inference(splitLeft,[status(thm)],[c_145]) ).
tff(c_82,plain,
group_member(d1,g1),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_138,plain,
( ( d1 = c )
| ( d1 = b )
| ( d1 = a ) ),
inference(resolution,[status(thm)],[c_82,c_109]) ).
tff(c_173,plain,
d1 = a,
inference(splitLeft,[status(thm)],[c_138]) ).
tff(c_90,plain,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_174,plain,
~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3)),
inference(demodulation,[status(thm),theory(equality)],[c_173,c_90]) ).
tff(c_177,plain,
~ product(g2,f,an_isomorphism(d2),an_isomorphism(d3)),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_174]) ).
tff(c_913,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_76,c_261,c_76,c_183,c_177]) ).
tff(c_914,plain,
( ( d3 = b )
| ( d3 = c ) ),
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_916,plain,
d3 = c,
inference(splitLeft,[status(thm)],[c_914]) ).
tff(c_915,plain,
d3 != a,
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_917,plain,
c != a,
inference(demodulation,[status(thm),theory(equality)],[c_916,c_915]) ).
tff(c_88,plain,
product(g1,d1,d2,d3),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_175,plain,
product(g1,a,d2,d3),
inference(demodulation,[status(thm),theory(equality)],[c_173,c_88]) ).
tff(c_184,plain,
product(g1,a,a,d3),
inference(demodulation,[status(thm),theory(equality)],[c_183,c_175]) ).
tff(c_918,plain,
product(g1,a,a,c),
inference(demodulation,[status(thm),theory(equality)],[c_916,c_184]) ).
tff(c_40,plain,
product(g1,a,a,a),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_191,plain,
! [X_54,Z_53,Xg_55,W_52,Y_56] :
( ( Z_53 = W_52 )
| ~ product(Xg_55,X_54,Y_56,W_52)
| ~ product(Xg_55,X_54,Y_56,Z_53) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_1480,plain,
! [Z_130] :
( ( a = Z_130 )
| ~ product(g1,a,a,Z_130) ),
inference(resolution,[status(thm)],[c_40,c_191]) ).
tff(c_1487,plain,
c = a,
inference(resolution,[status(thm)],[c_918,c_1480]) ).
tff(c_1497,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_917,c_1487]) ).
tff(c_1498,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_914]) ).
tff(c_1500,plain,
b != a,
inference(demodulation,[status(thm),theory(equality)],[c_1498,c_915]) ).
tff(c_1501,plain,
product(g1,a,a,b),
inference(demodulation,[status(thm),theory(equality)],[c_1498,c_184]) ).
tff(c_1943,plain,
! [Z_161] :
( ( a = Z_161 )
| ~ product(g1,a,a,Z_161) ),
inference(resolution,[status(thm)],[c_40,c_191]) ).
tff(c_1950,plain,
b = a,
inference(resolution,[status(thm)],[c_1501,c_1943]) ).
tff(c_1960,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1500,c_1950]) ).
tff(c_1961,plain,
( ( d2 = b )
| ( d2 = c ) ),
inference(splitRight,[status(thm)],[c_145]) ).
tff(c_2033,plain,
d2 = c,
inference(splitLeft,[status(thm)],[c_1961]) ).
tff(c_1962,plain,
d2 != a,
inference(splitRight,[status(thm)],[c_145]) ).
tff(c_2034,plain,
c != a,
inference(demodulation,[status(thm),theory(equality)],[c_2033,c_1962]) ).
tff(c_2056,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_146]) ).
tff(c_2035,plain,
product(g1,a,c,d3),
inference(demodulation,[status(thm),theory(equality)],[c_2033,c_175]) ).
tff(c_2057,plain,
product(g1,a,c,a),
inference(demodulation,[status(thm),theory(equality)],[c_2056,c_2035]) ).
tff(c_46,plain,
product(g1,a,c,c),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_1963,plain,
! [Z_163,W_162,Xg_165,Y_166,X_164] :
( ( Z_163 = W_162 )
| ~ product(Xg_165,X_164,Y_166,W_162)
| ~ product(Xg_165,X_164,Y_166,Z_163) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_2433,plain,
! [Z_195] :
( ( c = Z_195 )
| ~ product(g1,a,c,Z_195) ),
inference(resolution,[status(thm)],[c_46,c_1963]) ).
tff(c_2440,plain,
c = a,
inference(resolution,[status(thm)],[c_2057,c_2433]) ).
tff(c_2450,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2034,c_2440]) ).
tff(c_2451,plain,
( ( d3 = b )
| ( d3 = c ) ),
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_2457,plain,
d3 = c,
inference(splitLeft,[status(thm)],[c_2451]) ).
tff(c_3094,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_64,c_80,c_2457,c_80,c_2033,c_177]) ).
tff(c_3095,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_2451]) ).
tff(c_3096,plain,
d3 != c,
inference(splitRight,[status(thm)],[c_2451]) ).
tff(c_3105,plain,
c != b,
inference(demodulation,[status(thm),theory(equality)],[c_3095,c_3096]) ).
tff(c_3098,plain,
product(g1,a,c,b),
inference(demodulation,[status(thm),theory(equality)],[c_3095,c_2035]) ).
tff(c_3619,plain,
! [Z_259] :
( ( c = Z_259 )
| ~ product(g1,a,c,Z_259) ),
inference(resolution,[status(thm)],[c_46,c_1963]) ).
tff(c_3622,plain,
c = b,
inference(resolution,[status(thm)],[c_3098,c_3619]) ).
tff(c_3633,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3105,c_3622]) ).
tff(c_3634,plain,
d2 = b,
inference(splitRight,[status(thm)],[c_1961]) ).
tff(c_3635,plain,
d2 != c,
inference(splitRight,[status(thm)],[c_1961]) ).
tff(c_3644,plain,
c != b,
inference(demodulation,[status(thm),theory(equality)],[c_3634,c_3635]) ).
tff(c_3636,plain,
b != a,
inference(demodulation,[status(thm),theory(equality)],[c_3634,c_1962]) ).
tff(c_3659,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_146]) ).
tff(c_3637,plain,
product(g1,a,b,d3),
inference(demodulation,[status(thm),theory(equality)],[c_3634,c_175]) ).
tff(c_3660,plain,
product(g1,a,b,a),
inference(demodulation,[status(thm),theory(equality)],[c_3659,c_3637]) ).
tff(c_42,plain,
product(g1,a,b,b),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_4279,plain,
! [Z_297] :
( ( b = Z_297 )
| ~ product(g1,a,b,Z_297) ),
inference(resolution,[status(thm)],[c_42,c_1963]) ).
tff(c_4286,plain,
b = a,
inference(resolution,[status(thm)],[c_3660,c_4279]) ).
tff(c_4296,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3636,c_4286]) ).
tff(c_4297,plain,
( ( d3 = b )
| ( d3 = c ) ),
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_4299,plain,
d3 = c,
inference(splitLeft,[status(thm)],[c_4297]) ).
tff(c_4301,plain,
product(g1,a,b,c),
inference(demodulation,[status(thm),theory(equality)],[c_4299,c_3637]) ).
tff(c_4785,plain,
! [Z_327] :
( ( b = Z_327 )
| ~ product(g1,a,b,Z_327) ),
inference(resolution,[status(thm)],[c_42,c_1963]) ).
tff(c_4788,plain,
c = b,
inference(resolution,[status(thm)],[c_4301,c_4785]) ).
tff(c_4799,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3644,c_4788]) ).
tff(c_4800,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_4297]) ).
tff(c_5429,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_78,c_4800,c_78,c_3634,c_177]) ).
tff(c_5430,plain,
( ( d1 = b )
| ( d1 = c ) ),
inference(splitRight,[status(thm)],[c_138]) ).
tff(c_5432,plain,
d1 = c,
inference(splitLeft,[status(thm)],[c_5430]) ).
tff(c_5431,plain,
d1 != a,
inference(splitRight,[status(thm)],[c_138]) ).
tff(c_5433,plain,
c != a,
inference(demodulation,[status(thm),theory(equality)],[c_5432,c_5431]) ).
tff(c_48,plain,
product(g1,c,a,c),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_7304,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_146]) ).
tff(c_66,plain,
product(g2,h,f,h),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_5535,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_146]) ).
tff(c_5513,plain,
d2 = a,
inference(splitLeft,[status(thm)],[c_145]) ).
tff(c_5435,plain,
product(g1,c,d2,d3),
inference(demodulation,[status(thm),theory(equality)],[c_5432,c_88]) ).
tff(c_5514,plain,
product(g1,c,a,d3),
inference(demodulation,[status(thm),theory(equality)],[c_5513,c_5435]) ).
tff(c_5536,plain,
product(g1,c,a,a),
inference(demodulation,[status(thm),theory(equality)],[c_5535,c_5514]) ).
tff(c_5443,plain,
! [Xg_366,Z_364,Y_367,X_365,W_363] :
( ( Z_364 = W_363 )
| ~ product(Xg_366,X_365,Y_367,W_363)
| ~ product(Xg_366,X_365,Y_367,Z_364) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_6006,plain,
! [Z_400] :
( ( c = Z_400 )
| ~ product(g1,c,a,Z_400) ),
inference(resolution,[status(thm)],[c_48,c_5443]) ).
tff(c_6013,plain,
c = a,
inference(resolution,[status(thm)],[c_5536,c_6006]) ).
tff(c_6023,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5433,c_6013]) ).
tff(c_6024,plain,
( ( d3 = b )
| ( d3 = c ) ),
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_6026,plain,
d3 = c,
inference(splitLeft,[status(thm)],[c_6024]) ).
tff(c_5434,plain,
~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(d3)),
inference(demodulation,[status(thm),theory(equality)],[c_5432,c_90]) ).
tff(c_5437,plain,
~ product(g2,h,an_isomorphism(d2),an_isomorphism(d3)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_5434]) ).
tff(c_6667,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_66,c_80,c_6026,c_76,c_5513,c_5437]) ).
tff(c_6668,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_6024]) ).
tff(c_6669,plain,
d3 != c,
inference(splitRight,[status(thm)],[c_6024]) ).
tff(c_6682,plain,
c != b,
inference(demodulation,[status(thm),theory(equality)],[c_6668,c_6669]) ).
tff(c_6675,plain,
product(g1,c,a,b),
inference(demodulation,[status(thm),theory(equality)],[c_6668,c_5514]) ).
tff(c_7264,plain,
! [Z_469] :
( ( c = Z_469 )
| ~ product(g1,c,a,Z_469) ),
inference(resolution,[status(thm)],[c_48,c_5443]) ).
tff(c_7267,plain,
c = b,
inference(resolution,[status(thm)],[c_6675,c_7264]) ).
tff(c_7278,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6682,c_7267]) ).
tff(c_7279,plain,
( ( d2 = b )
| ( d2 = c ) ),
inference(splitRight,[status(thm)],[c_145]) ).
tff(c_7292,plain,
d2 = c,
inference(splitLeft,[status(thm)],[c_7279]) ).
tff(c_7294,plain,
product(g1,c,c,d3),
inference(demodulation,[status(thm),theory(equality)],[c_7292,c_5435]) ).
tff(c_7309,plain,
product(g1,c,c,a),
inference(demodulation,[status(thm),theory(equality)],[c_7304,c_7294]) ).
tff(c_56,plain,
product(g1,c,c,b),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_7319,plain,
! [Z_476] :
( ( b = Z_476 )
| ~ product(g1,c,c,Z_476) ),
inference(resolution,[status(thm)],[c_56,c_5443]) ).
tff(c_7330,plain,
b = a,
inference(resolution,[status(thm)],[c_7309,c_7319]) ).
tff(c_54,plain,
product(g1,c,b,a),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_5504,plain,
! [Z_364] :
( ( a = Z_364 )
| ~ product(g1,c,b,Z_364) ),
inference(resolution,[status(thm)],[c_54,c_5443]) ).
tff(c_7559,plain,
! [Z_491] :
( ( a = Z_491 )
| ~ product(g1,c,a,Z_491) ),
inference(demodulation,[status(thm),theory(equality)],[c_7330,c_5504]) ).
tff(c_7569,plain,
c = a,
inference(resolution,[status(thm)],[c_48,c_7559]) ).
tff(c_7578,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5433,c_7569]) ).
tff(c_7579,plain,
( ( d3 = b )
| ( d3 = c ) ),
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_7581,plain,
d3 = c,
inference(splitLeft,[status(thm)],[c_7579]) ).
tff(c_7583,plain,
product(g1,c,c,c),
inference(demodulation,[status(thm),theory(equality)],[c_7581,c_7294]) ).
tff(c_7697,plain,
! [Z_503] :
( ( b = Z_503 )
| ~ product(g1,c,c,Z_503) ),
inference(resolution,[status(thm)],[c_56,c_5443]) ).
tff(c_7708,plain,
c = b,
inference(resolution,[status(thm)],[c_7583,c_7697]) ).
tff(c_7718,plain,
b != a,
inference(demodulation,[status(thm),theory(equality)],[c_7708,c_5433]) ).
tff(c_52,plain,
product(g1,b,c,a),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_7722,plain,
product(g1,b,b,a),
inference(demodulation,[status(thm),theory(equality)],[c_7708,c_52]) ).
tff(c_50,plain,
product(g1,b,b,c),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_5494,plain,
! [Z_364] :
( ( c = Z_364 )
| ~ product(g1,b,b,Z_364) ),
inference(resolution,[status(thm)],[c_50,c_5443]) ).
tff(c_7945,plain,
! [Z_514] :
( ( b = Z_514 )
| ~ product(g1,b,b,Z_514) ),
inference(demodulation,[status(thm),theory(equality)],[c_7708,c_5494]) ).
tff(c_7948,plain,
b = a,
inference(resolution,[status(thm)],[c_7722,c_7945]) ).
tff(c_7959,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7718,c_7948]) ).
tff(c_7960,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_7579]) ).
tff(c_8603,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_74,c_78,c_7960,c_80,c_7292,c_5437]) ).
tff(c_8604,plain,
d2 = b,
inference(splitRight,[status(thm)],[c_7279]) ).
tff(c_7280,plain,
d2 != a,
inference(splitRight,[status(thm)],[c_145]) ).
tff(c_8610,plain,
b != a,
inference(demodulation,[status(thm),theory(equality)],[c_8604,c_7280]) ).
tff(c_72,plain,
product(g2,h,g,f),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_8622,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_146]) ).
tff(c_9261,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_72,c_76,c_8622,c_78,c_8604,c_5437]) ).
tff(c_9262,plain,
( ( d3 = b )
| ( d3 = c ) ),
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_9337,plain,
d3 = c,
inference(splitLeft,[status(thm)],[c_9262]) ).
tff(c_8611,plain,
product(g1,c,b,d3),
inference(demodulation,[status(thm),theory(equality)],[c_8604,c_5435]) ).
tff(c_9339,plain,
product(g1,c,b,c),
inference(demodulation,[status(thm),theory(equality)],[c_9337,c_8611]) ).
tff(c_9425,plain,
! [Z_599] :
( ( a = Z_599 )
| ~ product(g1,c,b,Z_599) ),
inference(resolution,[status(thm)],[c_54,c_5443]) ).
tff(c_9428,plain,
c = a,
inference(resolution,[status(thm)],[c_9339,c_9425]) ).
tff(c_9439,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5433,c_9428]) ).
tff(c_9440,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_9262]) ).
tff(c_9443,plain,
product(g1,c,b,b),
inference(demodulation,[status(thm),theory(equality)],[c_9440,c_8611]) ).
tff(c_9705,plain,
! [Z_614] :
( ( a = Z_614 )
| ~ product(g1,c,b,Z_614) ),
inference(resolution,[status(thm)],[c_54,c_5443]) ).
tff(c_9708,plain,
b = a,
inference(resolution,[status(thm)],[c_9443,c_9705]) ).
tff(c_9719,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8610,c_9708]) ).
tff(c_9720,plain,
d1 = b,
inference(splitRight,[status(thm)],[c_5430]) ).
tff(c_9721,plain,
d1 != c,
inference(splitRight,[status(thm)],[c_5430]) ).
tff(c_9732,plain,
c != b,
inference(demodulation,[status(thm),theory(equality)],[c_9720,c_9721]) ).
tff(c_9722,plain,
b != a,
inference(demodulation,[status(thm),theory(equality)],[c_9720,c_5431]) ).
tff(c_62,plain,
product(g2,g,f,g),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_12414,plain,
d2 = a,
inference(splitLeft,[status(thm)],[c_145]) ).
tff(c_68,plain,
product(g2,g,g,h),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_24,plain,
group_member(a,g1),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_14,plain,
! [Xg_13,X_12,Y_14] :
( product(Xg_13,X_12,Y_14,multiply(Xg_13,X_12,Y_14))
| ~ group_member(Y_14,Xg_13)
| ~ group_member(X_12,Xg_13) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_9734,plain,
! [X_617,Xg_618,Z_616,W_615,Y_619] :
( ( Z_616 = W_615 )
| ~ product(Xg_618,X_617,Y_619,W_615)
| ~ product(Xg_618,X_617,Y_619,Z_616) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_11112,plain,
! [Z_706] :
( ( a = Z_706 )
| ~ product(g1,a,a,Z_706) ),
inference(resolution,[status(thm)],[c_40,c_9734]) ).
tff(c_11116,plain,
( ( multiply(g1,a,a) = a )
| ~ group_member(a,g1) ),
inference(resolution,[status(thm)],[c_14,c_11112]) ).
tff(c_11122,plain,
multiply(g1,a,a) = a,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_11116]) ).
tff(c_70,plain,
product(g2,g,h,f),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_9814,plain,
d2 = a,
inference(splitLeft,[status(thm)],[c_145]) ).
tff(c_9733,plain,
d3 = a,
inference(splitLeft,[status(thm)],[c_146]) ).
tff(c_9724,plain,
product(g1,b,d2,d3),
inference(demodulation,[status(thm),theory(equality)],[c_9720,c_88]) ).
tff(c_9804,plain,
product(g1,b,d2,a),
inference(demodulation,[status(thm),theory(equality)],[c_9733,c_9724]) ).
tff(c_9826,plain,
product(g1,b,a,a),
inference(demodulation,[status(thm),theory(equality)],[c_9814,c_9804]) ).
tff(c_44,plain,
product(g1,b,a,b),
inference(cnfTransformation,[status(thm)],[f_148]) ).
tff(c_10378,plain,
! [Z_655] :
( ( b = Z_655 )
| ~ product(g1,b,a,Z_655) ),
inference(resolution,[status(thm)],[c_44,c_9734]) ).
tff(c_10385,plain,
b = a,
inference(resolution,[status(thm)],[c_9826,c_10378]) ).
tff(c_10395,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9722,c_10385]) ).
tff(c_10396,plain,
( ( d2 = b )
| ( d2 = c ) ),
inference(splitRight,[status(thm)],[c_145]) ).
tff(c_10398,plain,
d2 = c,
inference(splitLeft,[status(thm)],[c_10396]) ).
tff(c_9723,plain,
~ product(g2,an_isomorphism(b),an_isomorphism(d2),an_isomorphism(d3)),
inference(demodulation,[status(thm),theory(equality)],[c_9720,c_90]) ).
tff(c_9726,plain,
~ product(g2,g,an_isomorphism(d2),an_isomorphism(d3)),
inference(demodulation,[status(thm),theory(equality)],[c_78,c_9723]) ).
tff(c_10847,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_70,c_80,c_10398,c_76,c_9733,c_9726]) ).
tff(c_10848,plain,
d2 = b,
inference(splitRight,[status(thm)],[c_10396]) ).
tff(c_10851,plain,
product(g1,b,b,a),
inference(demodulation,[status(thm),theory(equality)],[c_10848,c_9804]) ).
tff(c_11239,plain,
! [Z_715] :
( ( c = Z_715 )
| ~ product(g1,b,b,Z_715) ),
inference(resolution,[status(thm)],[c_50,c_9734]) ).
tff(c_11253,plain,
c = a,
inference(resolution,[status(thm)],[c_10851,c_11239]) ).
tff(c_28,plain,
group_member(c,g1),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_11212,plain,
! [Z_714] :
( ( b = Z_714 )
| ~ product(g1,c,c,Z_714) ),
inference(resolution,[status(thm)],[c_56,c_9734]) ).
tff(c_11216,plain,
( ( multiply(g1,c,c) = b )
| ~ group_member(c,g1) ),
inference(resolution,[status(thm)],[c_14,c_11212]) ).
tff(c_11222,plain,
multiply(g1,c,c) = b,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_11216]) ).
tff(c_11257,plain,
multiply(g1,a,a) = b,
inference(demodulation,[status(thm),theory(equality)],[c_11253,c_11253,c_11222]) ).
tff(c_11273,plain,
b = a,
inference(demodulation,[status(thm),theory(equality)],[c_11122,c_11257]) ).
tff(c_11275,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9722,c_11273]) ).
tff(c_11276,plain,
( ( d3 = b )
| ( d3 = c ) ),
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_11278,plain,
d3 = c,
inference(splitLeft,[status(thm)],[c_11276]) ).
tff(c_11277,plain,
d3 != a,
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_11279,plain,
c != a,
inference(demodulation,[status(thm),theory(equality)],[c_11278,c_11277]) ).
tff(c_11357,plain,
d2 = a,
inference(splitLeft,[status(thm)],[c_145]) ).
tff(c_11280,plain,
product(g1,b,d2,c),
inference(demodulation,[status(thm),theory(equality)],[c_11278,c_9724]) ).
tff(c_11358,plain,
product(g1,b,a,c),
inference(demodulation,[status(thm),theory(equality)],[c_11357,c_11280]) ).
tff(c_11287,plain,
! [X_718,Xg_719,Y_720,Z_717,W_716] :
( ( Z_717 = W_716 )
| ~ product(Xg_719,X_718,Y_720,W_716)
| ~ product(Xg_719,X_718,Y_720,Z_717) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_11391,plain,
! [Z_726] :
( ( b = Z_726 )
| ~ product(g1,b,a,Z_726) ),
inference(resolution,[status(thm)],[c_44,c_11287]) ).
tff(c_11394,plain,
c = b,
inference(resolution,[status(thm)],[c_11358,c_11391]) ).
tff(c_11401,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9732,c_11394]) ).
tff(c_11402,plain,
( ( d2 = b )
| ( d2 = c ) ),
inference(splitRight,[status(thm)],[c_145]) ).
tff(c_11415,plain,
d2 = c,
inference(splitLeft,[status(thm)],[c_11402]) ).
tff(c_11417,plain,
product(g1,b,c,c),
inference(demodulation,[status(thm),theory(equality)],[c_11415,c_11280]) ).
tff(c_11941,plain,
! [Z_761] :
( ( a = Z_761 )
| ~ product(g1,b,c,Z_761) ),
inference(resolution,[status(thm)],[c_52,c_11287]) ).
tff(c_11948,plain,
c = a,
inference(resolution,[status(thm)],[c_11417,c_11941]) ).
tff(c_11958,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11279,c_11948]) ).
tff(c_11959,plain,
d2 = b,
inference(splitRight,[status(thm)],[c_11402]) ).
tff(c_12332,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_68,c_78,c_11959,c_80,c_11278,c_9726]) ).
tff(c_12333,plain,
d3 = b,
inference(splitRight,[status(thm)],[c_11276]) ).
tff(c_12465,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_62,c_76,c_12414,c_78,c_12333,c_9726]) ).
tff(c_12466,plain,
( ( d2 = b )
| ( d2 = c ) ),
inference(splitRight,[status(thm)],[c_145]) ).
tff(c_12479,plain,
d2 = c,
inference(splitLeft,[status(thm)],[c_12466]) ).
tff(c_12336,plain,
product(g1,b,d2,b),
inference(demodulation,[status(thm),theory(equality)],[c_12333,c_9724]) ).
tff(c_12481,plain,
product(g1,b,c,b),
inference(demodulation,[status(thm),theory(equality)],[c_12479,c_12336]) ).
tff(c_12344,plain,
! [Xg_790,Z_788,Y_791,X_789,W_787] :
( ( Z_788 = W_787 )
| ~ product(Xg_790,X_789,Y_791,W_787)
| ~ product(Xg_790,X_789,Y_791,Z_788) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_12885,plain,
! [Z_829] :
( ( a = Z_829 )
| ~ product(g1,b,c,Z_829) ),
inference(resolution,[status(thm)],[c_52,c_12344]) ).
tff(c_12888,plain,
b = a,
inference(resolution,[status(thm)],[c_12481,c_12885]) ).
tff(c_12899,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9722,c_12888]) ).
tff(c_12900,plain,
d2 = b,
inference(splitRight,[status(thm)],[c_12466]) ).
tff(c_12903,plain,
product(g1,b,b,b),
inference(demodulation,[status(thm),theory(equality)],[c_12900,c_12336]) ).
tff(c_13145,plain,
! [Z_850] :
( ( c = Z_850 )
| ~ product(g1,b,b,Z_850) ),
inference(resolution,[status(thm)],[c_50,c_12344]) ).
tff(c_13148,plain,
c = b,
inference(resolution,[status(thm)],[c_12903,c_13145]) ).
tff(c_13159,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9732,c_13148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP026-1 : TPTP v8.1.2. Bugfixed v2.0.0.
% 0.13/0.13 % 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
% 0.13/0.34 % Computer : n004.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 : Thu Aug 3 22:01:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 9.32/3.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.32/3.43
% 9.32/3.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.17/3.50
% 10.17/3.50 Inference rules
% 10.17/3.50 ----------------------
% 10.17/3.50 #Ref : 0
% 10.17/3.50 #Sup : 3283
% 10.17/3.50 #Fact : 0
% 10.17/3.50 #Define : 0
% 10.17/3.50 #Split : 26
% 10.17/3.50 #Chain : 0
% 10.17/3.50 #Close : 0
% 10.17/3.50
% 10.17/3.50 Ordering : KBO
% 10.17/3.50
% 10.17/3.50 Simplification rules
% 10.17/3.50 ----------------------
% 10.17/3.50 #Subsume : 19
% 10.17/3.50 #Demod : 2550
% 10.17/3.50 #Tautology : 1612
% 10.17/3.50 #SimpNegUnit : 18
% 10.17/3.50 #BackRed : 168
% 10.17/3.50
% 10.17/3.50 #Partial instantiations: 0
% 10.17/3.50 #Strategies tried : 1
% 10.17/3.50
% 10.17/3.50 Timing (in seconds)
% 10.17/3.50 ----------------------
% 10.17/3.50 Preprocessing : 0.52
% 10.17/3.50 Parsing : 0.25
% 10.17/3.50 CNF conversion : 0.03
% 10.17/3.51 Main loop : 1.85
% 10.17/3.51 Inferencing : 0.66
% 10.17/3.51 Reduction : 0.60
% 10.17/3.51 Demodulation : 0.46
% 10.17/3.51 BG Simplification : 0.06
% 10.17/3.51 Subsumption : 0.38
% 10.17/3.51 Abstraction : 0.05
% 10.17/3.51 MUC search : 0.00
% 10.17/3.51 Cooper : 0.00
% 10.17/3.51 Total : 2.49
% 10.17/3.51 Index Insertion : 0.00
% 10.17/3.51 Index Deletion : 0.00
% 10.17/3.51 Index Matching : 0.00
% 10.17/3.51 BG Taut test : 0.00
%------------------------------------------------------------------------------