TSTP Solution File: FLD029-3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : FLD029-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n023.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 10:37:31 EDT 2023
% Result : Unsatisfiable 112.11s 95.92s
% Output : CNFRefutation 112.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 34
% Syntax : Number of formulae : 145 ( 54 unt; 14 typ; 0 def)
% Number of atoms : 280 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 296 ( 147 ~; 149 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 166 (; 166 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > v > u > multiplicative_identity > b > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(u,type,
u: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(additive_inverse,type,
additive_inverse: $i > $i ).
tff(b,type,
b: $i ).
tff(defined,type,
defined: $i > $o ).
tff(multiplicative_inverse,type,
multiplicative_inverse: $i > $i ).
tff(v,type,
v: $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(f_258,axiom,
~ product(multiplicative_identity,u,v),
file(unknown,unknown) ).
tff(f_252,axiom,
defined(v),
file(unknown,unknown) ).
tff(f_254,axiom,
~ sum(additive_identity,b,additive_identity),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_250,axiom,
defined(b),
file(unknown,unknown) ).
tff(f_173,axiom,
defined(multiplicative_identity),
file(unknown,unknown) ).
tff(f_251,axiom,
defined(u),
file(unknown,unknown) ).
tff(f_117,axiom,
! [X] :
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_255,axiom,
product(a,u,b),
file(unknown,unknown) ).
tff(f_122,axiom,
! [Y,X,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_94,axiom,
! [W,U,Z,X,Y,V] :
( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [W,U,Z,X,Y,V] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file(unknown,unknown) ).
tff(f_136,axiom,
! [A,Z,B,C,X,Y,D] :
( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [W,U,Z,X,Y,V] :
( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) ),
file(unknown,unknown) ).
tff(f_256,axiom,
product(a,v,b),
file(unknown,unknown) ).
tff(f_105,axiom,
! [W,U,Z,X,Y,V] :
( product(U,Z,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) ),
file(unknown,unknown) ).
tff(c_68,plain,
~ product(multiplicative_identity,u,v),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_60,plain,
defined(v),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_62,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_8,plain,
! [X_14] :
( ~ defined(X_14)
| sum(additive_inverse(X_14),X_14,additive_identity) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_56,plain,
defined(b),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_34,plain,
defined(multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_58,plain,
defined(u),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_18,plain,
! [X_31] :
( ~ defined(X_31)
| sum(additive_identity,X_31,additive_identity)
| product(multiplicative_inverse(X_31),X_31,multiplicative_identity) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_64,plain,
product(a,u,b),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_89,plain,
! [X_85,Y_86,Z_87] :
( ~ product(X_85,Y_86,Z_87)
| product(Y_86,X_85,Z_87) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_98,plain,
product(u,a,b),
inference(resolution,[status(thm)],[c_64,c_89]) ).
tff(c_16,plain,
! [X_30] :
( ~ defined(X_30)
| product(multiplicative_identity,X_30,X_30) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_475,plain,
! [U_138,W_140,Z_139,X_141,V_142,Y_143] :
( ~ product(U_138,Z_139,W_140)
| ~ product(Y_143,Z_139,V_142)
| ~ product(X_141,Y_143,U_138)
| product(X_141,V_142,W_140) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_1846,plain,
! [Y_216,X_217,V_218,X_219] :
( ~ product(Y_216,X_217,V_218)
| ~ product(X_219,Y_216,multiplicative_identity)
| product(X_219,V_218,X_217)
| ~ defined(X_217) ),
inference(resolution,[status(thm)],[c_16,c_475]) ).
tff(c_1900,plain,
! [X_219] :
( ~ product(X_219,u,multiplicative_identity)
| product(X_219,b,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_98,c_1846]) ).
tff(c_1976,plain,
! [X_220] :
( ~ product(X_220,u,multiplicative_identity)
| product(X_220,b,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_1900]) ).
tff(c_1980,plain,
( product(multiplicative_inverse(u),b,a)
| ~ defined(u)
| sum(additive_identity,u,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_1976]) ).
tff(c_1983,plain,
( product(multiplicative_inverse(u),b,a)
| sum(additive_identity,u,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_1980]) ).
tff(c_107773,plain,
sum(additive_identity,u,additive_identity),
inference(splitLeft,[status(thm)],[c_1983]) ).
tff(c_10,plain,
! [X_16,Y_15,Z_17] :
( ~ sum(X_16,Y_15,Z_17)
| sum(Y_15,X_16,Z_17) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_107972,plain,
sum(u,additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_107773,c_10]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_670,plain,
! [Y_156,X_159,U_158,W_160,Z_155,V_157] :
( ~ sum(U_158,Z_155,W_160)
| ~ sum(Y_156,Z_155,V_157)
| ~ sum(X_159,Y_156,U_158)
| sum(X_159,V_157,W_160) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_107635,plain,
! [Y_1049,X_1050,V_1051,X_1052] :
( ~ sum(Y_1049,X_1050,V_1051)
| ~ sum(X_1052,Y_1049,additive_identity)
| sum(X_1052,V_1051,X_1050)
| ~ defined(X_1050) ),
inference(resolution,[status(thm)],[c_6,c_670]) ).
tff(c_115416,plain,
! [X_1166,X_1167] :
( ~ sum(X_1166,additive_identity,additive_identity)
| sum(X_1166,X_1167,X_1167)
| ~ defined(X_1167) ),
inference(resolution,[status(thm)],[c_6,c_107635]) ).
tff(c_115452,plain,
! [X_1167] :
( sum(u,X_1167,X_1167)
| ~ defined(X_1167) ),
inference(resolution,[status(thm)],[c_107972,c_115416]) ).
tff(c_861,plain,
! [B_180,C_182,X_181,Z_179,Y_178,D_183,A_177] :
( ~ product(Y_178,Z_179,D_183)
| ~ product(X_181,Z_179,C_182)
| ~ product(A_177,Z_179,B_180)
| ~ sum(X_181,Y_178,A_177)
| sum(C_182,D_183,B_180) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_115866,plain,
! [A_1176,B_1174,X_1175,C_1173,X_1177] :
( ~ product(X_1177,X_1175,C_1173)
| ~ product(A_1176,X_1175,B_1174)
| ~ sum(X_1177,multiplicative_identity,A_1176)
| sum(C_1173,X_1175,B_1174)
| ~ defined(X_1175) ),
inference(resolution,[status(thm)],[c_16,c_861]) ).
tff(c_115956,plain,
! [A_1176,B_1174] :
( ~ product(A_1176,a,B_1174)
| ~ sum(u,multiplicative_identity,A_1176)
| sum(b,a,B_1174)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_98,c_115866]) ).
tff(c_145972,plain,
! [A_1436,B_1437] :
( ~ product(A_1436,a,B_1437)
| ~ sum(u,multiplicative_identity,A_1436)
| sum(b,a,B_1437) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_115956]) ).
tff(c_146029,plain,
( ~ sum(u,multiplicative_identity,multiplicative_identity)
| sum(b,a,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_16,c_145972]) ).
tff(c_146063,plain,
( ~ sum(u,multiplicative_identity,multiplicative_identity)
| sum(b,a,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_146029]) ).
tff(c_146137,plain,
~ sum(u,multiplicative_identity,multiplicative_identity),
inference(splitLeft,[status(thm)],[c_146063]) ).
tff(c_146140,plain,
~ defined(multiplicative_identity),
inference(resolution,[status(thm)],[c_115452,c_146137]) ).
tff(c_146144,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_146140]) ).
tff(c_146145,plain,
sum(b,a,a),
inference(splitRight,[status(thm)],[c_146063]) ).
tff(c_146217,plain,
sum(a,b,a),
inference(resolution,[status(thm)],[c_146145,c_10]) ).
tff(c_694,plain,
! [Y_156,X_13,V_157,X_159] :
( ~ sum(Y_156,X_13,V_157)
| ~ sum(X_159,Y_156,additive_identity)
| sum(X_159,V_157,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_670]) ).
tff(c_146459,plain,
! [X_159] :
( ~ sum(X_159,a,additive_identity)
| sum(X_159,a,b)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_146217,c_694]) ).
tff(c_161734,plain,
! [X_1548] :
( ~ sum(X_1548,a,additive_identity)
| sum(X_1548,a,b) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_146459]) ).
tff(c_161841,plain,
! [X_1549] :
( sum(a,X_1549,b)
| ~ sum(X_1549,a,additive_identity) ),
inference(resolution,[status(thm)],[c_161734,c_10]) ).
tff(c_161850,plain,
( sum(a,additive_inverse(a),b)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_8,c_161841]) ).
tff(c_161857,plain,
sum(a,additive_inverse(a),b),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_161850]) ).
tff(c_161918,plain,
sum(additive_inverse(a),a,b),
inference(resolution,[status(thm)],[c_161857,c_10]) ).
tff(c_74,plain,
! [X_80,Y_81,Z_82] :
( ~ sum(X_80,Y_81,Z_82)
| sum(Y_81,X_80,Z_82) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_80,plain,
! [X_13] :
( sum(X_13,additive_identity,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_74]) ).
tff(c_546,plain,
! [X_149,Z_145,V_148,Y_150,U_147,W_146] :
( ~ sum(X_149,V_148,W_146)
| ~ sum(Y_150,Z_145,V_148)
| ~ sum(X_149,Y_150,U_147)
| sum(U_147,Z_145,W_146) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_108797,plain,
! [Y_1076,Z_1077,X_1078,U_1079] :
( ~ sum(Y_1076,Z_1077,X_1078)
| ~ sum(additive_inverse(X_1078),Y_1076,U_1079)
| sum(U_1079,Z_1077,additive_identity)
| ~ defined(X_1078) ),
inference(resolution,[status(thm)],[c_8,c_546]) ).
tff(c_108831,plain,
! [X_13,U_1079] :
( ~ sum(additive_inverse(X_13),X_13,U_1079)
| sum(U_1079,additive_identity,additive_identity)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_80,c_108797]) ).
tff(c_161930,plain,
( sum(b,additive_identity,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_161918,c_108831]) ).
tff(c_161971,plain,
sum(b,additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_161930]) ).
tff(c_162056,plain,
sum(additive_identity,b,additive_identity),
inference(resolution,[status(thm)],[c_161971,c_10]) ).
tff(c_162102,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62,c_162056]) ).
tff(c_162104,plain,
~ sum(additive_identity,u,additive_identity),
inference(splitRight,[status(thm)],[c_1983]) ).
tff(c_66,plain,
product(a,v,b),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_1906,plain,
! [X_219] :
( ~ product(X_219,a,multiplicative_identity)
| product(X_219,b,v)
| ~ defined(v) ),
inference(resolution,[status(thm)],[c_66,c_1846]) ).
tff(c_1992,plain,
! [X_222] :
( ~ product(X_222,a,multiplicative_identity)
| product(X_222,b,v) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1906]) ).
tff(c_20,plain,
! [X_33,Y_32,Z_34] :
( ~ product(X_33,Y_32,Z_34)
| product(Y_32,X_33,Z_34) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_2019,plain,
! [X_223] :
( product(b,X_223,v)
| ~ product(X_223,a,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_1992,c_20]) ).
tff(c_2022,plain,
( product(b,multiplicative_inverse(a),v)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_2019]) ).
tff(c_2025,plain,
( product(b,multiplicative_inverse(a),v)
| sum(additive_identity,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_2022]) ).
tff(c_163820,plain,
sum(additive_identity,a,additive_identity),
inference(splitLeft,[status(thm)],[c_2025]) ).
tff(c_163904,plain,
sum(a,additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_163820,c_10]) ).
tff(c_107663,plain,
! [X_1052,X_13] :
( ~ sum(X_1052,additive_identity,additive_identity)
| sum(X_1052,X_13,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_107635]) ).
tff(c_163963,plain,
! [X_13] :
( sum(a,X_13,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_163904,c_107663]) ).
tff(c_167345,plain,
! [X_1662,X_1660,A_1661,B_1659,C_1658] :
( ~ product(X_1662,X_1660,C_1658)
| ~ product(A_1661,X_1660,B_1659)
| ~ sum(X_1662,multiplicative_identity,A_1661)
| sum(C_1658,X_1660,B_1659)
| ~ defined(X_1660) ),
inference(resolution,[status(thm)],[c_16,c_861]) ).
tff(c_167451,plain,
! [A_1661,B_1659] :
( ~ product(A_1661,u,B_1659)
| ~ sum(a,multiplicative_identity,A_1661)
| sum(b,u,B_1659)
| ~ defined(u) ),
inference(resolution,[status(thm)],[c_64,c_167345]) ).
tff(c_184586,plain,
! [A_1809,B_1810] :
( ~ product(A_1809,u,B_1810)
| ~ sum(a,multiplicative_identity,A_1809)
| sum(b,u,B_1810) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_167451]) ).
tff(c_184612,plain,
( ~ sum(a,multiplicative_identity,multiplicative_identity)
| sum(b,u,u)
| ~ defined(u) ),
inference(resolution,[status(thm)],[c_16,c_184586]) ).
tff(c_184635,plain,
( ~ sum(a,multiplicative_identity,multiplicative_identity)
| sum(b,u,u) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_184612]) ).
tff(c_186935,plain,
~ sum(a,multiplicative_identity,multiplicative_identity),
inference(splitLeft,[status(thm)],[c_184635]) ).
tff(c_186991,plain,
~ defined(multiplicative_identity),
inference(resolution,[status(thm)],[c_163963,c_186935]) ).
tff(c_186995,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_186991]) ).
tff(c_186996,plain,
sum(b,u,u),
inference(splitRight,[status(thm)],[c_184635]) ).
tff(c_187068,plain,
sum(u,b,u),
inference(resolution,[status(thm)],[c_186996,c_10]) ).
tff(c_187160,plain,
! [X_159] :
( ~ sum(X_159,u,additive_identity)
| sum(X_159,u,b)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_187068,c_694]) ).
tff(c_197116,plain,
! [X_1907] :
( ~ sum(X_1907,u,additive_identity)
| sum(X_1907,u,b) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_187160]) ).
tff(c_197310,plain,
! [X_1914] :
( sum(u,X_1914,b)
| ~ sum(X_1914,u,additive_identity) ),
inference(resolution,[status(thm)],[c_197116,c_10]) ).
tff(c_197316,plain,
( sum(u,additive_inverse(u),b)
| ~ defined(u) ),
inference(resolution,[status(thm)],[c_8,c_197310]) ).
tff(c_197322,plain,
sum(u,additive_inverse(u),b),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_197316]) ).
tff(c_197383,plain,
sum(additive_inverse(u),u,b),
inference(resolution,[status(thm)],[c_197322,c_10]) ).
tff(c_163031,plain,
! [Y_1569,Z_1570,X_1571,U_1572] :
( ~ sum(Y_1569,Z_1570,X_1571)
| ~ sum(additive_inverse(X_1571),Y_1569,U_1572)
| sum(U_1572,Z_1570,additive_identity)
| ~ defined(X_1571) ),
inference(resolution,[status(thm)],[c_8,c_546]) ).
tff(c_163055,plain,
! [X_13,U_1572] :
( ~ sum(additive_inverse(X_13),X_13,U_1572)
| sum(U_1572,additive_identity,additive_identity)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_80,c_163031]) ).
tff(c_197389,plain,
( sum(b,additive_identity,additive_identity)
| ~ defined(u) ),
inference(resolution,[status(thm)],[c_197383,c_163055]) ).
tff(c_197428,plain,
sum(b,additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_197389]) ).
tff(c_197513,plain,
sum(additive_identity,b,additive_identity),
inference(resolution,[status(thm)],[c_197428,c_10]) ).
tff(c_197556,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62,c_197513]) ).
tff(c_197557,plain,
product(b,multiplicative_inverse(a),v),
inference(splitRight,[status(thm)],[c_2025]) ).
tff(c_197591,plain,
product(multiplicative_inverse(a),b,v),
inference(resolution,[status(thm)],[c_197557,c_20]) ).
tff(c_197558,plain,
~ sum(additive_identity,a,additive_identity),
inference(splitRight,[status(thm)],[c_2025]) ).
tff(c_162103,plain,
product(multiplicative_inverse(u),b,a),
inference(splitRight,[status(thm)],[c_1983]) ).
tff(c_162131,plain,
product(b,multiplicative_inverse(u),a),
inference(resolution,[status(thm)],[c_162103,c_20]) ).
tff(c_751,plain,
! [Z_167,W_170,U_168,Y_166,X_169,V_171] :
( ~ product(X_169,V_171,W_170)
| ~ product(Y_166,Z_167,V_171)
| ~ product(X_169,Y_166,U_168)
| product(U_168,Z_167,W_170) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_202720,plain,
! [Y_2022,Z_2023,X_2024,U_2025] :
( ~ product(Y_2022,Z_2023,X_2024)
| ~ product(multiplicative_inverse(X_2024),Y_2022,U_2025)
| product(U_2025,Z_2023,multiplicative_identity)
| ~ defined(X_2024)
| sum(additive_identity,X_2024,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_751]) ).
tff(c_202788,plain,
! [U_2025] :
( ~ product(multiplicative_inverse(a),b,U_2025)
| product(U_2025,multiplicative_inverse(u),multiplicative_identity)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[c_162131,c_202720]) ).
tff(c_202989,plain,
! [U_2025] :
( ~ product(multiplicative_inverse(a),b,U_2025)
| product(U_2025,multiplicative_inverse(u),multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_202788]) ).
tff(c_340465,plain,
! [U_2952] :
( ~ product(multiplicative_inverse(a),b,U_2952)
| product(U_2952,multiplicative_inverse(u),multiplicative_identity) ),
inference(negUnitSimplification,[status(thm)],[c_197558,c_202989]) ).
tff(c_340548,plain,
product(v,multiplicative_inverse(u),multiplicative_identity),
inference(resolution,[status(thm)],[c_197591,c_340465]) ).
tff(c_1957,plain,
! [X_219,X_31] :
( ~ product(X_219,multiplicative_inverse(X_31),multiplicative_identity)
| product(X_219,multiplicative_identity,X_31)
| ~ defined(X_31)
| sum(additive_identity,X_31,additive_identity) ),
inference(resolution,[status(thm)],[c_18,c_1846]) ).
tff(c_341561,plain,
( product(v,multiplicative_identity,u)
| ~ defined(u)
| sum(additive_identity,u,additive_identity) ),
inference(resolution,[status(thm)],[c_340548,c_1957]) ).
tff(c_341620,plain,
( product(v,multiplicative_identity,u)
| sum(additive_identity,u,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_341561]) ).
tff(c_341621,plain,
product(v,multiplicative_identity,u),
inference(negUnitSimplification,[status(thm)],[c_162104,c_341620]) ).
tff(c_96,plain,
! [X_30] :
( product(X_30,multiplicative_identity,X_30)
| ~ defined(X_30) ),
inference(resolution,[status(thm)],[c_16,c_89]) ).
tff(c_245584,plain,
! [Y_2460,Z_2461,X_2462,U_2463] :
( ~ product(Y_2460,Z_2461,multiplicative_identity)
| ~ product(X_2462,Y_2460,U_2463)
| product(U_2463,Z_2461,X_2462)
| ~ defined(X_2462) ),
inference(resolution,[status(thm)],[c_96,c_751]) ).
tff(c_245767,plain,
! [X_2462,U_2463] :
( ~ product(X_2462,multiplicative_identity,U_2463)
| product(U_2463,multiplicative_identity,X_2462)
| ~ defined(X_2462)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_16,c_245584]) ).
tff(c_245887,plain,
! [X_2462,U_2463] :
( ~ product(X_2462,multiplicative_identity,U_2463)
| product(U_2463,multiplicative_identity,X_2462)
| ~ defined(X_2462) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_245767]) ).
tff(c_341844,plain,
( product(u,multiplicative_identity,v)
| ~ defined(v) ),
inference(resolution,[status(thm)],[c_341621,c_245887]) ).
tff(c_341916,plain,
product(u,multiplicative_identity,v),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_341844]) ).
tff(c_342043,plain,
product(multiplicative_identity,u,v),
inference(resolution,[status(thm)],[c_341916,c_20]) ).
tff(c_342125,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_68,c_342043]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : FLD029-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.14 % 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
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 20:10:52 EDT 2023
% 0.14/0.36 % CPUTime :
% 112.11/95.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 112.11/95.93
% 112.11/95.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 112.11/95.98
% 112.11/95.98 Inference rules
% 112.11/95.98 ----------------------
% 112.11/95.98 #Ref : 0
% 112.11/95.98 #Sup : 76037
% 112.11/95.98 #Fact : 16
% 112.11/95.98 #Define : 0
% 112.11/95.98 #Split : 379
% 112.11/95.98 #Chain : 0
% 112.11/95.99 #Close : 0
% 112.11/95.99
% 112.11/95.99 Ordering : KBO
% 112.11/95.99
% 112.11/95.99 Simplification rules
% 112.11/95.99 ----------------------
% 112.11/95.99 #Subsume : 7167
% 112.11/95.99 #Demod : 53990
% 112.11/95.99 #Tautology : 13865
% 112.11/95.99 #SimpNegUnit : 1971
% 112.11/95.99 #BackRed : 0
% 112.11/95.99
% 112.11/95.99 #Partial instantiations: 0
% 112.11/95.99 #Strategies tried : 1
% 112.11/95.99
% 112.11/95.99 Timing (in seconds)
% 112.11/95.99 ----------------------
% 112.41/95.99 Preprocessing : 0.51
% 112.41/95.99 Parsing : 0.29
% 112.41/95.99 CNF conversion : 0.03
% 112.41/95.99 Main loop : 94.35
% 112.41/95.99 Inferencing : 9.35
% 112.41/95.99 Reduction : 48.43
% 112.41/95.99 Demodulation : 41.11
% 112.41/95.99 BG Simplification : 0.35
% 112.41/95.99 Subsumption : 28.29
% 112.41/95.99 Abstraction : 0.52
% 112.41/95.99 MUC search : 0.00
% 112.41/95.99 Cooper : 0.00
% 112.41/95.99 Total : 94.94
% 112.41/95.99 Index Insertion : 0.00
% 112.41/95.99 Index Deletion : 0.00
% 112.41/95.99 Index Matching : 0.00
% 112.41/95.99 BG Taut test : 0.00
%------------------------------------------------------------------------------