TSTP Solution File: GRP124-7.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% 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 : n016.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 10:39:56 EDT 2023
% Result : Unsatisfiable 10.17s 3.42s
% Output : CNFRefutation 10.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 35
% Syntax : Number of formulae : 327 ( 167 unt; 11 typ; 0 def)
% Number of atoms : 636 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 516 ( 196 ~; 320 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 7 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 153 (; 153 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product2 > product1 > product > next > greater > equalish > group_element > #nlpp > e_4 > e_3 > e_2 > e_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(next,type,
next: ( $i * $i ) > $o ).
tff(product1,type,
product1: ( $i * $i * $i ) > $o ).
tff(e_4,type,
e_4: $i ).
tff(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(product2,type,
product2: ( $i * $i * $i ) > $o ).
tff(f_65,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_69,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_71,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_117,axiom,
! [X] : product1(X,X,X),
file(unknown,unknown) ).
tff(f_63,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_77,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_51,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_53,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product1(X,Y,e_1)
| product1(X,Y,e_2)
| product1(X,Y,e_3)
| product1(X,Y,e_4) ),
file(unknown,unknown) ).
tff(f_115,axiom,
! [W,Y,X,Z] :
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_52,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_67,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_59,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_50,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_57,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_107,axiom,
! [X,W,Y,Z] :
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_73,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_165,axiom,
! [X,Y,Z1,Z2] :
( ~ product1(X,Y,Z1)
| ~ product1(Z1,X,Z2)
| product2(Z2,Y,X) ),
file(unknown,unknown) ).
tff(f_157,axiom,
! [X] : product2(X,X,X),
file(unknown,unknown) ).
tff(f_139,axiom,
! [X,Y,W,Z] :
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_131,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product2(X,Y,e_1)
| product2(X,Y,e_2)
| product2(X,Y,e_3)
| product2(X,Y,e_4) ),
file(unknown,unknown) ).
tff(f_147,axiom,
! [X,W,Y,Z] :
( ~ product2(X,W,Y)
| ~ product2(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_155,axiom,
! [W,Y,X,Z] :
( ~ product2(W,Y,X)
| ~ product2(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_75,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(c_40,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_44,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_46,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_62,plain,
! [X_18] : product1(X_18,X_18,X_18),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_38,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_52,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_24,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_28,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_194,plain,
! [X_92,Y_93] :
( product1(X_92,Y_93,e_4)
| product1(X_92,Y_93,e_3)
| product1(X_92,Y_93,e_2)
| product1(X_92,Y_93,e_1)
| ~ group_element(Y_93)
| ~ group_element(X_92) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_106,plain,
! [W_53,Z_54,Y_55,X_56] :
( equalish(W_53,Z_54)
| ~ product1(Z_54,Y_55,X_56)
| ~ product1(W_53,Y_55,X_56) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_109,plain,
! [W_53,X_18] :
( equalish(W_53,X_18)
| ~ product1(W_53,X_18,X_18) ),
inference(resolution,[status(thm)],[c_62,c_106]) ).
tff(c_212,plain,
! [X_92] :
( equalish(X_92,e_4)
| product1(X_92,e_4,e_3)
| product1(X_92,e_4,e_2)
| product1(X_92,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_92) ),
inference(resolution,[status(thm)],[c_194,c_109]) ).
tff(c_224,plain,
! [X_92] :
( equalish(X_92,e_4)
| product1(X_92,e_4,e_3)
| product1(X_92,e_4,e_2)
| product1(X_92,e_4,e_1)
| ~ group_element(X_92) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_212]) ).
tff(c_26,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_54,plain,
! [X_4,Y_5] :
( product1(X_4,Y_5,e_4)
| product1(X_4,Y_5,e_3)
| product1(X_4,Y_5,e_2)
| product1(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_42,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_34,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_22,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_32,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_132,plain,
! [W_68,Z_69,X_70,Y_71] :
( equalish(W_68,Z_69)
| ~ product1(X_70,Z_69,Y_71)
| ~ product1(X_70,W_68,Y_71) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_135,plain,
! [W_68,X_18] :
( equalish(W_68,X_18)
| ~ product1(X_18,W_68,X_18) ),
inference(resolution,[status(thm)],[c_62,c_132]) ).
tff(c_206,plain,
! [Y_93] :
( equalish(Y_93,e_4)
| product1(e_4,Y_93,e_3)
| product1(e_4,Y_93,e_2)
| product1(e_4,Y_93,e_1)
| ~ group_element(Y_93)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_194,c_135]) ).
tff(c_1817,plain,
! [Y_174] :
( equalish(Y_174,e_4)
| product1(e_4,Y_174,e_3)
| product1(e_4,Y_174,e_2)
| product1(e_4,Y_174,e_1)
| ~ group_element(Y_174) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_206]) ).
tff(c_48,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_266,plain,
! [X_105] :
( equalish(X_105,e_4)
| product1(X_105,e_4,e_3)
| product1(X_105,e_4,e_2)
| product1(X_105,e_4,e_1)
| ~ group_element(X_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_212]) ).
tff(c_282,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_266,c_135]) ).
tff(c_299,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_282]) ).
tff(c_300,plain,
( product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_46,c_52,c_299]) ).
tff(c_344,plain,
product1(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_300]) ).
tff(c_74,plain,
! [Z2_37,Y_35,X_34,Z1_36] :
( product2(Z2_37,Y_35,X_34)
| ~ product1(Z1_36,X_34,Z2_37)
| ~ product1(X_34,Y_35,Z1_36) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_392,plain,
! [Y_111] :
( product2(e_1,Y_111,e_4)
| ~ product1(e_4,Y_111,e_3) ),
inference(resolution,[status(thm)],[c_344,c_74]) ).
tff(c_72,plain,
! [X_33] : product2(X_33,X_33,X_33),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_122,plain,
! [W_62,Z_63,X_64,Y_65] :
( equalish(W_62,Z_63)
| ~ product2(X_64,Y_65,Z_63)
| ~ product2(X_64,Y_65,W_62) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_125,plain,
! [W_62,X_33] :
( equalish(W_62,X_33)
| ~ product2(X_33,X_33,W_62) ),
inference(resolution,[status(thm)],[c_72,c_122]) ).
tff(c_406,plain,
( equalish(e_4,e_1)
| ~ product1(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[c_392,c_125]) ).
tff(c_423,plain,
~ product1(e_4,e_1,e_3),
inference(negUnitSimplification,[status(thm)],[c_48,c_406]) ).
tff(c_1834,plain,
( equalish(e_1,e_4)
| product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_1817,c_423]) ).
tff(c_1870,plain,
( equalish(e_1,e_4)
| product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1834]) ).
tff(c_1871,plain,
( product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_1870]) ).
tff(c_1960,plain,
product1(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_1871]) ).
tff(c_303,plain,
! [X_106,Y_107] :
( product2(X_106,Y_107,e_4)
| product2(X_106,Y_107,e_3)
| product2(X_106,Y_107,e_2)
| product2(X_106,Y_107,e_1)
| ~ group_element(Y_107)
| ~ group_element(X_106) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_97,plain,
! [W_44,Z_45,X_46,Y_47] :
( equalish(W_44,Z_45)
| ~ product2(X_46,Z_45,Y_47)
| ~ product2(X_46,W_44,Y_47) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_100,plain,
! [W_44,X_33] :
( equalish(W_44,X_33)
| ~ product2(X_33,W_44,X_33) ),
inference(resolution,[status(thm)],[c_72,c_97]) ).
tff(c_326,plain,
! [Y_107] :
( equalish(Y_107,e_4)
| product2(e_4,Y_107,e_3)
| product2(e_4,Y_107,e_2)
| product2(e_4,Y_107,e_1)
| ~ group_element(Y_107)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_303,c_100]) ).
tff(c_1094,plain,
! [Y_141] :
( equalish(Y_141,e_4)
| product2(e_4,Y_141,e_3)
| product2(e_4,Y_141,e_2)
| product2(e_4,Y_141,e_1)
| ~ group_element(Y_141) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_326]) ).
tff(c_152,plain,
! [W_80,Z_81,Y_82,X_83] :
( equalish(W_80,Z_81)
| ~ product2(Z_81,Y_82,X_83)
| ~ product2(W_80,Y_82,X_83) ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_155,plain,
! [W_80,X_33] :
( equalish(W_80,X_33)
| ~ product2(W_80,X_33,X_33) ),
inference(resolution,[status(thm)],[c_72,c_152]) ).
tff(c_1102,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product2(e_4,e_3,e_2)
| product2(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_1094,c_155]) ).
tff(c_1120,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product2(e_4,e_3,e_2)
| product2(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_1102]) ).
tff(c_1121,plain,
( product2(e_4,e_3,e_2)
| product2(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_46,c_52,c_1120]) ).
tff(c_1129,plain,
product2(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_1121]) ).
tff(c_162,plain,
! [Z2_86,Y_87,X_88,Z1_89] :
( product2(Z2_86,Y_87,X_88)
| ~ product1(Z1_89,X_88,Z2_86)
| ~ product1(X_88,Y_87,Z1_89) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_166,plain,
! [X_90,Y_91] :
( product2(X_90,Y_91,X_90)
| ~ product1(X_90,Y_91,X_90) ),
inference(resolution,[status(thm)],[c_62,c_162]) ).
tff(c_66,plain,
! [W_23,Z_24,X_21,Y_22] :
( equalish(W_23,Z_24)
| ~ product2(X_21,Y_22,Z_24)
| ~ product2(X_21,Y_22,W_23) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_191,plain,
! [W_23,X_90,Y_91] :
( equalish(W_23,X_90)
| ~ product2(X_90,Y_91,W_23)
| ~ product1(X_90,Y_91,X_90) ),
inference(resolution,[status(thm)],[c_166,c_66]) ).
tff(c_1141,plain,
( equalish(e_1,e_4)
| ~ product1(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[c_1129,c_191]) ).
tff(c_1152,plain,
~ product1(e_4,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_34,c_1141]) ).
tff(c_1161,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_54,c_1152]) ).
tff(c_1164,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_1161]) ).
tff(c_1227,plain,
product1(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_1164]) ).
tff(c_58,plain,
! [W_11,Z_13,X_10,Y_12] :
( equalish(W_11,Z_13)
| ~ product1(X_10,Z_13,Y_12)
| ~ product1(X_10,W_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_1244,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product1(e_4,W_11,e_1) ),
inference(resolution,[status(thm)],[c_1227,c_58]) ).
tff(c_1965,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_1960,c_1244]) ).
tff(c_1986,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_1965]) ).
tff(c_1987,plain,
product1(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_1871]) ).
tff(c_1309,plain,
! [Y_154] :
( product2(e_1,Y_154,e_3)
| ~ product1(e_3,Y_154,e_4) ),
inference(resolution,[status(thm)],[c_1227,c_74]) ).
tff(c_1326,plain,
( equalish(e_3,e_1)
| ~ product1(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_1309,c_125]) ).
tff(c_1346,plain,
~ product1(e_3,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_42,c_1326]) ).
tff(c_1357,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_1346]) ).
tff(c_1360,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_22,c_1357]) ).
tff(c_1588,plain,
product1(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_1360]) ).
tff(c_355,plain,
! [W_11] :
( equalish(W_11,e_4)
| ~ product1(e_3,W_11,e_1) ),
inference(resolution,[status(thm)],[c_344,c_58]) ).
tff(c_1594,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_1588,c_355]) ).
tff(c_1613,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_1594]) ).
tff(c_1614,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_1360]) ).
tff(c_1616,plain,
product1(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_1614]) ).
tff(c_68,plain,
! [W_26,Z_28,X_25,Y_27] :
( equalish(W_26,Z_28)
| ~ product2(X_25,Z_28,Y_27)
| ~ product2(X_25,W_26,Y_27) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_236,plain,
! [W_97,Y_98,X_99] :
( equalish(W_97,Y_98)
| ~ product2(X_99,W_97,X_99)
| ~ product1(X_99,Y_98,X_99) ),
inference(resolution,[status(thm)],[c_166,c_68]) ).
tff(c_242,plain,
! [X_33,Y_98] :
( equalish(X_33,Y_98)
| ~ product1(X_33,Y_98,X_33) ),
inference(resolution,[status(thm)],[c_72,c_236]) ).
tff(c_1621,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_1616,c_242]) ).
tff(c_1640,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_1621]) ).
tff(c_1641,plain,
product1(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_1614]) ).
tff(c_60,plain,
! [W_14,Z_17,Y_15,X_16] :
( equalish(W_14,Z_17)
| ~ product1(Z_17,Y_15,X_16)
| ~ product1(W_14,Y_15,X_16) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_1706,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product1(W_14,e_1,e_2) ),
inference(resolution,[status(thm)],[c_1641,c_60]) ).
tff(c_1991,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_1987,c_1706]) ).
tff(c_2007,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_1991]) ).
tff(c_2008,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_1164]) ).
tff(c_2031,plain,
product1(e_4,e_3,e_3),
inference(splitLeft,[status(thm)],[c_2008]) ).
tff(c_2045,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_2031,c_109]) ).
tff(c_2059,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_2045]) ).
tff(c_2060,plain,
product1(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_2008]) ).
tff(c_2180,plain,
! [Y_185] :
( product2(e_2,Y_185,e_3)
| ~ product1(e_3,Y_185,e_4) ),
inference(resolution,[status(thm)],[c_2060,c_74]) ).
tff(c_2194,plain,
( equalish(e_3,e_2)
| ~ product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[c_2180,c_125]) ).
tff(c_2211,plain,
~ product1(e_3,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_44,c_2194]) ).
tff(c_2280,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_2211]) ).
tff(c_2283,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_2280]) ).
tff(c_2433,plain,
product1(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_2283]) ).
tff(c_2438,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_2433,c_355]) ).
tff(c_2454,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_2438]) ).
tff(c_2455,plain,
( product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_2283]) ).
tff(c_2502,plain,
product1(e_3,e_2,e_3),
inference(splitLeft,[status(thm)],[c_2455]) ).
tff(c_2509,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_2502,c_242]) ).
tff(c_2531,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_2509]) ).
tff(c_2532,plain,
product1(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_2455]) ).
tff(c_2578,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_2532,c_109]) ).
tff(c_2594,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_2578]) ).
tff(c_2595,plain,
product2(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_1121]) ).
tff(c_2608,plain,
( equalish(e_2,e_4)
| ~ product1(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[c_2595,c_191]) ).
tff(c_2619,plain,
~ product1(e_4,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_40,c_2608]) ).
tff(c_2628,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_54,c_2619]) ).
tff(c_2631,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_2628]) ).
tff(c_2694,plain,
product1(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_2631]) ).
tff(c_2813,plain,
! [Y_212] :
( product2(e_1,Y_212,e_3)
| ~ product1(e_3,Y_212,e_4) ),
inference(resolution,[status(thm)],[c_2694,c_74]) ).
tff(c_2832,plain,
( equalish(e_3,e_1)
| ~ product1(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_2813,c_125]) ).
tff(c_2856,plain,
~ product1(e_3,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_42,c_2832]) ).
tff(c_2867,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_2856]) ).
tff(c_2870,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_22,c_2867]) ).
tff(c_6219,plain,
product1(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_2870]) ).
tff(c_6226,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_6219,c_355]) ).
tff(c_6248,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_6226]) ).
tff(c_6249,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_2870]) ).
tff(c_6343,plain,
product1(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_6249]) ).
tff(c_6350,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_6343,c_242]) ).
tff(c_6372,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_6350]) ).
tff(c_6373,plain,
product1(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_6249]) ).
tff(c_5434,plain,
! [Y_289] :
( equalish(Y_289,e_4)
| product1(e_4,Y_289,e_3)
| product1(e_4,Y_289,e_2)
| product1(e_4,Y_289,e_1)
| ~ group_element(Y_289) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_206]) ).
tff(c_5451,plain,
( equalish(e_1,e_4)
| product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_5434,c_423]) ).
tff(c_5487,plain,
( equalish(e_1,e_4)
| product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_5451]) ).
tff(c_5488,plain,
( product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_5487]) ).
tff(c_5511,plain,
product1(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_5488]) ).
tff(c_2711,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product1(e_4,W_11,e_1) ),
inference(resolution,[status(thm)],[c_2694,c_58]) ).
tff(c_5532,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_5511,c_2711]) ).
tff(c_5554,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_5532]) ).
tff(c_5555,plain,
product1(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_5488]) ).
tff(c_5579,plain,
! [W_14] :
( equalish(W_14,e_4)
| ~ product1(W_14,e_1,e_2) ),
inference(resolution,[status(thm)],[c_5555,c_60]) ).
tff(c_6377,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_6373,c_5579]) ).
tff(c_6393,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_6377]) ).
tff(c_6394,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_2631]) ).
tff(c_6454,plain,
product1(e_4,e_3,e_3),
inference(splitLeft,[status(thm)],[c_6394]) ).
tff(c_6468,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_6454,c_109]) ).
tff(c_6482,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_6468]) ).
tff(c_6483,plain,
product1(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_6394]) ).
tff(c_6603,plain,
! [Y_324] :
( product2(e_2,Y_324,e_3)
| ~ product1(e_3,Y_324,e_4) ),
inference(resolution,[status(thm)],[c_6483,c_74]) ).
tff(c_6619,plain,
( equalish(e_3,e_2)
| ~ product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[c_6603,c_125]) ).
tff(c_6640,plain,
~ product1(e_3,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_44,c_6619]) ).
tff(c_6666,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_6640]) ).
tff(c_6669,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_6666]) ).
tff(c_6819,plain,
product1(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_6669]) ).
tff(c_6824,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_6819,c_355]) ).
tff(c_6840,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_6824]) ).
tff(c_6841,plain,
( product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_6669]) ).
tff(c_6887,plain,
product1(e_3,e_2,e_3),
inference(splitLeft,[status(thm)],[c_6841]) ).
tff(c_6894,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_6887,c_242]) ).
tff(c_6916,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_6894]) ).
tff(c_6917,plain,
product1(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_6841]) ).
tff(c_6932,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_6917,c_109]) ).
tff(c_6949,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_6932]) ).
tff(c_6950,plain,
product1(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_300]) ).
tff(c_50,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_7087,plain,
! [W_350,Y_351,X_352] :
( equalish(W_350,Y_351)
| ~ product1(X_352,W_350,e_4)
| product1(X_352,Y_351,e_3)
| product1(X_352,Y_351,e_2)
| product1(X_352,Y_351,e_1)
| ~ group_element(Y_351)
| ~ group_element(X_352) ),
inference(resolution,[status(thm)],[c_194,c_58]) ).
tff(c_7092,plain,
! [Y_351] :
( equalish(e_4,Y_351)
| product1(e_4,Y_351,e_3)
| product1(e_4,Y_351,e_2)
| product1(e_4,Y_351,e_1)
| ~ group_element(Y_351)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_62,c_7087]) ).
tff(c_8322,plain,
! [Y_422] :
( equalish(e_4,Y_422)
| product1(e_4,Y_422,e_3)
| product1(e_4,Y_422,e_2)
| product1(e_4,Y_422,e_1)
| ~ group_element(Y_422) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_7092]) ).
tff(c_7009,plain,
! [Y_345] :
( product2(e_2,Y_345,e_4)
| ~ product1(e_4,Y_345,e_3) ),
inference(resolution,[status(thm)],[c_6950,c_74]) ).
tff(c_7025,plain,
( equalish(e_4,e_2)
| ~ product1(e_4,e_2,e_3) ),
inference(resolution,[status(thm)],[c_7009,c_125]) ).
tff(c_7045,plain,
~ product1(e_4,e_2,e_3),
inference(negUnitSimplification,[status(thm)],[c_50,c_7025]) ).
tff(c_8342,plain,
( equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_8322,c_7045]) ).
tff(c_8382,plain,
( equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_8342]) ).
tff(c_8383,plain,
( product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_50,c_8382]) ).
tff(c_8495,plain,
product1(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_8383]) ).
tff(c_7144,plain,
! [Y_357] :
( equalish(Y_357,e_4)
| product2(e_4,Y_357,e_3)
| product2(e_4,Y_357,e_2)
| product2(e_4,Y_357,e_1)
| ~ group_element(Y_357) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_326]) ).
tff(c_7154,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product2(e_4,e_3,e_2)
| product2(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_7144,c_155]) ).
tff(c_7176,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product2(e_4,e_3,e_2)
| product2(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_7154]) ).
tff(c_7177,plain,
( product2(e_4,e_3,e_2)
| product2(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_46,c_52,c_7176]) ).
tff(c_7185,plain,
product2(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7177]) ).
tff(c_7189,plain,
( equalish(e_1,e_4)
| ~ product1(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[c_7185,c_191]) ).
tff(c_7204,plain,
~ product1(e_4,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_34,c_7189]) ).
tff(c_7213,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_54,c_7204]) ).
tff(c_7216,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_7213]) ).
tff(c_7284,plain,
product1(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7216]) ).
tff(c_7323,plain,
! [Y_367] :
( product2(e_1,Y_367,e_3)
| ~ product1(e_3,Y_367,e_4) ),
inference(resolution,[status(thm)],[c_7284,c_74]) ).
tff(c_7339,plain,
( equalish(e_3,e_1)
| ~ product1(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_7323,c_125]) ).
tff(c_7360,plain,
~ product1(e_3,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_42,c_7339]) ).
tff(c_7371,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_7360]) ).
tff(c_7374,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_22,c_7371]) ).
tff(c_7471,plain,
product1(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_7374]) ).
tff(c_7482,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_7471,c_109]) ).
tff(c_7495,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_7482]) ).
tff(c_7496,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_7374]) ).
tff(c_7498,plain,
product1(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_7496]) ).
tff(c_7513,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_7498,c_242]) ).
tff(c_7532,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_7513]) ).
tff(c_7533,plain,
product1(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_7496]) ).
tff(c_6962,plain,
! [W_11] :
( equalish(W_11,e_4)
| ~ product1(e_3,W_11,e_2) ),
inference(resolution,[status(thm)],[c_6950,c_58]) ).
tff(c_7539,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_7533,c_6962]) ).
tff(c_7555,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_7539]) ).
tff(c_7556,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_7216]) ).
tff(c_7615,plain,
product1(e_4,e_3,e_3),
inference(splitLeft,[status(thm)],[c_7556]) ).
tff(c_7627,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_7615,c_109]) ).
tff(c_7637,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_7627]) ).
tff(c_7638,plain,
product1(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_7556]) ).
tff(c_7704,plain,
! [Y_389] :
( product2(e_2,Y_389,e_3)
| ~ product1(e_3,Y_389,e_4) ),
inference(resolution,[status(thm)],[c_7638,c_74]) ).
tff(c_7723,plain,
( equalish(e_3,e_2)
| ~ product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[c_7704,c_125]) ).
tff(c_7747,plain,
~ product1(e_3,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_44,c_7723]) ).
tff(c_7758,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_7747]) ).
tff(c_7761,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_7758]) ).
tff(c_7946,plain,
product1(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_7761]) ).
tff(c_7964,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product1(W_14,e_2,e_1) ),
inference(resolution,[status(thm)],[c_7946,c_60]) ).
tff(c_8500,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_8495,c_7964]) ).
tff(c_8518,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_8500]) ).
tff(c_8519,plain,
product1(e_4,e_2,e_2),
inference(splitRight,[status(thm)],[c_8383]) ).
tff(c_7650,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product1(e_4,W_11,e_2) ),
inference(resolution,[status(thm)],[c_7638,c_58]) ).
tff(c_8525,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_8519,c_7650]) ).
tff(c_8545,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_8525]) ).
tff(c_8546,plain,
( product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_7761]) ).
tff(c_8548,plain,
product1(e_3,e_2,e_3),
inference(splitLeft,[status(thm)],[c_8546]) ).
tff(c_8553,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_8548,c_242]) ).
tff(c_8572,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_8553]) ).
tff(c_8573,plain,
product1(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_8546]) ).
tff(c_8589,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_8573,c_6962]) ).
tff(c_8608,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_8589]) ).
tff(c_8609,plain,
product2(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_7177]) ).
tff(c_70,plain,
! [W_29,Z_32,Y_30,X_31] :
( equalish(W_29,Z_32)
| ~ product2(Z_32,Y_30,X_31)
| ~ product2(W_29,Y_30,X_31) ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_187,plain,
! [W_29,X_90,Y_91] :
( equalish(W_29,X_90)
| ~ product2(W_29,Y_91,X_90)
| ~ product1(X_90,Y_91,X_90) ),
inference(resolution,[status(thm)],[c_166,c_70]) ).
tff(c_8616,plain,
( equalish(e_4,e_2)
| ~ product1(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[c_8609,c_187]) ).
tff(c_8632,plain,
~ product1(e_2,e_3,e_2),
inference(negUnitSimplification,[status(thm)],[c_50,c_8616]) ).
tff(c_8614,plain,
( equalish(e_2,e_4)
| ~ product1(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[c_8609,c_191]) ).
tff(c_8629,plain,
~ product1(e_4,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_40,c_8614]) ).
tff(c_8638,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_54,c_8629]) ).
tff(c_8641,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_8638]) ).
tff(c_8705,plain,
product1(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_8641]) ).
tff(c_8744,plain,
! [Y_438] :
( product2(e_1,Y_438,e_3)
| ~ product1(e_3,Y_438,e_4) ),
inference(resolution,[status(thm)],[c_8705,c_74]) ).
tff(c_8760,plain,
( equalish(e_3,e_1)
| ~ product1(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_8744,c_125]) ).
tff(c_8781,plain,
~ product1(e_3,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_42,c_8760]) ).
tff(c_8792,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_8781]) ).
tff(c_8795,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_22,c_8792]) ).
tff(c_8876,plain,
product1(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_8795]) ).
tff(c_8885,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_8876,c_109]) ).
tff(c_8894,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_8885]) ).
tff(c_8895,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_8795]) ).
tff(c_8897,plain,
product1(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_8895]) ).
tff(c_8900,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_8897,c_242]) ).
tff(c_8915,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_8900]) ).
tff(c_8916,plain,
product1(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_8895]) ).
tff(c_8941,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_8916,c_6962]) ).
tff(c_8953,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_8941]) ).
tff(c_8954,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_8641]) ).
tff(c_9013,plain,
product1(e_4,e_3,e_3),
inference(splitLeft,[status(thm)],[c_8954]) ).
tff(c_9025,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_9013,c_109]) ).
tff(c_9035,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_9025]) ).
tff(c_9036,plain,
product1(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_8954]) ).
tff(c_9086,plain,
! [Y_460] :
( product2(e_2,Y_460,e_3)
| ~ product1(e_3,Y_460,e_4) ),
inference(resolution,[status(thm)],[c_9036,c_74]) ).
tff(c_9105,plain,
( equalish(e_3,e_2)
| ~ product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[c_9086,c_125]) ).
tff(c_9129,plain,
~ product1(e_3,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_44,c_9105]) ).
tff(c_9140,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_9129]) ).
tff(c_9143,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_9140]) ).
tff(c_9272,plain,
product1(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_9143]) ).
tff(c_9382,plain,
! [Y_477] :
( product2(e_1,Y_477,e_2)
| ~ product1(e_2,Y_477,e_3) ),
inference(resolution,[status(thm)],[c_9272,c_74]) ).
tff(c_8633,plain,
! [W_29] :
( equalish(W_29,e_4)
| ~ product2(W_29,e_3,e_2) ),
inference(resolution,[status(thm)],[c_8609,c_70]) ).
tff(c_9386,plain,
( equalish(e_1,e_4)
| ~ product1(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[c_9382,c_8633]) ).
tff(c_9409,plain,
~ product1(e_2,e_3,e_3),
inference(negUnitSimplification,[status(thm)],[c_34,c_9386]) ).
tff(c_9553,plain,
! [Y_489,Y_490,X_491] :
( product2(e_4,Y_489,Y_490)
| ~ product1(Y_490,Y_489,X_491)
| product1(X_491,Y_490,e_3)
| product1(X_491,Y_490,e_2)
| product1(X_491,Y_490,e_1)
| ~ group_element(Y_490)
| ~ group_element(X_491) ),
inference(resolution,[status(thm)],[c_194,c_74]) ).
tff(c_9561,plain,
( product2(e_4,e_4,e_3)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_6950,c_9553]) ).
tff(c_9579,plain,
( product2(e_4,e_4,e_3)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_9561]) ).
tff(c_9580,plain,
( product2(e_4,e_4,e_3)
| product1(e_2,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_8632,c_9409,c_9579]) ).
tff(c_9588,plain,
product1(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_9580]) ).
tff(c_9638,plain,
! [Y_495] :
( product2(e_1,Y_495,e_3)
| ~ product1(e_3,Y_495,e_2) ),
inference(resolution,[status(thm)],[c_9588,c_74]) ).
tff(c_9427,plain,
! [W_23,Y_477] :
( equalish(W_23,e_2)
| ~ product2(e_1,Y_477,W_23)
| ~ product1(e_2,Y_477,e_3) ),
inference(resolution,[status(thm)],[c_9382,c_66]) ).
tff(c_9641,plain,
! [Y_495] :
( equalish(e_3,e_2)
| ~ product1(e_2,Y_495,e_3)
| ~ product1(e_3,Y_495,e_2) ),
inference(resolution,[status(thm)],[c_9638,c_9427]) ).
tff(c_9780,plain,
! [Y_500] :
( ~ product1(e_2,Y_500,e_3)
| ~ product1(e_3,Y_500,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_44,c_9641]) ).
tff(c_9784,plain,
~ product1(e_2,e_4,e_3),
inference(resolution,[status(thm)],[c_6950,c_9780]) ).
tff(c_9787,plain,
( equalish(e_2,e_4)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_224,c_9784]) ).
tff(c_9790,plain,
( equalish(e_2,e_4)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_9787]) ).
tff(c_9791,plain,
( product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_40,c_9790]) ).
tff(c_9792,plain,
product1(e_2,e_4,e_1),
inference(splitLeft,[status(thm)],[c_9791]) ).
tff(c_9610,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product1(e_2,W_11,e_1) ),
inference(resolution,[status(thm)],[c_9588,c_58]) ).
tff(c_9795,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_9792,c_9610]) ).
tff(c_9811,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_9795]) ).
tff(c_9812,plain,
product1(e_2,e_4,e_2),
inference(splitRight,[status(thm)],[c_9791]) ).
tff(c_6963,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product1(W_14,e_4,e_2) ),
inference(resolution,[status(thm)],[c_6950,c_60]) ).
tff(c_9820,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_9812,c_6963]) ).
tff(c_9846,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_9820]) ).
tff(c_9847,plain,
product2(e_4,e_4,e_3),
inference(splitRight,[status(thm)],[c_9580]) ).
tff(c_9939,plain,
( equalish(e_3,e_4)
| ~ product1(e_4,e_4,e_4) ),
inference(resolution,[status(thm)],[c_9847,c_191]) ).
tff(c_9960,plain,
equalish(e_3,e_4),
inference(demodulation,[status(thm),theory(equality)],[c_62,c_9939]) ).
tff(c_9962,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_9960]) ).
tff(c_9963,plain,
( product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_9143]) ).
tff(c_9965,plain,
product1(e_3,e_2,e_3),
inference(splitLeft,[status(thm)],[c_9963]) ).
tff(c_10035,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_9965,c_242]) ).
tff(c_10054,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_10035]) ).
tff(c_10055,plain,
product1(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_9963]) ).
tff(c_10061,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_10055,c_6962]) ).
tff(c_10080,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_10061]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14 % 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
% 0.14/0.38 % Computer : n016.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Thu Aug 3 22:41:38 EDT 2023
% 0.14/0.38 % CPUTime :
% 10.17/3.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.24/3.49
% 10.24/3.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.24/3.55
% 10.24/3.55 Inference rules
% 10.24/3.55 ----------------------
% 10.24/3.55 #Ref : 0
% 10.24/3.55 #Sup : 1873
% 10.24/3.55 #Fact : 0
% 10.24/3.55 #Define : 0
% 10.24/3.55 #Split : 50
% 10.24/3.55 #Chain : 0
% 10.24/3.55 #Close : 0
% 10.24/3.55
% 10.24/3.55 Ordering : KBO
% 10.24/3.55
% 10.24/3.55 Simplification rules
% 10.24/3.55 ----------------------
% 10.24/3.55 #Subsume : 363
% 10.24/3.55 #Demod : 1481
% 10.24/3.55 #Tautology : 542
% 10.24/3.55 #SimpNegUnit : 826
% 10.24/3.55 #BackRed : 0
% 10.24/3.55
% 10.24/3.55 #Partial instantiations: 0
% 10.24/3.55 #Strategies tried : 1
% 10.24/3.55
% 10.24/3.55 Timing (in seconds)
% 10.24/3.55 ----------------------
% 10.24/3.55 Preprocessing : 0.47
% 10.24/3.55 Parsing : 0.26
% 10.24/3.55 CNF conversion : 0.03
% 10.24/3.55 Main loop : 1.90
% 10.24/3.55 Inferencing : 0.64
% 10.24/3.55 Reduction : 0.59
% 10.24/3.55 Demodulation : 0.36
% 10.24/3.55 BG Simplification : 0.05
% 10.24/3.55 Subsumption : 0.51
% 10.24/3.55 Abstraction : 0.05
% 10.24/3.55 MUC search : 0.00
% 10.24/3.55 Cooper : 0.00
% 10.24/3.55 Total : 2.52
% 10.24/3.55 Index Insertion : 0.00
% 10.24/3.55 Index Deletion : 0.00
% 10.24/3.55 Index Matching : 0.00
% 10.24/3.55 BG Taut test : 0.00
%------------------------------------------------------------------------------