TSTP Solution File: GRP133-2.003 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP133-2.003 : 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 : n029.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 10:40:15 EDT 2023
% Result : Unsatisfiable 12.96s 4.67s
% Output : CNFRefutation 13.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 25
% Syntax : Number of formulae : 199 ( 83 unt; 8 typ; 0 def)
% Number of atoms : 492 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 472 ( 171 ~; 301 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 136 (; 136 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > next > greater > equalish > group_element > #nlpp > 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(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_56,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_48,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_44,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_54,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_50,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_46,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_45,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3) ),
file(unknown,unknown) ).
tff(f_102,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,X) ),
file(unknown,unknown) ).
tff(f_52,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_58,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_34,axiom,
greater(e_3,e_2),
file(unknown,unknown) ).
tff(f_43,axiom,
! [X,Y,X1] :
( ~ product(X,e_1,Y)
| ~ next(X,X1)
| ~ greater(Y,X1) ),
file(unknown,unknown) ).
tff(f_86,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_30,axiom,
next(e_1,e_2),
file(unknown,unknown) ).
tff(f_94,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(c_28,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_20,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_14,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_26,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_22,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_18,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_16,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_32,plain,
! [X_4,Y_5] :
( product(X_4,Y_5,e_3)
| product(X_4,Y_5,e_2)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_58,plain,
! [X_44,Y_45] :
( product(X_44,Y_45,e_3)
| product(X_44,Y_45,e_2)
| product(X_44,Y_45,e_1)
| ~ group_element(Y_45)
| ~ group_element(X_44) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_40,plain,
! [Z1_20,Z2_21,X_18,Y_19] :
( product(Z1_20,Z2_21,X_18)
| ~ product(Y_19,X_18,Z2_21)
| ~ product(X_18,Y_19,Z1_20) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_281,plain,
! [Z1_73,Y_74,X_75] :
( product(Z1_73,e_3,Y_74)
| ~ product(Y_74,X_75,Z1_73)
| product(X_75,Y_74,e_2)
| product(X_75,Y_74,e_1)
| ~ group_element(Y_74)
| ~ group_element(X_75) ),
inference(resolution,[status(thm)],[c_58,c_40]) ).
tff(c_294,plain,
! [X_4,Y_5] :
( product(e_3,e_3,X_4)
| product(Y_5,X_4,e_2)
| product(Y_5,X_4,e_1)
| product(X_4,Y_5,e_2)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_32,c_281]) ).
tff(c_378,plain,
! [Y_5] :
( product(e_3,e_3,Y_5)
| product(Y_5,Y_5,e_1)
| ~ group_element(Y_5)
| product(Y_5,Y_5,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_294]) ).
tff(c_517,plain,
! [Y_79] :
( product(e_3,e_3,Y_79)
| product(Y_79,Y_79,e_1)
| ~ group_element(Y_79)
| product(Y_79,Y_79,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_294]) ).
tff(c_2222,plain,
! [Z1_123,Y_124] :
( product(Z1_123,e_2,Y_124)
| ~ product(Y_124,Y_124,Z1_123)
| product(e_3,e_3,Y_124)
| product(Y_124,Y_124,e_1)
| ~ group_element(Y_124) ),
inference(resolution,[status(thm)],[c_517,c_40]) ).
tff(c_2279,plain,
! [Y_5] :
( product(e_2,e_2,Y_5)
| product(e_3,e_3,Y_5)
| product(Y_5,Y_5,e_1)
| ~ group_element(Y_5) ),
inference(resolution,[status(thm)],[c_378,c_2222]) ).
tff(c_2290,plain,
! [Y_125] :
( product(e_2,e_2,Y_125)
| product(e_3,e_3,Y_125)
| product(Y_125,Y_125,e_1)
| ~ group_element(Y_125) ),
inference(resolution,[status(thm)],[c_378,c_2222]) ).
tff(c_3016,plain,
! [Z1_143,Y_144] :
( product(Z1_143,e_1,Y_144)
| ~ product(Y_144,Y_144,Z1_143)
| product(e_2,e_2,Y_144)
| product(e_3,e_3,Y_144)
| ~ group_element(Y_144) ),
inference(resolution,[status(thm)],[c_2290,c_40]) ).
tff(c_3065,plain,
! [Y_5] :
( product(e_1,e_1,Y_5)
| product(e_2,e_2,Y_5)
| product(e_3,e_3,Y_5)
| ~ group_element(Y_5) ),
inference(resolution,[status(thm)],[c_2279,c_3016]) ).
tff(c_24,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_30,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_10,plain,
greater(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_41,plain,
! [Y_22,X1_23,X_24] :
( ~ greater(Y_22,X1_23)
| ~ next(X_24,X1_23)
| ~ product(X_24,e_1,Y_22) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_50,plain,
! [X_24] :
( ~ next(X_24,e_2)
| ~ product(X_24,e_1,e_3) ),
inference(resolution,[status(thm)],[c_10,c_41]) ).
tff(c_72,plain,
! [X_44] :
( ~ next(X_44,e_2)
| product(X_44,e_1,e_2)
| product(X_44,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_44) ),
inference(resolution,[status(thm)],[c_58,c_50]) ).
tff(c_134,plain,
! [X_54] :
( ~ next(X_54,e_2)
| product(X_54,e_1,e_2)
| product(X_54,e_1,e_1)
| ~ group_element(X_54) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_72]) ).
tff(c_36,plain,
! [W_11,Z_13,X_10,Y_12] :
( equalish(W_11,Z_13)
| ~ product(X_10,Z_13,Y_12)
| ~ product(X_10,W_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_148,plain,
! [W_11,X_54] :
( equalish(W_11,e_1)
| ~ product(X_54,W_11,e_2)
| ~ next(X_54,e_2)
| product(X_54,e_1,e_1)
| ~ group_element(X_54) ),
inference(resolution,[status(thm)],[c_134,c_36]) ).
tff(c_3614,plain,
! [Y_157] :
( equalish(Y_157,e_1)
| ~ next(Y_157,e_2)
| product(Y_157,e_1,e_1)
| product(e_3,e_3,Y_157)
| product(Y_157,Y_157,e_1)
| ~ group_element(Y_157) ),
inference(resolution,[status(thm)],[c_517,c_148]) ).
tff(c_2,plain,
next(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_83,plain,
! [X_44] :
( ~ next(X_44,e_2)
| product(X_44,e_1,e_2)
| product(X_44,e_1,e_1)
| ~ group_element(X_44) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_72]) ).
tff(c_176,plain,
! [Z1_64,X_65] :
( product(Z1_64,e_2,e_1)
| ~ product(e_1,X_65,Z1_64)
| ~ next(X_65,e_2)
| product(X_65,e_1,e_1)
| ~ group_element(X_65) ),
inference(resolution,[status(thm)],[c_134,c_40]) ).
tff(c_179,plain,
( product(e_2,e_2,e_1)
| ~ next(e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_83,c_176]) ).
tff(c_185,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_2,c_179]) ).
tff(c_199,plain,
product(e_1,e_1,e_1),
inference(splitLeft,[status(thm)],[c_185]) ).
tff(c_38,plain,
! [W_14,Z_17,Y_15,X_16] :
( equalish(W_14,Z_17)
| ~ product(Z_17,Y_15,X_16)
| ~ product(W_14,Y_15,X_16) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_228,plain,
! [W_14] :
( equalish(W_14,e_1)
| ~ product(W_14,e_1,e_1) ),
inference(resolution,[status(thm)],[c_199,c_38]) ).
tff(c_3870,plain,
! [Y_158] :
( equalish(Y_158,e_1)
| ~ next(Y_158,e_2)
| product(e_3,e_3,Y_158)
| product(Y_158,Y_158,e_1)
| ~ group_element(Y_158) ),
inference(resolution,[status(thm)],[c_3614,c_228]) ).
tff(c_34,plain,
! [W_8,Z_9,X_6,Y_7] :
( equalish(W_8,Z_9)
| ~ product(X_6,Y_7,Z_9)
| ~ product(X_6,Y_7,W_8) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_2404,plain,
! [W_8,Y_125] :
( equalish(W_8,e_1)
| ~ product(Y_125,Y_125,W_8)
| product(e_2,e_2,Y_125)
| product(e_3,e_3,Y_125)
| ~ group_element(Y_125) ),
inference(resolution,[status(thm)],[c_2290,c_34]) ).
tff(c_3891,plain,
! [Y_158] :
( product(e_2,e_2,e_3)
| product(e_3,e_3,e_3)
| ~ group_element(e_3)
| equalish(Y_158,e_1)
| ~ next(Y_158,e_2)
| product(Y_158,Y_158,e_1)
| ~ group_element(Y_158) ),
inference(resolution,[status(thm)],[c_3870,c_2404]) ).
tff(c_4006,plain,
! [Y_158] :
( product(e_2,e_2,e_3)
| product(e_3,e_3,e_3)
| equalish(Y_158,e_1)
| ~ next(Y_158,e_2)
| product(Y_158,Y_158,e_1)
| ~ group_element(Y_158) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_3891]) ).
tff(c_5178,plain,
product(e_3,e_3,e_3),
inference(splitLeft,[status(thm)],[c_4006]) ).
tff(c_5508,plain,
! [W_180] :
( equalish(W_180,e_3)
| ~ product(e_3,W_180,e_3) ),
inference(resolution,[status(thm)],[c_5178,c_36]) ).
tff(c_5547,plain,
! [Y_5] :
( equalish(Y_5,e_3)
| product(e_3,Y_5,e_2)
| product(e_3,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_32,c_5508]) ).
tff(c_5578,plain,
! [Y_5] :
( equalish(Y_5,e_3)
| product(e_3,Y_5,e_2)
| product(e_3,Y_5,e_1)
| ~ group_element(Y_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_5547]) ).
tff(c_5579,plain,
! [W_181] :
( equalish(W_181,e_3)
| ~ product(W_181,e_3,e_3) ),
inference(resolution,[status(thm)],[c_5178,c_38]) ).
tff(c_5626,plain,
! [X_4] :
( equalish(X_4,e_3)
| product(X_4,e_3,e_2)
| product(X_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_32,c_5579]) ).
tff(c_5661,plain,
! [X_4] :
( equalish(X_4,e_3)
| product(X_4,e_3,e_2)
| product(X_4,e_3,e_1)
| ~ group_element(X_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_5626]) ).
tff(c_2394,plain,
! [W_8,Y_125] :
( equalish(W_8,Y_125)
| ~ product(e_3,e_3,W_8)
| product(e_2,e_2,Y_125)
| product(Y_125,Y_125,e_1)
| ~ group_element(Y_125) ),
inference(resolution,[status(thm)],[c_2290,c_34]) ).
tff(c_6302,plain,
! [Y_188] :
( equalish(e_3,Y_188)
| product(e_2,e_2,Y_188)
| product(Y_188,Y_188,e_1)
| ~ group_element(Y_188) ),
inference(resolution,[status(thm)],[c_5178,c_2394]) ).
tff(c_9139,plain,
! [W_204,Y_205] :
( equalish(W_204,e_2)
| ~ product(e_2,W_204,Y_205)
| equalish(e_3,Y_205)
| product(Y_205,Y_205,e_1)
| ~ group_element(Y_205) ),
inference(resolution,[status(thm)],[c_6302,c_36]) ).
tff(c_9154,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_1)
| equalish(e_2,e_3)
| product(e_2,e_3,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_5661,c_9139]) ).
tff(c_9218,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_1)
| equalish(e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_9154]) ).
tff(c_9219,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_30,c_9218]) ).
tff(c_9274,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_9219]) ).
tff(c_2405,plain,
! [W_11,Y_125] :
( equalish(W_11,Y_125)
| ~ product(Y_125,W_11,e_1)
| product(e_2,e_2,Y_125)
| product(e_3,e_3,Y_125)
| ~ group_element(Y_125) ),
inference(resolution,[status(thm)],[c_2290,c_36]) ).
tff(c_9294,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_3,e_3,e_2)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_9274,c_2405]) ).
tff(c_9349,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_3,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_9294]) ).
tff(c_9350,plain,
( product(e_2,e_2,e_2)
| product(e_3,e_3,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_9349]) ).
tff(c_9879,plain,
product(e_3,e_3,e_2),
inference(splitLeft,[status(thm)],[c_9350]) ).
tff(c_5408,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product(e_3,e_3,W_8) ),
inference(resolution,[status(thm)],[c_5178,c_34]) ).
tff(c_9891,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_9879,c_5408]) ).
tff(c_9972,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_9891]) ).
tff(c_9973,plain,
product(e_2,e_2,e_2),
inference(splitRight,[status(thm)],[c_9350]) ).
tff(c_10599,plain,
! [W_218] :
( equalish(W_218,e_2)
| ~ product(W_218,e_2,e_2) ),
inference(resolution,[status(thm)],[c_9973,c_38]) ).
tff(c_10620,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_3,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_5578,c_10599]) ).
tff(c_10687,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_10620]) ).
tff(c_10688,plain,
product(e_3,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_26,c_30,c_10687]) ).
tff(c_9366,plain,
! [Z1_20] :
( product(Z1_20,e_1,e_3)
| ~ product(e_3,e_2,Z1_20) ),
inference(resolution,[status(thm)],[c_9274,c_40]) ).
tff(c_10768,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_10688,c_9366]) ).
tff(c_226,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_1,e_1,W_8) ),
inference(resolution,[status(thm)],[c_199,c_34]) ).
tff(c_10943,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_10768,c_226]) ).
tff(c_11001,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_10943]) ).
tff(c_11002,plain,
product(e_2,e_2,e_1),
inference(splitRight,[status(thm)],[c_9219]) ).
tff(c_11515,plain,
! [Z1_226] :
( product(Z1_226,e_1,e_2)
| ~ product(e_2,e_2,Z1_226) ),
inference(resolution,[status(thm)],[c_11002,c_40]) ).
tff(c_11561,plain,
product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[c_11002,c_11515]) ).
tff(c_11773,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_11561,c_226]) ).
tff(c_11838,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_11773]) ).
tff(c_11840,plain,
~ product(e_3,e_3,e_3),
inference(splitRight,[status(thm)],[c_4006]) ).
tff(c_11849,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_3065,c_11840]) ).
tff(c_11878,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_11849]) ).
tff(c_11897,plain,
product(e_2,e_2,e_3),
inference(splitLeft,[status(thm)],[c_11878]) ).
tff(c_77,plain,
! [W_11,Y_45,X_44] :
( equalish(W_11,Y_45)
| ~ product(X_44,W_11,e_3)
| product(X_44,Y_45,e_2)
| product(X_44,Y_45,e_1)
| ~ group_element(Y_45)
| ~ group_element(X_44) ),
inference(resolution,[status(thm)],[c_58,c_36]) ).
tff(c_11913,plain,
! [Y_45] :
( equalish(e_2,Y_45)
| product(e_2,Y_45,e_2)
| product(e_2,Y_45,e_1)
| ~ group_element(Y_45)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_11897,c_77]) ).
tff(c_12961,plain,
! [Y_243] :
( equalish(e_2,Y_243)
| product(e_2,Y_243,e_2)
| product(e_2,Y_243,e_1)
| ~ group_element(Y_243) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_11913]) ).
tff(c_12157,plain,
! [Z1_235] :
( product(Z1_235,e_3,e_2)
| ~ product(e_2,e_2,Z1_235) ),
inference(resolution,[status(thm)],[c_11897,c_40]) ).
tff(c_12185,plain,
product(e_3,e_3,e_2),
inference(resolution,[status(thm)],[c_11897,c_12157]) ).
tff(c_12353,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product(W_14,e_3,e_2) ),
inference(resolution,[status(thm)],[c_12185,c_38]) ).
tff(c_12967,plain,
( equalish(e_2,e_3)
| product(e_2,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_12961,c_12353]) ).
tff(c_13040,plain,
( equalish(e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_12967]) ).
tff(c_13041,plain,
product(e_2,e_3,e_1),
inference(negUnitSimplification,[status(thm)],[c_26,c_13040]) ).
tff(c_75,plain,
! [Z1_20,Y_45,X_44] :
( product(Z1_20,e_3,Y_45)
| ~ product(Y_45,X_44,Z1_20)
| product(X_44,Y_45,e_2)
| product(X_44,Y_45,e_1)
| ~ group_element(Y_45)
| ~ group_element(X_44) ),
inference(resolution,[status(thm)],[c_58,c_40]) ).
tff(c_13306,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_13041,c_75]) ).
tff(c_13363,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_16,c_13306]) ).
tff(c_13752,plain,
product(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_13363]) ).
tff(c_13368,plain,
! [Z1_20] :
( product(Z1_20,e_1,e_3)
| ~ product(e_3,e_2,Z1_20) ),
inference(resolution,[status(thm)],[c_13041,c_40]) ).
tff(c_13790,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_13752,c_13368]) ).
tff(c_13924,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_13790,c_226]) ).
tff(c_13982,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_13924]) ).
tff(c_13983,plain,
( product(e_3,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_13363]) ).
tff(c_13987,plain,
product(e_1,e_3,e_2),
inference(splitLeft,[status(thm)],[c_13983]) ).
tff(c_13996,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_13987,c_12353]) ).
tff(c_14043,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_13996]) ).
tff(c_14044,plain,
product(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_13983]) ).
tff(c_12352,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_3,W_11,e_2) ),
inference(resolution,[status(thm)],[c_12185,c_36]) ).
tff(c_14198,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_14044,c_12352]) ).
tff(c_14249,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_14198]) ).
tff(c_14250,plain,
product(e_1,e_1,e_3),
inference(splitRight,[status(thm)],[c_11878]) ).
tff(c_14268,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_14250,c_226]) ).
tff(c_14318,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_14268]) ).
tff(c_14319,plain,
product(e_2,e_2,e_1),
inference(splitRight,[status(thm)],[c_185]) ).
tff(c_14365,plain,
! [Z1_261] :
( product(Z1_261,e_1,e_2)
| ~ product(e_2,e_2,Z1_261) ),
inference(resolution,[status(thm)],[c_14319,c_40]) ).
tff(c_14371,plain,
product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[c_14319,c_14365]) ).
tff(c_150,plain,
! [W_14,X_54] :
( equalish(W_14,X_54)
| ~ product(W_14,e_1,e_2)
| ~ next(X_54,e_2)
| product(X_54,e_1,e_1)
| ~ group_element(X_54) ),
inference(resolution,[status(thm)],[c_134,c_38]) ).
tff(c_14503,plain,
! [X_269] :
( equalish(e_1,X_269)
| ~ next(X_269,e_2)
| product(X_269,e_1,e_1)
| ~ group_element(X_269) ),
inference(resolution,[status(thm)],[c_14371,c_150]) ).
tff(c_14512,plain,
! [X_269] :
( product(e_1,e_3,X_269)
| product(e_1,X_269,e_2)
| product(e_1,X_269,e_1)
| ~ group_element(e_1)
| equalish(e_1,X_269)
| ~ next(X_269,e_2)
| ~ group_element(X_269) ),
inference(resolution,[status(thm)],[c_14503,c_75]) ).
tff(c_22168,plain,
! [X_435] :
( product(e_1,e_3,X_435)
| product(e_1,X_435,e_2)
| product(e_1,X_435,e_1)
| equalish(e_1,X_435)
| ~ next(X_435,e_2)
| ~ group_element(X_435) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_14512]) ).
tff(c_14562,plain,
! [Z1_20,X_269] :
( product(Z1_20,e_1,e_1)
| ~ product(e_1,X_269,Z1_20)
| equalish(e_1,X_269)
| ~ next(X_269,e_2)
| ~ group_element(X_269) ),
inference(resolution,[status(thm)],[c_14503,c_40]) ).
tff(c_22425,plain,
! [X_435] :
( product(e_2,e_1,e_1)
| product(e_1,e_3,X_435)
| product(e_1,X_435,e_1)
| equalish(e_1,X_435)
| ~ next(X_435,e_2)
| ~ group_element(X_435) ),
inference(resolution,[status(thm)],[c_22168,c_14562]) ).
tff(c_23715,plain,
product(e_2,e_1,e_1),
inference(splitLeft,[status(thm)],[c_22425]) ).
tff(c_14337,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product(e_2,W_11,e_1) ),
inference(resolution,[status(thm)],[c_14319,c_36]) ).
tff(c_23748,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_23715,c_14337]) ).
tff(c_23808,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_23748]) ).
tff(c_23810,plain,
~ product(e_2,e_1,e_1),
inference(splitRight,[status(thm)],[c_22425]) ).
tff(c_14320,plain,
~ product(e_1,e_1,e_1),
inference(splitRight,[status(thm)],[c_185]) ).
tff(c_14418,plain,
! [Z1_262,Y_263,X_264] :
( product(Z1_262,e_3,Y_263)
| ~ product(Y_263,X_264,Z1_262)
| product(X_264,Y_263,e_2)
| product(X_264,Y_263,e_1)
| ~ group_element(Y_263)
| ~ group_element(X_264) ),
inference(resolution,[status(thm)],[c_58,c_40]) ).
tff(c_14437,plain,
! [X_4,Y_5] :
( product(e_3,e_3,X_4)
| product(Y_5,X_4,e_2)
| product(Y_5,X_4,e_1)
| product(X_4,Y_5,e_2)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_32,c_14418]) ).
tff(c_15050,plain,
! [Y_289] :
( product(e_3,e_3,Y_289)
| product(Y_289,Y_289,e_1)
| ~ group_element(Y_289)
| product(Y_289,Y_289,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_14437]) ).
tff(c_15068,plain,
! [Y_45] :
( equalish(e_3,Y_45)
| product(e_3,Y_45,e_2)
| product(e_3,Y_45,e_1)
| ~ group_element(Y_45)
| product(e_3,e_3,e_1)
| ~ group_element(e_3)
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[c_15050,c_77]) ).
tff(c_15135,plain,
! [Y_45] :
( equalish(e_3,Y_45)
| product(e_3,Y_45,e_2)
| product(e_3,Y_45,e_1)
| ~ group_element(Y_45)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_15068]) ).
tff(c_26800,plain,
product(e_3,e_3,e_2),
inference(splitLeft,[status(thm)],[c_15135]) ).
tff(c_27449,plain,
! [Z1_514] :
( product(Z1_514,e_2,e_3)
| ~ product(e_3,e_3,Z1_514) ),
inference(resolution,[status(thm)],[c_26800,c_40]) ).
tff(c_27487,plain,
product(e_2,e_2,e_3),
inference(resolution,[status(thm)],[c_26800,c_27449]) ).
tff(c_14336,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_2,e_2,W_8) ),
inference(resolution,[status(thm)],[c_14319,c_34]) ).
tff(c_27539,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_27487,c_14336]) ).
tff(c_27605,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_27539]) ).
tff(c_27606,plain,
! [Y_45] :
( product(e_3,e_3,e_1)
| equalish(e_3,Y_45)
| product(e_3,Y_45,e_2)
| product(e_3,Y_45,e_1)
| ~ group_element(Y_45) ),
inference(splitRight,[status(thm)],[c_15135]) ).
tff(c_27673,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_27606]) ).
tff(c_28202,plain,
! [Z1_522] :
( product(Z1_522,e_1,e_3)
| ~ product(e_3,e_3,Z1_522) ),
inference(resolution,[status(thm)],[c_27673,c_40]) ).
tff(c_28240,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_27673,c_28202]) ).
tff(c_14414,plain,
! [W_8] :
( equalish(W_8,e_2)
| ~ product(e_1,e_1,W_8) ),
inference(resolution,[status(thm)],[c_14371,c_34]) ).
tff(c_28291,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_28240,c_14414]) ).
tff(c_28369,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_28291]) ).
tff(c_28414,plain,
! [Y_523] :
( equalish(e_3,Y_523)
| product(e_3,Y_523,e_2)
| product(e_3,Y_523,e_1)
| ~ group_element(Y_523) ),
inference(splitRight,[status(thm)],[c_27606]) ).
tff(c_14417,plain,
! [W_14] :
( equalish(W_14,e_1)
| ~ product(W_14,e_1,e_2) ),
inference(resolution,[status(thm)],[c_14371,c_38]) ).
tff(c_28518,plain,
( equalish(e_3,e_1)
| product(e_3,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_28414,c_14417]) ).
tff(c_28672,plain,
( equalish(e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_28518]) ).
tff(c_28673,plain,
product(e_3,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_28,c_28672]) ).
tff(c_28728,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_28673,c_75]) ).
tff(c_28794,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_18,c_28728]) ).
tff(c_29712,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_28794]) ).
tff(c_28803,plain,
! [Z1_20] :
( product(Z1_20,e_1,e_1)
| ~ product(e_1,e_3,Z1_20) ),
inference(resolution,[status(thm)],[c_28673,c_40]) ).
tff(c_29714,plain,
product(e_1,e_1,e_1),
inference(resolution,[status(thm)],[c_29712,c_28803]) ).
tff(c_29760,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14320,c_29714]) ).
tff(c_29761,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_28794]) ).
tff(c_30084,plain,
product(e_1,e_3,e_3),
inference(splitLeft,[status(thm)],[c_29761]) ).
tff(c_14820,plain,
! [Y_5] :
( product(e_3,e_3,Y_5)
| product(Y_5,Y_5,e_1)
| ~ group_element(Y_5)
| product(Y_5,Y_5,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_14437]) ).
tff(c_18930,plain,
! [Z1_362,Y_363] :
( product(Z1_362,e_2,Y_363)
| ~ product(Y_363,Y_363,Z1_362)
| product(e_3,e_3,Y_363)
| product(Y_363,Y_363,e_1)
| ~ group_element(Y_363) ),
inference(resolution,[status(thm)],[c_15050,c_40]) ).
tff(c_19088,plain,
! [Y_367] :
( product(e_2,e_2,Y_367)
| product(e_3,e_3,Y_367)
| product(Y_367,Y_367,e_1)
| ~ group_element(Y_367) ),
inference(resolution,[status(thm)],[c_14820,c_18930]) ).
tff(c_19247,plain,
! [W_11,Y_367] :
( equalish(W_11,Y_367)
| ~ product(Y_367,W_11,e_1)
| product(e_2,e_2,Y_367)
| product(e_3,e_3,Y_367)
| ~ group_element(Y_367) ),
inference(resolution,[status(thm)],[c_19088,c_36]) ).
tff(c_28720,plain,
( equalish(e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_3,e_3)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_28673,c_19247]) ).
tff(c_28778,plain,
( equalish(e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_3,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_28720]) ).
tff(c_28779,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_3,e_3) ),
inference(negUnitSimplification,[status(thm)],[c_22,c_28778]) ).
tff(c_29167,plain,
product(e_3,e_3,e_3),
inference(splitLeft,[status(thm)],[c_28779]) ).
tff(c_29341,plain,
! [W_14] :
( equalish(W_14,e_3)
| ~ product(W_14,e_3,e_3) ),
inference(resolution,[status(thm)],[c_29167,c_38]) ).
tff(c_30087,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_30084,c_29341]) ).
tff(c_30135,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_30087]) ).
tff(c_30136,plain,
product(e_1,e_3,e_2),
inference(splitRight,[status(thm)],[c_29761]) ).
tff(c_30141,plain,
product(e_2,e_1,e_1),
inference(resolution,[status(thm)],[c_30136,c_28803]) ).
tff(c_30217,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23810,c_30141]) ).
tff(c_30218,plain,
product(e_2,e_2,e_3),
inference(splitRight,[status(thm)],[c_28779]) ).
tff(c_30250,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_30218,c_14336]) ).
tff(c_30321,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_30250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP133-2.003 : 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
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 22:12:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 12.96/4.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.02/4.69
% 13.02/4.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.28/4.74
% 13.28/4.74 Inference rules
% 13.28/4.74 ----------------------
% 13.28/4.74 #Ref : 0
% 13.28/4.74 #Sup : 5596
% 13.28/4.74 #Fact : 24
% 13.28/4.74 #Define : 0
% 13.28/4.74 #Split : 25
% 13.28/4.74 #Chain : 0
% 13.28/4.74 #Close : 0
% 13.28/4.74
% 13.28/4.74 Ordering : KBO
% 13.28/4.74
% 13.28/4.74 Simplification rules
% 13.28/4.74 ----------------------
% 13.28/4.74 #Subsume : 1330
% 13.28/4.74 #Demod : 7131
% 13.28/4.74 #Tautology : 1965
% 13.28/4.74 #SimpNegUnit : 1641
% 13.28/4.74 #BackRed : 0
% 13.28/4.74
% 13.28/4.74 #Partial instantiations: 0
% 13.28/4.74 #Strategies tried : 1
% 13.28/4.74
% 13.28/4.74 Timing (in seconds)
% 13.28/4.74 ----------------------
% 13.28/4.75 Preprocessing : 0.45
% 13.28/4.75 Parsing : 0.25
% 13.28/4.75 CNF conversion : 0.02
% 13.28/4.75 Main loop : 3.13
% 13.28/4.75 Inferencing : 0.75
% 13.28/4.75 Reduction : 0.86
% 13.28/4.75 Demodulation : 0.57
% 13.28/4.75 BG Simplification : 0.07
% 13.28/4.75 Subsumption : 1.27
% 13.28/4.75 Abstraction : 0.08
% 13.28/4.75 MUC search : 0.00
% 13.28/4.75 Cooper : 0.00
% 13.28/4.75 Total : 3.66
% 13.28/4.75 Index Insertion : 0.00
% 13.28/4.75 Index Deletion : 0.00
% 13.28/4.75 Index Matching : 0.00
% 13.28/4.75 BG Taut test : 0.00
%------------------------------------------------------------------------------