TSTP Solution File: GRP134-1.003 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP134-1.003 : 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/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 : n027.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 10.42s 3.47s
% Output : CNFRefutation 10.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 20
% Syntax : Number of formulae : 175 ( 82 unt; 6 typ; 0 def)
% Number of atoms : 368 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 313 ( 114 ~; 199 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 96 (; 96 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > 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(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $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_40,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_42,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_28,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_30,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_38,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_34,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_29,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_54,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_86,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,Y) ),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_36,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_32,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(c_16,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_18,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_2,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_6,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_14,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_10,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_4,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_20,plain,
! [X_1,Y_2] :
( product(X_1,Y_2,e_3)
| product(X_1,Y_2,e_2)
| product(X_1,Y_2,e_1)
| ~ group_element(Y_2)
| ~ group_element(X_1) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_33,plain,
! [X_35,Y_36] :
( product(X_35,Y_36,e_3)
| product(X_35,Y_36,e_2)
| product(X_35,Y_36,e_1)
| ~ group_element(Y_36)
| ~ group_element(X_35) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_28,plain,
! [Z1_17,Z2_18,Y_16,X_15] :
( product(Z1_17,Z2_18,Y_16)
| ~ product(Y_16,X_15,Z2_18)
| ~ product(X_15,Y_16,Z1_17) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_59,plain,
! [Z1_46,X_47,Y_48] :
( product(Z1_46,e_3,X_47)
| ~ product(Y_48,X_47,Z1_46)
| product(X_47,Y_48,e_2)
| product(X_47,Y_48,e_1)
| ~ group_element(Y_48)
| ~ group_element(X_47) ),
inference(resolution,[status(thm)],[c_33,c_28]) ).
tff(c_62,plain,
! [Y_2,X_1] :
( product(e_3,e_3,Y_2)
| product(Y_2,X_1,e_2)
| product(Y_2,X_1,e_1)
| product(X_1,Y_2,e_2)
| product(X_1,Y_2,e_1)
| ~ group_element(Y_2)
| ~ group_element(X_1) ),
inference(resolution,[status(thm)],[c_20,c_59]) ).
tff(c_150,plain,
! [Y_51] :
( product(e_3,e_3,Y_51)
| product(Y_51,Y_51,e_1)
| ~ group_element(Y_51)
| product(Y_51,Y_51,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_62]) ).
tff(c_24,plain,
! [W_8,Z_10,X_7,Y_9] :
( equalish(W_8,Z_10)
| ~ product(X_7,Z_10,Y_9)
| ~ product(X_7,W_8,Y_9) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_45,plain,
! [W_8,Y_36,X_35] :
( equalish(W_8,Y_36)
| ~ product(X_35,W_8,e_3)
| product(X_35,Y_36,e_2)
| product(X_35,Y_36,e_1)
| ~ group_element(Y_36)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_33,c_24]) ).
tff(c_157,plain,
! [Y_36] :
( equalish(e_3,Y_36)
| product(e_3,Y_36,e_2)
| product(e_3,Y_36,e_1)
| ~ group_element(Y_36)
| product(e_3,e_3,e_1)
| ~ group_element(e_3)
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[c_150,c_45]) ).
tff(c_189,plain,
! [Y_36] :
( equalish(e_3,Y_36)
| product(e_3,Y_36,e_2)
| product(e_3,Y_36,e_1)
| ~ group_element(Y_36)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_157]) ).
tff(c_3104,plain,
product(e_3,e_3,e_2),
inference(splitLeft,[status(thm)],[c_189]) ).
tff(c_3625,plain,
! [Z1_148] :
( product(Z1_148,e_2,e_3)
| ~ product(e_3,e_3,Z1_148) ),
inference(resolution,[status(thm)],[c_3104,c_28]) ).
tff(c_3663,plain,
product(e_2,e_2,e_3),
inference(resolution,[status(thm)],[c_3104,c_3625]) ).
tff(c_26,plain,
! [W_11,Z_14,Y_12,X_13] :
( equalish(W_11,Z_14)
| ~ product(Z_14,Y_12,X_13)
| ~ product(W_11,Y_12,X_13) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_43,plain,
! [W_11,X_35,Y_36] :
( equalish(W_11,X_35)
| ~ product(W_11,Y_36,e_3)
| product(X_35,Y_36,e_2)
| product(X_35,Y_36,e_1)
| ~ group_element(Y_36)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_33,c_26]) ).
tff(c_3772,plain,
! [X_35] :
( equalish(e_2,X_35)
| product(X_35,e_2,e_2)
| product(X_35,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_3663,c_43]) ).
tff(c_5466,plain,
! [X_167] :
( equalish(e_2,X_167)
| product(X_167,e_2,e_2)
| product(X_167,e_2,e_1)
| ~ group_element(X_167) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3772]) ).
tff(c_3328,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product(e_3,W_8,e_2) ),
inference(resolution,[status(thm)],[c_3104,c_24]) ).
tff(c_5481,plain,
( equalish(e_2,e_3)
| product(e_3,e_2,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_5466,c_3328]) ).
tff(c_5544,plain,
( equalish(e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_5481]) ).
tff(c_5545,plain,
product(e_3,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_14,c_5544]) ).
tff(c_42,plain,
! [Z1_17,X_35,Y_36] :
( product(Z1_17,e_3,X_35)
| ~ product(Y_36,X_35,Z1_17)
| product(X_35,Y_36,e_2)
| product(X_35,Y_36,e_1)
| ~ group_element(Y_36)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_33,c_28]) ).
tff(c_5621,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_5545,c_42]) ).
tff(c_5670,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_5621]) ).
tff(c_6508,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_5670]) ).
tff(c_5675,plain,
! [Z1_17] :
( product(Z1_17,e_1,e_3)
| ~ product(e_2,e_3,Z1_17) ),
inference(resolution,[status(thm)],[c_5545,c_28]) ).
tff(c_6542,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_6508,c_5675]) ).
tff(c_12,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_75,plain,
! [Y_2] :
( product(e_3,e_3,Y_2)
| product(Y_2,Y_2,e_1)
| ~ group_element(Y_2)
| product(Y_2,Y_2,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_62]) ).
tff(c_1666,plain,
! [Z1_100,Y_101] :
( product(Z1_100,e_2,Y_101)
| ~ product(Y_101,Y_101,Z1_100)
| product(e_3,e_3,Y_101)
| product(Y_101,Y_101,e_1)
| ~ group_element(Y_101) ),
inference(resolution,[status(thm)],[c_150,c_28]) ).
tff(c_1722,plain,
! [Y_102] :
( product(e_2,e_2,Y_102)
| product(e_3,e_3,Y_102)
| product(Y_102,Y_102,e_1)
| ~ group_element(Y_102) ),
inference(resolution,[status(thm)],[c_75,c_1666]) ).
tff(c_22,plain,
! [W_5,Z_6,X_3,Y_4] :
( equalish(W_5,Z_6)
| ~ product(X_3,Y_4,Z_6)
| ~ product(X_3,Y_4,W_5) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_1811,plain,
! [W_5,Y_102] :
( equalish(W_5,Y_102)
| ~ product(e_3,e_3,W_5)
| product(e_2,e_2,Y_102)
| product(Y_102,Y_102,e_1)
| ~ group_element(Y_102) ),
inference(resolution,[status(thm)],[c_1722,c_22]) ).
tff(c_3294,plain,
! [Y_102] :
( equalish(e_2,Y_102)
| product(e_2,e_2,Y_102)
| product(Y_102,Y_102,e_1)
| ~ group_element(Y_102) ),
inference(resolution,[status(thm)],[c_3104,c_1811]) ).
tff(c_5679,plain,
! [W_168] :
( equalish(W_168,e_3)
| ~ product(W_168,e_2,e_1) ),
inference(resolution,[status(thm)],[c_5545,c_26]) ).
tff(c_5690,plain,
( equalish(e_2,e_3)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_3294,c_5679]) ).
tff(c_5721,plain,
( equalish(e_2,e_3)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5690]) ).
tff(c_5722,plain,
product(e_1,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_12,c_14,c_5721]) ).
tff(c_5953,plain,
! [W_5] :
( equalish(W_5,e_1)
| ~ product(e_1,e_1,W_5) ),
inference(resolution,[status(thm)],[c_5722,c_22]) ).
tff(c_6594,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_6542,c_5953]) ).
tff(c_6627,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_6594]) ).
tff(c_6628,plain,
( product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_5670]) ).
tff(c_6783,plain,
product(e_1,e_3,e_2),
inference(splitLeft,[status(thm)],[c_6628]) ).
tff(c_3326,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_3,e_2) ),
inference(resolution,[status(thm)],[c_3104,c_26]) ).
tff(c_6796,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_6783,c_3326]) ).
tff(c_6846,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_6796]) ).
tff(c_6847,plain,
product(e_2,e_3,e_2),
inference(splitRight,[status(thm)],[c_6628]) ).
tff(c_6972,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_6847,c_3326]) ).
tff(c_7025,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_6972]) ).
tff(c_7026,plain,
! [Y_36] :
( product(e_3,e_3,e_1)
| equalish(e_3,Y_36)
| product(e_3,Y_36,e_2)
| product(e_3,Y_36,e_1)
| ~ group_element(Y_36) ),
inference(splitRight,[status(thm)],[c_189]) ).
tff(c_14085,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7026]) ).
tff(c_14537,plain,
! [Z1_287] :
( product(Z1_287,e_1,e_3)
| ~ product(e_3,e_3,Z1_287) ),
inference(resolution,[status(thm)],[c_14085,c_28]) ).
tff(c_14575,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_14085,c_14537]) ).
tff(c_8,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_7496,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7026]) ).
tff(c_7934,plain,
! [Z1_202] :
( product(Z1_202,e_1,e_3)
| ~ product(e_3,e_3,Z1_202) ),
inference(resolution,[status(thm)],[c_7496,c_28]) ).
tff(c_7972,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_7496,c_7934]) ).
tff(c_8012,plain,
! [X_35] :
( equalish(e_1,X_35)
| product(X_35,e_1,e_2)
| product(X_35,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_7972,c_43]) ).
tff(c_9835,plain,
! [X_216] :
( equalish(e_1,X_216)
| product(X_216,e_1,e_2)
| product(X_216,e_1,e_1)
| ~ group_element(X_216) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8012]) ).
tff(c_7027,plain,
~ product(e_3,e_3,e_2),
inference(splitRight,[status(thm)],[c_189]) ).
tff(c_7056,plain,
( product(e_2,e_2,e_1)
| ~ group_element(e_2)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[c_75,c_7027]) ).
tff(c_7089,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_7056]) ).
tff(c_7093,plain,
product(e_2,e_2,e_2),
inference(splitLeft,[status(thm)],[c_7089]) ).
tff(c_7175,plain,
! [W_8] :
( equalish(W_8,e_2)
| ~ product(e_2,W_8,e_2) ),
inference(resolution,[status(thm)],[c_7093,c_24]) ).
tff(c_9848,plain,
( equalish(e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_9835,c_7175]) ).
tff(c_9910,plain,
( equalish(e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9848]) ).
tff(c_9911,plain,
product(e_2,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_8,c_9910]) ).
tff(c_9975,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_9911,c_42]) ).
tff(c_10004,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4,c_9975]) ).
tff(c_10467,plain,
product(e_1,e_2,e_1),
inference(splitLeft,[status(thm)],[c_10004]) ).
tff(c_10009,plain,
! [Z1_17] :
( product(Z1_17,e_1,e_2)
| ~ product(e_1,e_2,Z1_17) ),
inference(resolution,[status(thm)],[c_9911,c_28]) ).
tff(c_10490,plain,
product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[c_10467,c_10009]) ).
tff(c_8053,plain,
! [W_5] :
( equalish(W_5,e_3)
| ~ product(e_1,e_1,W_5) ),
inference(resolution,[status(thm)],[c_7972,c_22]) ).
tff(c_10526,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_10490,c_8053]) ).
tff(c_10569,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_10526]) ).
tff(c_10570,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_3,e_1) ),
inference(splitRight,[status(thm)],[c_10004]) ).
tff(c_10574,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_10570]) ).
tff(c_7612,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_3,e_1) ),
inference(resolution,[status(thm)],[c_7496,c_26]) ).
tff(c_10683,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_10574,c_7612]) ).
tff(c_10719,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_10683]) ).
tff(c_10720,plain,
product(e_1,e_2,e_2),
inference(splitRight,[status(thm)],[c_10570]) ).
tff(c_7173,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product(W_11,e_2,e_2) ),
inference(resolution,[status(thm)],[c_7093,c_26]) ).
tff(c_10732,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_10720,c_7173]) ).
tff(c_10768,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_10732]) ).
tff(c_10769,plain,
! [Y_36] :
( equalish(e_3,Y_36)
| product(e_3,Y_36,e_2)
| product(e_3,Y_36,e_1)
| ~ group_element(Y_36) ),
inference(splitRight,[status(thm)],[c_7026]) ).
tff(c_11336,plain,
! [Y_239] :
( equalish(e_3,Y_239)
| product(e_3,Y_239,e_2)
| product(e_3,Y_239,e_1)
| ~ group_element(Y_239) ),
inference(splitRight,[status(thm)],[c_7026]) ).
tff(c_11347,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_11336,c_7173]) ).
tff(c_11436,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11347]) ).
tff(c_11437,plain,
product(e_3,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_18,c_11436]) ).
tff(c_11548,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_11437,c_42]) ).
tff(c_11589,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_11548]) ).
tff(c_12456,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_11589]) ).
tff(c_11594,plain,
! [Z1_17] :
( product(Z1_17,e_1,e_3)
| ~ product(e_2,e_3,Z1_17) ),
inference(resolution,[status(thm)],[c_11437,c_28]) ).
tff(c_12493,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_12456,c_11594]) ).
tff(c_10770,plain,
~ product(e_3,e_3,e_1),
inference(splitRight,[status(thm)],[c_7026]) ).
tff(c_10886,plain,
( product(e_1,e_1,e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[c_75,c_10770]) ).
tff(c_10904,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10886]) ).
tff(c_10908,plain,
product(e_1,e_1,e_2),
inference(splitLeft,[status(thm)],[c_10904]) ).
tff(c_1821,plain,
! [W_5,Y_102] :
( equalish(W_5,e_1)
| ~ product(Y_102,Y_102,W_5)
| product(e_2,e_2,Y_102)
| product(e_3,e_3,Y_102)
| ~ group_element(Y_102) ),
inference(resolution,[status(thm)],[c_1722,c_22]) ).
tff(c_10918,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_3,e_3,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_10908,c_1821]) ).
tff(c_10958,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_3,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10918]) ).
tff(c_10959,plain,
product(e_2,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_10770,c_12,c_10958]) ).
tff(c_7174,plain,
! [W_5] :
( equalish(W_5,e_2)
| ~ product(e_2,e_2,W_5) ),
inference(resolution,[status(thm)],[c_7093,c_22]) ).
tff(c_10995,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_10959,c_7174]) ).
tff(c_11026,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_10995]) ).
tff(c_11027,plain,
product(e_1,e_1,e_1),
inference(splitRight,[status(thm)],[c_10904]) ).
tff(c_11092,plain,
! [W_5] :
( equalish(W_5,e_1)
| ~ product(e_1,e_1,W_5) ),
inference(resolution,[status(thm)],[c_11027,c_22]) ).
tff(c_12617,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_12493,c_11092]) ).
tff(c_12656,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_12617]) ).
tff(c_12657,plain,
( product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_11589]) ).
tff(c_12662,plain,
product(e_1,e_3,e_2),
inference(splitLeft,[status(thm)],[c_12657]) ).
tff(c_13070,plain,
! [Z1_263] :
( product(Z1_263,e_2,e_1)
| ~ product(e_3,e_1,Z1_263) ),
inference(resolution,[status(thm)],[c_12662,c_28]) ).
tff(c_13073,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| product(e_3,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_10769,c_13070]) ).
tff(c_13097,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13073]) ).
tff(c_13098,plain,
( product(e_2,e_2,e_1)
| product(e_3,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_16,c_13097]) ).
tff(c_13114,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_13098]) ).
tff(c_11597,plain,
! [W_8] :
( equalish(W_8,e_2)
| ~ product(e_3,W_8,e_1) ),
inference(resolution,[status(thm)],[c_11437,c_24]) ).
tff(c_13121,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_13114,c_11597]) ).
tff(c_13162,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_13121]) ).
tff(c_13163,plain,
product(e_2,e_2,e_1),
inference(splitRight,[status(thm)],[c_13098]) ).
tff(c_11595,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_2,e_1) ),
inference(resolution,[status(thm)],[c_11437,c_26]) ).
tff(c_13171,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_13163,c_11595]) ).
tff(c_13212,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_13171]) ).
tff(c_13213,plain,
product(e_2,e_3,e_2),
inference(splitRight,[status(thm)],[c_12657]) ).
tff(c_13227,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_13213,c_7175]) ).
tff(c_13277,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_13227]) ).
tff(c_13278,plain,
product(e_2,e_2,e_1),
inference(splitRight,[status(thm)],[c_7089]) ).
tff(c_13574,plain,
! [Z1_270] :
( product(Z1_270,e_1,e_2)
| ~ product(e_2,e_2,Z1_270) ),
inference(resolution,[status(thm)],[c_13278,c_28]) ).
tff(c_13600,plain,
product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[c_13278,c_13574]) ).
tff(c_13689,plain,
! [W_5] :
( equalish(W_5,e_2)
| ~ product(e_1,e_1,W_5) ),
inference(resolution,[status(thm)],[c_13600,c_22]) ).
tff(c_14604,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_14575,c_13689]) ).
tff(c_14639,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_14604]) ).
tff(c_14787,plain,
! [Y_291] :
( equalish(e_3,Y_291)
| product(e_3,Y_291,e_2)
| product(e_3,Y_291,e_1)
| ~ group_element(Y_291) ),
inference(splitRight,[status(thm)],[c_7026]) ).
tff(c_13688,plain,
! [W_11] :
( equalish(W_11,e_1)
| ~ product(W_11,e_1,e_2) ),
inference(resolution,[status(thm)],[c_13600,c_26]) ).
tff(c_14798,plain,
( equalish(e_3,e_1)
| product(e_3,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_14787,c_13688]) ).
tff(c_14889,plain,
( equalish(e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14798]) ).
tff(c_14890,plain,
product(e_3,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_16,c_14889]) ).
tff(c_15008,plain,
( 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_14890,c_42]) ).
tff(c_15053,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_15008]) ).
tff(c_15374,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_15053]) ).
tff(c_15058,plain,
! [Z1_17] :
( product(Z1_17,e_1,e_3)
| ~ product(e_1,e_3,Z1_17) ),
inference(resolution,[status(thm)],[c_14890,c_28]) ).
tff(c_15408,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_15374,c_15058]) ).
tff(c_15605,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_15408,c_13689]) ).
tff(c_15644,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_15605]) ).
tff(c_15645,plain,
product(e_1,e_3,e_2),
inference(splitRight,[status(thm)],[c_15053]) ).
tff(c_13690,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_1,W_8,e_2) ),
inference(resolution,[status(thm)],[c_13600,c_24]) ).
tff(c_15657,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_15645,c_13690]) ).
tff(c_15704,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_15657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP134-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % 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
% 0.13/0.35 % Computer : n027.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 22:19:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 10.42/3.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.51/3.49
% 10.51/3.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.65/3.55
% 10.65/3.55 Inference rules
% 10.65/3.55 ----------------------
% 10.65/3.55 #Ref : 0
% 10.65/3.55 #Sup : 2921
% 10.65/3.55 #Fact : 12
% 10.65/3.55 #Define : 0
% 10.65/3.55 #Split : 18
% 10.65/3.55 #Chain : 0
% 10.65/3.55 #Close : 0
% 10.65/3.55
% 10.65/3.55 Ordering : KBO
% 10.65/3.55
% 10.65/3.55 Simplification rules
% 10.65/3.55 ----------------------
% 10.65/3.55 #Subsume : 303
% 10.65/3.55 #Demod : 3491
% 10.65/3.55 #Tautology : 1194
% 10.65/3.55 #SimpNegUnit : 896
% 10.65/3.55 #BackRed : 0
% 10.65/3.55
% 10.65/3.55 #Partial instantiations: 0
% 10.65/3.55 #Strategies tried : 1
% 10.65/3.55
% 10.65/3.55 Timing (in seconds)
% 10.65/3.55 ----------------------
% 10.65/3.55 Preprocessing : 0.41
% 10.65/3.55 Parsing : 0.23
% 10.65/3.55 CNF conversion : 0.02
% 10.65/3.55 Main loop : 2.03
% 10.65/3.55 Inferencing : 0.59
% 10.65/3.55 Reduction : 0.55
% 10.65/3.55 Demodulation : 0.35
% 10.65/3.55 BG Simplification : 0.06
% 10.65/3.55 Subsumption : 0.70
% 10.65/3.55 Abstraction : 0.06
% 10.65/3.55 MUC search : 0.00
% 10.65/3.55 Cooper : 0.00
% 10.65/3.55 Total : 2.53
% 10.65/3.55 Index Insertion : 0.00
% 10.65/3.55 Index Deletion : 0.00
% 10.65/3.55 Index Matching : 0.00
% 10.65/3.55 BG Taut test : 0.00
%------------------------------------------------------------------------------