TSTP Solution File: GRP124-2.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP124-2.004 : 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 : n024.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 10:39:55 EDT 2023
% Result : Unsatisfiable 7.43s 2.69s
% Output : CNFRefutation 7.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 33
% Syntax : Number of formulae : 151 ( 74 unt; 9 typ; 0 def)
% Number of atoms : 319 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 304 ( 127 ~; 177 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 101 (; 101 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ 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(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(f_72,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_66,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_58,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_62,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_70,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_64,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_53,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_54,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_36,axiom,
next(e_2,e_3),
file(unknown,unknown) ).
tff(f_94,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ),
file(unknown,unknown) ).
tff(f_43,axiom,
greater(e_4,e_3),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X,Y,X1] :
( ~ product(X,e_1,Y)
| ~ next(X,X1)
| ~ greater(Y,X1) ),
file(unknown,unknown) ).
tff(f_120,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_60,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_55,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_68,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_78,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_56,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_74,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_80,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_118,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_148,axiom,
! [Y1,X1,Z2,Y2,X2,Z1] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(Y1,Y2) ),
file(unknown,unknown) ).
tff(f_102,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(c_44,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_38,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_30,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_34,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_42,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_36,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_22,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_24,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_4,plain,
next(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_141,plain,
! [X_80,Y_81] :
( product(X_80,Y_81,e_4)
| product(X_80,Y_81,e_3)
| product(X_80,Y_81,e_2)
| product(X_80,Y_81,e_1)
| ~ group_element(Y_81)
| ~ group_element(X_80) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_18,plain,
greater(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_68,plain,
! [Y_32,X1_33,X_34] :
( ~ greater(Y_32,X1_33)
| ~ next(X_34,X1_33)
| ~ product(X_34,e_1,Y_32) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_83,plain,
! [X_34] :
( ~ next(X_34,e_3)
| ~ product(X_34,e_1,e_4) ),
inference(resolution,[status(thm)],[c_18,c_68]) ).
tff(c_169,plain,
! [X_80] :
( ~ next(X_80,e_3)
| product(X_80,e_1,e_3)
| product(X_80,e_1,e_2)
| product(X_80,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_80) ),
inference(resolution,[status(thm)],[c_141,c_83]) ).
tff(c_195,plain,
! [X_80] :
( ~ next(X_80,e_3)
| product(X_80,e_1,e_3)
| product(X_80,e_1,e_2)
| product(X_80,e_1,e_1)
| ~ group_element(X_80) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_169]) ).
tff(c_62,plain,
! [X_18] : product(X_18,X_18,X_18),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_32,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_26,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_54,plain,
! [X_4,Y_5] :
( product(X_4,Y_5,e_4)
| 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_94]) ).
tff(c_40,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_50,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_28,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_102,plain,
! [W_47,Z_48,X_49,Y_50] :
( equalish(W_47,Z_48)
| ~ product(X_49,Z_48,Y_50)
| ~ product(X_49,W_47,Y_50) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_105,plain,
! [W_47,X_18] :
( equalish(W_47,X_18)
| ~ product(X_18,W_47,X_18) ),
inference(resolution,[status(thm)],[c_62,c_102]) ).
tff(c_159,plain,
! [Y_81] :
( equalish(Y_81,e_4)
| product(e_4,Y_81,e_3)
| product(e_4,Y_81,e_2)
| product(e_4,Y_81,e_1)
| ~ group_element(Y_81)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_141,c_105]) ).
tff(c_188,plain,
! [Y_81] :
( equalish(Y_81,e_4)
| product(e_4,Y_81,e_3)
| product(e_4,Y_81,e_2)
| product(e_4,Y_81,e_1)
| ~ group_element(Y_81) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_159]) ).
tff(c_46,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_52,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_1031,plain,
! [Y_121] :
( equalish(Y_121,e_4)
| product(e_4,Y_121,e_3)
| product(e_4,Y_121,e_2)
| product(e_4,Y_121,e_1)
| ~ group_element(Y_121) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_159]) ).
tff(c_89,plain,
! [W_37,Z_38,Y_39,X_40] :
( equalish(W_37,Z_38)
| ~ product(Z_38,Y_39,X_40)
| ~ product(W_37,Y_39,X_40) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_92,plain,
! [W_37,X_18] :
( equalish(W_37,X_18)
| ~ product(W_37,X_18,X_18) ),
inference(resolution,[status(thm)],[c_62,c_89]) ).
tff(c_1063,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_1031,c_92]) ).
tff(c_1099,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_1063]) ).
tff(c_1100,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_46,c_52,c_1099]) ).
tff(c_1106,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_1100]) ).
tff(c_117,plain,
! [Y2_60,Z1_63,Z2_58,X1_59,Y1_62,X2_61] :
( equalish(Y1_62,Y2_60)
| ~ product(Z2_58,X2_61,Y2_60)
| ~ product(Z2_58,X1_59,Y1_62)
| ~ product(X2_61,Y2_60,Z1_63)
| ~ product(X1_59,Y1_62,Z1_63) ),
inference(cnfTransformation,[status(thm)],[f_148]) ).
tff(c_120,plain,
! [Y1_62,X_18,X1_59,Z1_63] :
( equalish(Y1_62,X_18)
| ~ product(X_18,X1_59,Y1_62)
| ~ product(X_18,X_18,Z1_63)
| ~ product(X1_59,Y1_62,Z1_63) ),
inference(resolution,[status(thm)],[c_62,c_117]) ).
tff(c_1183,plain,
! [Z1_63] :
( equalish(e_1,e_4)
| ~ product(e_4,e_4,Z1_63)
| ~ product(e_3,e_1,Z1_63) ),
inference(resolution,[status(thm)],[c_1106,c_120]) ).
tff(c_1296,plain,
! [Z1_130] :
( ~ product(e_4,e_4,Z1_130)
| ~ product(e_3,e_1,Z1_130) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_1183]) ).
tff(c_1361,plain,
~ product(e_3,e_1,e_4),
inference(resolution,[status(thm)],[c_62,c_1296]) ).
tff(c_1364,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_54,c_1361]) ).
tff(c_1367,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_22,c_1364]) ).
tff(c_2094,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_1367]) ).
tff(c_165,plain,
! [X_80] :
( equalish(X_80,e_4)
| product(X_80,e_4,e_3)
| product(X_80,e_4,e_2)
| product(X_80,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_80) ),
inference(resolution,[status(thm)],[c_141,c_92]) ).
tff(c_1369,plain,
! [X_131] :
( equalish(X_131,e_4)
| product(X_131,e_4,e_3)
| product(X_131,e_4,e_2)
| product(X_131,e_4,e_1)
| ~ group_element(X_131) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_165]) ).
tff(c_1397,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_1369,c_105]) ).
tff(c_1424,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_1397]) ).
tff(c_1425,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_46,c_52,c_1424]) ).
tff(c_1428,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_1425]) ).
tff(c_58,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_110]) ).
tff(c_1483,plain,
! [W_11] :
( equalish(W_11,e_4)
| ~ product(e_3,W_11,e_1) ),
inference(resolution,[status(thm)],[c_1428,c_58]) ).
tff(c_2097,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_2094,c_1483]) ).
tff(c_2135,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_2097]) ).
tff(c_2136,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_1367]) ).
tff(c_2144,plain,
product(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_2136]) ).
tff(c_2166,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_2144,c_105]) ).
tff(c_2203,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_2166]) ).
tff(c_2204,plain,
product(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_2136]) ).
tff(c_1446,plain,
! [Z1_63] :
( equalish(e_1,e_3)
| ~ product(e_3,e_3,Z1_63)
| ~ product(e_4,e_1,Z1_63) ),
inference(resolution,[status(thm)],[c_1428,c_120]) ).
tff(c_1559,plain,
! [Z1_135] :
( ~ product(e_3,e_3,Z1_135)
| ~ product(e_4,e_1,Z1_135) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_1446]) ).
tff(c_1563,plain,
( ~ product(e_3,e_3,e_3)
| equalish(e_1,e_4)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_188,c_1559]) ).
tff(c_1582,plain,
( equalish(e_1,e_4)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_62,c_1563]) ).
tff(c_1583,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_1582]) ).
tff(c_1596,plain,
product(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_1583]) ).
tff(c_1220,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(e_4,W_11,e_1) ),
inference(resolution,[status(thm)],[c_1106,c_58]) ).
tff(c_1669,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_1596,c_1220]) ).
tff(c_1708,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_1669]) ).
tff(c_1709,plain,
product(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_1583]) ).
tff(c_60,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_118]) ).
tff(c_1773,plain,
! [W_14] :
( equalish(W_14,e_4)
| ~ product(W_14,e_1,e_2) ),
inference(resolution,[status(thm)],[c_1709,c_60]) ).
tff(c_2303,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_2204,c_1773]) ).
tff(c_2333,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_2303]) ).
tff(c_2334,plain,
product(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_1425]) ).
tff(c_2347,plain,
! [Z1_63] :
( equalish(e_2,e_3)
| ~ product(e_3,e_3,Z1_63)
| ~ product(e_4,e_2,Z1_63) ),
inference(resolution,[status(thm)],[c_2334,c_120]) ).
tff(c_2452,plain,
! [Z1_146] :
( ~ product(e_3,e_3,Z1_146)
| ~ product(e_4,e_2,Z1_146) ),
inference(negUnitSimplification,[status(thm)],[c_38,c_2347]) ).
tff(c_2456,plain,
( ~ product(e_3,e_3,e_3)
| equalish(e_2,e_4)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_188,c_2452]) ).
tff(c_2463,plain,
( equalish(e_2,e_4)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_62,c_2456]) ).
tff(c_2464,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_40,c_2463]) ).
tff(c_2535,plain,
product(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_2464]) ).
tff(c_2541,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_2535,c_1220]) ).
tff(c_2572,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_2541]) ).
tff(c_2573,plain,
product(e_4,e_2,e_2),
inference(splitRight,[status(thm)],[c_2464]) ).
tff(c_2598,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_2573,c_92]) ).
tff(c_2626,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_2598]) ).
tff(c_2627,plain,
product(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_1100]) ).
tff(c_2639,plain,
! [Z1_63] :
( equalish(e_2,e_4)
| ~ product(e_4,e_4,Z1_63)
| ~ product(e_3,e_2,Z1_63) ),
inference(resolution,[status(thm)],[c_2627,c_120]) ).
tff(c_2805,plain,
! [Z1_156] :
( ~ product(e_4,e_4,Z1_156)
| ~ product(e_3,e_2,Z1_156) ),
inference(negUnitSimplification,[status(thm)],[c_40,c_2639]) ).
tff(c_2870,plain,
~ product(e_3,e_2,e_4),
inference(resolution,[status(thm)],[c_62,c_2805]) ).
tff(c_2873,plain,
( product(e_3,e_2,e_3)
| 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_54,c_2870]) ).
tff(c_2876,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_2873]) ).
tff(c_2975,plain,
product(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_2876]) ).
tff(c_2993,plain,
! [Z1_63] :
( equalish(e_1,e_3)
| ~ product(e_3,e_3,Z1_63)
| ~ product(e_2,e_1,Z1_63) ),
inference(resolution,[status(thm)],[c_2975,c_120]) ).
tff(c_3098,plain,
! [Z1_161] :
( ~ product(e_3,e_3,Z1_161)
| ~ product(e_2,e_1,Z1_161) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_2993]) ).
tff(c_3158,plain,
~ product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[c_62,c_3098]) ).
tff(c_3161,plain,
( ~ next(e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_195,c_3158]) ).
tff(c_3164,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_3161]) ).
tff(c_3165,plain,
product(e_2,e_1,e_1),
inference(splitLeft,[status(thm)],[c_3164]) ).
tff(c_56,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_102]) ).
tff(c_608,plain,
! [W_105,X_106,Y_107] :
( equalish(W_105,e_4)
| ~ product(X_106,Y_107,W_105)
| product(X_106,Y_107,e_3)
| product(X_106,Y_107,e_2)
| product(X_106,Y_107,e_1)
| ~ group_element(Y_107)
| ~ group_element(X_106) ),
inference(resolution,[status(thm)],[c_141,c_56]) ).
tff(c_634,plain,
! [X_108] :
( equalish(X_108,e_4)
| product(X_108,X_108,e_3)
| product(X_108,X_108,e_2)
| product(X_108,X_108,e_1)
| ~ group_element(X_108) ),
inference(resolution,[status(thm)],[c_62,c_608]) ).
tff(c_113,plain,
! [W_54,Z_55,X_56,Y_57] :
( equalish(W_54,Z_55)
| ~ product(X_56,Y_57,Z_55)
| ~ product(X_56,Y_57,W_54) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_116,plain,
! [W_54,X_18] :
( equalish(W_54,X_18)
| ~ product(X_18,X_18,W_54) ),
inference(resolution,[status(thm)],[c_62,c_113]) ).
tff(c_705,plain,
! [X_109] :
( equalish(e_3,X_109)
| equalish(X_109,e_4)
| product(X_109,X_109,e_2)
| product(X_109,X_109,e_1)
| ~ group_element(X_109) ),
inference(resolution,[status(thm)],[c_634,c_116]) ).
tff(c_768,plain,
! [X_110] :
( equalish(e_2,X_110)
| equalish(e_3,X_110)
| equalish(X_110,e_4)
| product(X_110,X_110,e_1)
| ~ group_element(X_110) ),
inference(resolution,[status(thm)],[c_705,c_116]) ).
tff(c_833,plain,
! [W_14,X_110] :
( equalish(W_14,X_110)
| ~ product(W_14,X_110,e_1)
| equalish(e_2,X_110)
| equalish(e_3,X_110)
| equalish(X_110,e_4)
| ~ group_element(X_110) ),
inference(resolution,[status(thm)],[c_768,c_60]) ).
tff(c_3241,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_1,e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_3165,c_833]) ).
tff(c_3277,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_3241]) ).
tff(c_3279,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_42,c_36,c_3277]) ).
tff(c_3280,plain,
product(e_2,e_1,e_2),
inference(splitRight,[status(thm)],[c_3164]) ).
tff(c_3309,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_3280,c_105]) ).
tff(c_3343,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_3309]) ).
tff(c_3344,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_2876]) ).
tff(c_3431,plain,
product(e_3,e_2,e_3),
inference(splitLeft,[status(thm)],[c_3344]) ).
tff(c_3450,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_3431,c_105]) ).
tff(c_3477,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_3450]) ).
tff(c_3478,plain,
product(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_3344]) ).
tff(c_3500,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_3478,c_92]) ).
tff(c_3527,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_3500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP124-2.004 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.14 % 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
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 22:19:00 EDT 2023
% 0.14/0.35 % CPUTime :
% 7.43/2.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.43/2.71
% 7.43/2.71 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.43/2.76
% 7.43/2.76 Inference rules
% 7.43/2.76 ----------------------
% 7.43/2.76 #Ref : 0
% 7.43/2.76 #Sup : 687
% 7.43/2.76 #Fact : 0
% 7.43/2.76 #Define : 0
% 7.43/2.76 #Split : 17
% 7.43/2.76 #Chain : 0
% 7.43/2.76 #Close : 0
% 7.43/2.76
% 7.43/2.76 Ordering : KBO
% 7.43/2.76
% 7.43/2.76 Simplification rules
% 7.43/2.76 ----------------------
% 7.43/2.76 #Subsume : 87
% 7.43/2.76 #Demod : 494
% 7.43/2.76 #Tautology : 188
% 7.43/2.76 #SimpNegUnit : 269
% 7.43/2.76 #BackRed : 0
% 7.43/2.76
% 7.43/2.76 #Partial instantiations: 0
% 7.43/2.76 #Strategies tried : 1
% 7.43/2.76
% 7.43/2.76 Timing (in seconds)
% 7.43/2.76 ----------------------
% 7.43/2.76 Preprocessing : 0.47
% 7.43/2.76 Parsing : 0.26
% 7.43/2.76 CNF conversion : 0.03
% 7.43/2.76 Main loop : 1.19
% 7.43/2.76 Inferencing : 0.40
% 7.43/2.76 Reduction : 0.33
% 7.43/2.76 Demodulation : 0.21
% 7.43/2.76 BG Simplification : 0.04
% 7.43/2.76 Subsumption : 0.34
% 7.43/2.76 Abstraction : 0.05
% 7.43/2.76 MUC search : 0.00
% 7.43/2.76 Cooper : 0.00
% 7.43/2.76 Total : 1.74
% 7.72/2.76 Index Insertion : 0.00
% 7.72/2.76 Index Deletion : 0.00
% 7.72/2.76 Index Matching : 0.00
% 7.72/2.76 BG Taut test : 0.00
%------------------------------------------------------------------------------