TSTP Solution File: GRP124-4.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP124-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : 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 10:39:56 EDT 2023
% Result : Unsatisfiable 7.42s 2.78s
% Output : CNFRefutation 7.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 30
% Syntax : Number of formulae : 183 ( 87 unt; 7 typ; 0 def)
% Number of atoms : 419 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 416 ( 173 ~; 243 |; 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 : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 126 (; 126 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > 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(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $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(f_88,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_90,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_130,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_68,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_74,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_70,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_80,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_65,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_63,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,e_1,Y)
| product(X,e_2,Y)
| product(X,e_3,Y)
| product(X,e_4,Y) ),
file(unknown,unknown) ).
tff(f_86,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_78,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_64,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_66,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(e_1,X,Y)
| product(e_2,X,Y)
| product(e_3,X,Y)
| product(e_4,X,Y) ),
file(unknown,unknown) ).
tff(f_120,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_104,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_84,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_128,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_112,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_144,axiom,
! [Y1,X1,Z2,Y2,X2,Z1] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(X1,X2) ),
file(unknown,unknown) ).
tff(f_158,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_72,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(c_34,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_36,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_46,plain,
! [X_19] : product(X_19,X_19,X_19),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_14,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_20,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_16,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_26,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_10,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_6,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_4,plain,
! [X_3,Y_4] :
( product(X_3,e_4,Y_4)
| product(X_3,e_3,Y_4)
| product(X_3,e_2,Y_4)
| product(X_3,e_1,Y_4)
| ~ group_element(Y_4)
| ~ group_element(X_3) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_32,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_24,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_8,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_12,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_376,plain,
! [X_81,Y_82] :
( product(e_4,X_81,Y_82)
| product(e_3,X_81,Y_82)
| product(e_2,X_81,Y_82)
| product(e_1,X_81,Y_82)
| ~ group_element(Y_82)
| ~ group_element(X_81) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_52,plain,
! [W_33,Z_34,X_35,Y_36] :
( equalish(W_33,Z_34)
| ~ product(X_35,Z_34,Y_36)
| ~ product(X_35,W_33,Y_36) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_55,plain,
! [W_33,X_19] :
( equalish(W_33,X_19)
| ~ product(X_19,W_33,X_19) ),
inference(resolution,[status(thm)],[c_46,c_52]) ).
tff(c_400,plain,
! [X_81] :
( equalish(X_81,e_4)
| product(e_3,X_81,e_4)
| product(e_2,X_81,e_4)
| product(e_1,X_81,e_4)
| ~ group_element(e_4)
| ~ group_element(X_81) ),
inference(resolution,[status(thm)],[c_376,c_55]) ).
tff(c_415,plain,
! [X_81] :
( equalish(X_81,e_4)
| product(e_3,X_81,e_4)
| product(e_2,X_81,e_4)
| product(e_1,X_81,e_4)
| ~ group_element(X_81) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_400]) ).
tff(c_38,plain,
! [X_5,Y_6] :
( product(X_5,Y_6,e_4)
| product(X_5,Y_6,e_3)
| product(X_5,Y_6,e_2)
| product(X_5,Y_6,e_1)
| ~ group_element(Y_6)
| ~ group_element(X_5) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_30,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_141,plain,
! [X_74,Y_75] :
( product(X_74,Y_75,e_4)
| product(X_74,Y_75,e_3)
| product(X_74,Y_75,e_2)
| product(X_74,Y_75,e_1)
| ~ group_element(Y_75)
| ~ group_element(X_74) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_72,plain,
! [W_46,Z_47,Y_48,X_49] :
( equalish(W_46,Z_47)
| ~ product(Z_47,Y_48,X_49)
| ~ product(W_46,Y_48,X_49) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_75,plain,
! [W_46,X_19] :
( equalish(W_46,X_19)
| ~ product(W_46,X_19,X_19) ),
inference(resolution,[status(thm)],[c_46,c_72]) ).
tff(c_153,plain,
! [X_74] :
( equalish(X_74,e_4)
| product(X_74,e_4,e_3)
| product(X_74,e_4,e_2)
| product(X_74,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_74) ),
inference(resolution,[status(thm)],[c_141,c_75]) ).
tff(c_503,plain,
! [X_85] :
( equalish(X_85,e_4)
| product(X_85,e_4,e_3)
| product(X_85,e_4,e_2)
| product(X_85,e_4,e_1)
| ~ group_element(X_85) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_153]) ).
tff(c_523,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_503,c_55]) ).
tff(c_538,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_10,c_523]) ).
tff(c_539,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_36,c_538]) ).
tff(c_541,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_539]) ).
tff(c_1037,plain,
! [X_102] :
( equalish(X_102,e_4)
| product(e_3,X_102,e_4)
| product(e_2,X_102,e_4)
| product(e_1,X_102,e_4)
| ~ group_element(X_102) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_400]) ).
tff(c_61,plain,
! [W_39,Z_40,X_41,Y_42] :
( equalish(W_39,Z_40)
| ~ product(X_41,Y_42,Z_40)
| ~ product(X_41,Y_42,W_39) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_64,plain,
! [W_39,X_19] :
( equalish(W_39,X_19)
| ~ product(X_19,X_19,W_39) ),
inference(resolution,[status(thm)],[c_46,c_61]) ).
tff(c_1069,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_1037,c_64]) ).
tff(c_1102,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_1069]) ).
tff(c_1103,plain,
( product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_36,c_1102]) ).
tff(c_1182,plain,
product(e_1,e_3,e_4),
inference(splitLeft,[status(thm)],[c_1103]) ).
tff(c_82,plain,
! [Z2_53,Y2_54,X2_57,Y1_52,X1_55,Z1_56] :
( equalish(X1_55,X2_57)
| ~ product(Z2_53,X2_57,Y2_54)
| ~ product(Z2_53,X1_55,Y1_52)
| ~ product(X2_57,Y2_54,Z1_56)
| ~ product(X1_55,Y1_52,Z1_56) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_85,plain,
! [X1_55,X_19,Y1_52,Z1_56] :
( equalish(X1_55,X_19)
| ~ product(X_19,X1_55,Y1_52)
| ~ product(X_19,X_19,Z1_56)
| ~ product(X1_55,Y1_52,Z1_56) ),
inference(resolution,[status(thm)],[c_46,c_82]) ).
tff(c_1188,plain,
! [Z1_56] :
( equalish(e_3,e_1)
| ~ product(e_1,e_1,Z1_56)
| ~ product(e_3,e_4,Z1_56) ),
inference(resolution,[status(thm)],[c_1182,c_85]) ).
tff(c_1309,plain,
! [Z1_109] :
( ~ product(e_1,e_1,Z1_109)
| ~ product(e_3,e_4,Z1_109) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_1188]) ).
tff(c_1320,plain,
~ product(e_1,e_1,e_1),
inference(resolution,[status(thm)],[c_541,c_1309]) ).
tff(c_1342,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_46,c_1320]) ).
tff(c_1344,plain,
~ product(e_1,e_3,e_4),
inference(splitRight,[status(thm)],[c_1103]) ).
tff(c_1378,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_38,c_1344]) ).
tff(c_1381,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_6,c_10,c_1378]) ).
tff(c_1595,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_1381]) ).
tff(c_1612,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_1595,c_55]) ).
tff(c_1631,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_1612]) ).
tff(c_1632,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_1381]) ).
tff(c_1724,plain,
product(e_1,e_3,e_3),
inference(splitLeft,[status(thm)],[c_1632]) ).
tff(c_1739,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_1724,c_75]) ).
tff(c_1765,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_1739]) ).
tff(c_1766,plain,
product(e_1,e_3,e_2),
inference(splitRight,[status(thm)],[c_1632]) ).
tff(c_86,plain,
! [Z2_60,Y2_59,Z1_58,X1_62,X2_63,Y1_61] :
( equalish(Y1_61,Y2_59)
| ~ product(Z2_60,X2_63,Y2_59)
| ~ product(Z2_60,X1_62,Y1_61)
| ~ product(X2_63,Y2_59,Z1_58)
| ~ product(X1_62,Y1_61,Z1_58) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_89,plain,
! [Y1_61,X_19,X1_62,Z1_58] :
( equalish(Y1_61,X_19)
| ~ product(X_19,X1_62,Y1_61)
| ~ product(X_19,X_19,Z1_58)
| ~ product(X1_62,Y1_61,Z1_58) ),
inference(resolution,[status(thm)],[c_46,c_86]) ).
tff(c_1855,plain,
! [Z1_58] :
( equalish(e_2,e_1)
| ~ product(e_1,e_1,Z1_58)
| ~ product(e_3,e_2,Z1_58) ),
inference(resolution,[status(thm)],[c_1766,c_89]) ).
tff(c_1977,plain,
! [Z1_126] :
( ~ product(e_1,e_1,Z1_126)
| ~ product(e_3,e_2,Z1_126) ),
inference(negUnitSimplification,[status(thm)],[c_20,c_1855]) ).
tff(c_1981,plain,
( ~ product(e_1,e_1,e_4)
| equalish(e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_415,c_1977]) ).
tff(c_1996,plain,
( ~ product(e_1,e_1,e_4)
| equalish(e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1981]) ).
tff(c_1997,plain,
( ~ product(e_1,e_1,e_4)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_24,c_1996]) ).
tff(c_2097,plain,
~ product(e_1,e_1,e_4),
inference(splitLeft,[status(thm)],[c_1997]) ).
tff(c_18,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_174,plain,
! [X_74] :
( equalish(X_74,e_4)
| product(X_74,e_4,e_3)
| product(X_74,e_4,e_2)
| product(X_74,e_4,e_1)
| ~ group_element(X_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_153]) ).
tff(c_543,plain,
! [Z1_58] :
( equalish(e_1,e_3)
| ~ product(e_3,e_3,Z1_58)
| ~ product(e_4,e_1,Z1_58) ),
inference(resolution,[status(thm)],[c_541,c_89]) ).
tff(c_646,plain,
! [Z1_89] :
( ~ product(e_3,e_3,Z1_89)
| ~ product(e_4,e_1,Z1_89) ),
inference(negUnitSimplification,[status(thm)],[c_16,c_543]) ).
tff(c_658,plain,
( ~ product(e_3,e_3,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_38,c_646]) ).
tff(c_668,plain,
( ~ product(e_3,e_3,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_6,c_658]) ).
tff(c_1030,plain,
~ product(e_3,e_3,e_4),
inference(splitLeft,[status(thm)],[c_668]) ).
tff(c_1343,plain,
product(e_2,e_3,e_4),
inference(splitRight,[status(thm)],[c_1103]) ).
tff(c_48,plain,
! [X2_24,X1_21,Z1_25,Y2_23,Y1_20,Z2_22] :
( equalish(X1_21,X2_24)
| ~ product(Z2_22,X2_24,Y2_23)
| ~ product(Z2_22,X1_21,Y1_20)
| ~ product(X2_24,Y2_23,Z1_25)
| ~ product(X1_21,Y1_20,Z1_25) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_1775,plain,
! [X1_120,Y1_121,Z1_122] :
( equalish(X1_120,e_3)
| ~ product(e_2,X1_120,Y1_121)
| ~ product(e_3,e_4,Z1_122)
| ~ product(X1_120,Y1_121,Z1_122) ),
inference(resolution,[status(thm)],[c_1343,c_48]) ).
tff(c_1782,plain,
! [Z1_122] :
( equalish(e_4,e_3)
| ~ product(e_3,e_4,Z1_122)
| ~ product(e_4,e_3,Z1_122)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_174,c_1775]) ).
tff(c_1815,plain,
! [Z1_122] :
( equalish(e_4,e_3)
| ~ product(e_3,e_4,Z1_122)
| ~ product(e_4,e_3,Z1_122)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1782]) ).
tff(c_1816,plain,
! [Z1_122] :
( ~ product(e_3,e_4,Z1_122)
| ~ product(e_4,e_3,Z1_122)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_24,c_36,c_1815]) ).
tff(c_2329,plain,
! [Z1_139] :
( ~ product(e_3,e_4,Z1_139)
| ~ product(e_4,e_3,Z1_139) ),
inference(splitLeft,[status(thm)],[c_1816]) ).
tff(c_2341,plain,
( ~ product(e_3,e_4,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_38,c_2329]) ).
tff(c_2350,plain,
( ~ product(e_3,e_4,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_10,c_2341]) ).
tff(c_2419,plain,
~ product(e_3,e_4,e_4),
inference(splitLeft,[status(thm)],[c_2350]) ).
tff(c_2431,plain,
( product(e_3,e_3,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_4,c_2419]) ).
tff(c_2443,plain,
( product(e_3,e_3,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_12,c_2431]) ).
tff(c_2444,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_1,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_1030,c_2443]) ).
tff(c_2468,plain,
product(e_3,e_1,e_4),
inference(splitLeft,[status(thm)],[c_2444]) ).
tff(c_2482,plain,
! [Z1_56] :
( equalish(e_1,e_3)
| ~ product(e_3,e_3,Z1_56)
| ~ product(e_1,e_4,Z1_56) ),
inference(resolution,[status(thm)],[c_2468,c_85]) ).
tff(c_2706,plain,
! [Z1_150] :
( ~ product(e_3,e_3,Z1_150)
| ~ product(e_1,e_4,Z1_150) ),
inference(negUnitSimplification,[status(thm)],[c_16,c_2482]) ).
tff(c_2766,plain,
~ product(e_1,e_4,e_3),
inference(resolution,[status(thm)],[c_46,c_2706]) ).
tff(c_2769,plain,
( equalish(e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_174,c_2766]) ).
tff(c_2775,plain,
( equalish(e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2769]) ).
tff(c_2776,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_18,c_2775]) ).
tff(c_3097,plain,
product(e_1,e_4,e_1),
inference(splitLeft,[status(thm)],[c_2776]) ).
tff(c_44,plain,
! [W_15,Z_18,Y_16,X_17] :
( equalish(W_15,Z_18)
| ~ product(Z_18,Y_16,X_17)
| ~ product(W_15,Y_16,X_17) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_564,plain,
! [W_15] :
( equalish(W_15,e_3)
| ~ product(W_15,e_4,e_1) ),
inference(resolution,[status(thm)],[c_541,c_44]) ).
tff(c_3114,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_3097,c_564]) ).
tff(c_3159,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_3114]) ).
tff(c_3160,plain,
product(e_1,e_4,e_2),
inference(splitRight,[status(thm)],[c_2776]) ).
tff(c_42,plain,
! [W_12,Z_14,X_11,Y_13] :
( equalish(W_12,Z_14)
| ~ product(X_11,Z_14,Y_13)
| ~ product(X_11,W_12,Y_13) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_1886,plain,
! [W_12] :
( equalish(W_12,e_3)
| ~ product(e_1,W_12,e_2) ),
inference(resolution,[status(thm)],[c_1766,c_42]) ).
tff(c_3179,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_3160,c_1886]) ).
tff(c_3215,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_3179]) ).
tff(c_3217,plain,
~ product(e_3,e_1,e_4),
inference(splitRight,[status(thm)],[c_2444]) ).
tff(c_3298,plain,
( equalish(e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_415,c_3217]) ).
tff(c_3304,plain,
( equalish(e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_3298]) ).
tff(c_3305,plain,
product(e_2,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_2097,c_18,c_3304]) ).
tff(c_1375,plain,
! [W_12] :
( equalish(W_12,e_3)
| ~ product(e_2,W_12,e_4) ),
inference(resolution,[status(thm)],[c_1343,c_42]) ).
tff(c_3375,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_3305,c_1375]) ).
tff(c_3407,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_3375]) ).
tff(c_3409,plain,
product(e_1,e_1,e_4),
inference(splitRight,[status(thm)],[c_1997]) ).
tff(c_3502,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_3409,c_64]) ).
tff(c_3529,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_3502]) ).
tff(c_3531,plain,
~ product(e_3,e_4,e_1),
inference(splitRight,[status(thm)],[c_539]) ).
tff(c_3559,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_4,c_3531]) ).
tff(c_3562,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_6,c_3559]) ).
tff(c_3791,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_3562]) ).
tff(c_3806,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_3791,c_75]) ).
tff(c_3831,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_3806]) ).
tff(c_3832,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_3,e_1) ),
inference(splitRight,[status(thm)],[c_3562]) ).
tff(c_3834,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_3832]) ).
tff(c_3851,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_3834,c_64]) ).
tff(c_3874,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_3851]) ).
tff(c_3875,plain,
product(e_3,e_2,e_1),
inference(splitRight,[status(thm)],[c_3832]) ).
tff(c_3950,plain,
! [Z1_58] :
( equalish(e_1,e_3)
| ~ product(e_3,e_3,Z1_58)
| ~ product(e_2,e_1,Z1_58) ),
inference(resolution,[status(thm)],[c_3875,c_89]) ).
tff(c_4062,plain,
! [Z1_180] :
( ~ product(e_3,e_3,Z1_180)
| ~ product(e_2,e_1,Z1_180) ),
inference(negUnitSimplification,[status(thm)],[c_16,c_3950]) ).
tff(c_4107,plain,
~ product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[c_46,c_4062]) ).
tff(c_3530,plain,
product(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_539]) ).
tff(c_3553,plain,
! [X1_21,Y1_20,Z1_25] :
( equalish(X1_21,e_4)
| ~ product(e_3,X1_21,Y1_20)
| ~ product(e_4,e_2,Z1_25)
| ~ product(X1_21,Y1_20,Z1_25) ),
inference(resolution,[status(thm)],[c_3530,c_48]) ).
tff(c_3946,plain,
! [Z1_25] :
( equalish(e_2,e_4)
| ~ product(e_4,e_2,Z1_25)
| ~ product(e_2,e_1,Z1_25) ),
inference(resolution,[status(thm)],[c_3875,c_3553]) ).
tff(c_4108,plain,
! [Z1_181] :
( ~ product(e_4,e_2,Z1_181)
| ~ product(e_2,e_1,Z1_181) ),
inference(negUnitSimplification,[status(thm)],[c_24,c_3946]) ).
tff(c_4120,plain,
( ~ product(e_2,e_1,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_38,c_4108]) ).
tff(c_4130,plain,
( ~ product(e_2,e_1,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_8,c_4120]) ).
tff(c_4432,plain,
~ product(e_2,e_1,e_4),
inference(splitLeft,[status(thm)],[c_4130]) ).
tff(c_4435,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_38,c_4432]) ).
tff(c_4438,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6,c_4435]) ).
tff(c_4439,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_4107,c_4438]) ).
tff(c_4482,plain,
product(e_2,e_1,e_1),
inference(splitLeft,[status(thm)],[c_4439]) ).
tff(c_4497,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_4482,c_75]) ).
tff(c_4523,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_4497]) ).
tff(c_4524,plain,
product(e_2,e_1,e_2),
inference(splitRight,[status(thm)],[c_4439]) ).
tff(c_4660,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_4524,c_55]) ).
tff(c_4683,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_4660]) ).
tff(c_4684,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_4130]) ).
tff(c_4915,plain,
product(e_4,e_2,e_3),
inference(splitLeft,[status(thm)],[c_4684]) ).
tff(c_3535,plain,
! [Z1_56] :
( equalish(e_4,e_3)
| ~ product(e_3,e_3,Z1_56)
| ~ product(e_4,e_2,Z1_56) ),
inference(resolution,[status(thm)],[c_3530,c_85]) ).
tff(c_3551,plain,
! [Z1_56] :
( ~ product(e_3,e_3,Z1_56)
| ~ product(e_4,e_2,Z1_56) ),
inference(negUnitSimplification,[status(thm)],[c_36,c_3535]) ).
tff(c_4927,plain,
~ product(e_3,e_3,e_3),
inference(resolution,[status(thm)],[c_4915,c_3551]) ).
tff(c_4958,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_46,c_4927]) ).
tff(c_4959,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(splitRight,[status(thm)],[c_4684]) ).
tff(c_4967,plain,
product(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_4959]) ).
tff(c_3978,plain,
! [W_15] :
( equalish(W_15,e_3)
| ~ product(W_15,e_2,e_1) ),
inference(resolution,[status(thm)],[c_3875,c_44]) ).
tff(c_5024,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_4967,c_3978]) ).
tff(c_5057,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_5024]) ).
tff(c_5058,plain,
product(e_4,e_2,e_2),
inference(splitRight,[status(thm)],[c_4959]) ).
tff(c_5084,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_5058,c_75]) ).
tff(c_5118,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_5084]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP124-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n024.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 22:19:30 EDT 2023
% 0.13/0.36 % CPUTime :
% 7.42/2.78 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.42/2.80
% 7.42/2.80 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.78/2.86
% 7.78/2.86 Inference rules
% 7.78/2.86 ----------------------
% 7.78/2.86 #Ref : 0
% 7.78/2.86 #Sup : 947
% 7.78/2.86 #Fact : 0
% 7.78/2.86 #Define : 0
% 7.78/2.86 #Split : 19
% 7.78/2.86 #Chain : 0
% 7.78/2.86 #Close : 0
% 7.78/2.86
% 7.78/2.86 Ordering : KBO
% 7.78/2.86
% 7.78/2.86 Simplification rules
% 7.78/2.86 ----------------------
% 7.78/2.86 #Subsume : 84
% 7.78/2.86 #Demod : 1004
% 7.78/2.86 #Tautology : 366
% 7.78/2.86 #SimpNegUnit : 395
% 7.78/2.86 #BackRed : 0
% 7.78/2.86
% 7.78/2.86 #Partial instantiations: 0
% 7.78/2.86 #Strategies tried : 1
% 7.78/2.86
% 7.78/2.86 Timing (in seconds)
% 7.78/2.86 ----------------------
% 7.78/2.86 Preprocessing : 0.48
% 7.78/2.86 Parsing : 0.27
% 7.78/2.86 CNF conversion : 0.03
% 7.78/2.86 Main loop : 1.20
% 7.78/2.86 Inferencing : 0.37
% 7.78/2.86 Reduction : 0.33
% 7.78/2.86 Demodulation : 0.20
% 7.78/2.86 BG Simplification : 0.04
% 7.78/2.86 Subsumption : 0.40
% 7.78/2.86 Abstraction : 0.04
% 7.78/2.86 MUC search : 0.00
% 7.78/2.86 Cooper : 0.00
% 7.78/2.86 Total : 1.78
% 7.78/2.86 Index Insertion : 0.00
% 7.78/2.86 Index Deletion : 0.00
% 7.78/2.86 Index Matching : 0.00
% 7.78/2.86 BG Taut test : 0.00
%------------------------------------------------------------------------------