TSTP Solution File: GRP127-4.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP127-4.004 : 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 : n019.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 10:40:05 EDT 2023
% Result : Unsatisfiable 7.32s 2.64s
% Output : CNFRefutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 29
% Syntax : Number of formulae : 150 ( 70 unt; 7 typ; 0 def)
% Number of atoms : 308 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 292 ( 127 ~; 165 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 107 (; 107 !; 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_97,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_83,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_101,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_93,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_103,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_78,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_79,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_143,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_59,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_125,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_141,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_151,axiom,
! [Y,X,Z1,Z2] :
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| product(Z2,Y,X) ),
file(unknown,unknown) ).
tff(f_76,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_67,axiom,
! [Y,X,Z1,Z2] :
( product(Y,X,Z1)
| ~ product(Z2,Y,X)
| ~ product(Z1,Y,Z2) ),
file(unknown,unknown) ).
tff(f_99,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_77,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_117,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_133,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_81,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_45,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_75,axiom,
! [Z1,Y,Z2,X] :
( product(Z1,Y,Z2)
| ~ product(Z2,Y,X)
| ~ product(Y,X,Z1) ),
file(unknown,unknown) ).
tff(f_95,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(c_34,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_20,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_38,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_30,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_40,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_14,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_16,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_50,plain,
! [X_27] : product(X_27,X_27,X_27),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_355,plain,
! [X_76,Y_77] :
( product(X_76,e_4,Y_77)
| product(X_76,e_3,Y_77)
| product(X_76,e_2,Y_77)
| product(X_76,e_1,Y_77)
| ~ group_element(Y_77)
| ~ group_element(X_76) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_44,plain,
! [W_17,Z_18,X_15,Y_16] :
( equalish(W_17,Z_18)
| ~ product(X_15,Y_16,Z_18)
| ~ product(X_15,Y_16,W_17) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_1004,plain,
! [W_88,Y_89,X_90] :
( equalish(W_88,Y_89)
| ~ product(X_90,e_4,W_88)
| product(X_90,e_3,Y_89)
| product(X_90,e_2,Y_89)
| product(X_90,e_1,Y_89)
| ~ group_element(Y_89)
| ~ group_element(X_90) ),
inference(resolution,[status(thm)],[c_355,c_44]) ).
tff(c_1041,plain,
! [Y_89] :
( equalish(e_4,Y_89)
| product(e_4,e_3,Y_89)
| product(e_4,e_2,Y_89)
| product(e_4,e_1,Y_89)
| ~ group_element(Y_89)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_50,c_1004]) ).
tff(c_1295,plain,
! [Y_94] :
( equalish(e_4,Y_94)
| product(e_4,e_3,Y_94)
| product(e_4,e_2,Y_94)
| product(e_4,e_1,Y_94)
| ~ group_element(Y_94) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1041]) ).
tff(c_74,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_141]) ).
tff(c_77,plain,
! [W_46,X_27] :
( equalish(W_46,X_27)
| ~ product(W_46,X_27,X_27) ),
inference(resolution,[status(thm)],[c_50,c_74]) ).
tff(c_1311,plain,
( equalish(e_4,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_1295,c_77]) ).
tff(c_1334,plain,
( equalish(e_4,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_1311]) ).
tff(c_1335,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(negUnitSimplification,[status(thm)],[c_40,c_1334]) ).
tff(c_1343,plain,
product(e_4,e_1,e_3),
inference(splitLeft,[status(thm)],[c_1335]) ).
tff(c_52,plain,
! [Z2_31,Y_28,X_29,Z1_30] :
( product(Z2_31,Y_28,X_29)
| ~ product(Z1_30,Y_28,Z2_31)
| ~ product(Y_28,X_29,Z1_30) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_1600,plain,
! [X_102] :
( product(e_3,e_1,X_102)
| ~ product(e_1,X_102,e_4) ),
inference(resolution,[status(thm)],[c_1343,c_52]) ).
tff(c_1625,plain,
( equalish(e_3,e_1)
| ~ product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[c_1600,c_77]) ).
tff(c_1651,plain,
~ product(e_1,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_30,c_1625]) ).
tff(c_48,plain,
! [W_23,Z_26,Y_24,X_25] :
( equalish(W_23,Z_26)
| ~ product(Z_26,Y_24,X_25)
| ~ product(W_23,Y_24,X_25) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_1359,plain,
! [W_23] :
( equalish(W_23,e_4)
| ~ product(W_23,e_1,e_3) ),
inference(resolution,[status(thm)],[c_1343,c_48]) ).
tff(c_1609,plain,
( equalish(e_3,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[c_1600,c_1359]) ).
tff(c_1643,plain,
~ product(e_1,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_34,c_1609]) ).
tff(c_10,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_76]) ).
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_59]) ).
tff(c_6,plain,
! [Z1_7,Y_5,Z2_8,X_6] :
( ~ product(Z1_7,Y_5,Z2_8)
| ~ product(Z2_8,Y_5,X_6)
| product(Y_5,X_6,Z1_7) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_2053,plain,
! [X_113,X_114] :
( ~ product(X_113,e_1,X_114)
| product(e_1,X_114,e_3)
| ~ product(e_1,X_113,e_4) ),
inference(resolution,[status(thm)],[c_1600,c_6]) ).
tff(c_2102,plain,
( product(e_1,e_3,e_3)
| ~ product(e_1,e_4,e_4) ),
inference(resolution,[status(thm)],[c_1343,c_2053]) ).
tff(c_2148,plain,
~ product(e_1,e_4,e_4),
inference(splitLeft,[status(thm)],[c_2102]) ).
tff(c_2156,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_4,c_2148]) ).
tff(c_2165,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_16,c_2156]) ).
tff(c_2166,plain,
product(e_1,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_1651,c_1643,c_2165]) ).
tff(c_2495,plain,
! [X_122] :
( product(e_4,e_2,X_122)
| ~ product(e_2,X_122,e_1) ),
inference(resolution,[status(thm)],[c_2166,c_52]) ).
tff(c_2528,plain,
( equalish(e_4,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[c_2495,c_77]) ).
tff(c_2560,plain,
~ product(e_2,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_38,c_2528]) ).
tff(c_36,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_12,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_1082,plain,
! [Y_89] :
( equalish(e_4,Y_89)
| product(e_4,e_3,Y_89)
| product(e_4,e_2,Y_89)
| product(e_4,e_1,Y_89)
| ~ group_element(Y_89) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1041]) ).
tff(c_42,plain,
! [X_13,Y_14] :
( product(X_13,Y_14,e_4)
| product(X_13,Y_14,e_3)
| product(X_13,Y_14,e_2)
| product(X_13,Y_14,e_1)
| ~ group_element(Y_14)
| ~ group_element(X_13) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_1660,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_42,c_1643]) ).
tff(c_1663,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_10,c_14,c_1660]) ).
tff(c_3055,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_1663]) ).
tff(c_54,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_133]) ).
tff(c_57,plain,
! [W_33,X_27] :
( equalish(W_33,X_27)
| ~ product(X_27,W_33,X_27) ),
inference(resolution,[status(thm)],[c_50,c_54]) ).
tff(c_3076,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_3055,c_57]) ).
tff(c_3097,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_3076]) ).
tff(c_3098,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_1663]) ).
tff(c_3198,plain,
product(e_1,e_3,e_3),
inference(splitLeft,[status(thm)],[c_3098]) ).
tff(c_3215,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_3198,c_77]) ).
tff(c_3238,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_3215]) ).
tff(c_3239,plain,
product(e_1,e_3,e_2),
inference(splitRight,[status(thm)],[c_3098]) ).
tff(c_3321,plain,
! [W_142] :
( equalish(W_142,e_1)
| ~ product(W_142,e_3,e_2) ),
inference(resolution,[status(thm)],[c_3239,c_48]) ).
tff(c_3328,plain,
( equalish(e_4,e_1)
| equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_1,e_2)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_1082,c_3321]) ).
tff(c_3353,plain,
( equalish(e_4,e_1)
| equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_1,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_3328]) ).
tff(c_3354,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_1,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_38,c_36,c_3353]) ).
tff(c_4130,plain,
product(e_4,e_1,e_2),
inference(splitLeft,[status(thm)],[c_3354]) ).
tff(c_1652,plain,
! [W_23,X_102] :
( equalish(W_23,e_3)
| ~ product(W_23,e_1,X_102)
| ~ product(e_1,X_102,e_4) ),
inference(resolution,[status(thm)],[c_1600,c_48]) ).
tff(c_4143,plain,
( equalish(e_4,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[c_4130,c_1652]) ).
tff(c_4176,plain,
equalish(e_4,e_3),
inference(demodulation,[status(thm),theory(equality)],[c_2166,c_4143]) ).
tff(c_4178,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_4176]) ).
tff(c_4179,plain,
product(e_4,e_2,e_2),
inference(splitRight,[status(thm)],[c_3354]) ).
tff(c_2191,plain,
! [X_6] :
( ~ product(e_4,e_2,X_6)
| product(e_2,X_6,e_1) ),
inference(resolution,[status(thm)],[c_2166,c_6]) ).
tff(c_4192,plain,
product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[c_4179,c_2191]) ).
tff(c_4227,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2560,c_4192]) ).
tff(c_4228,plain,
product(e_1,e_3,e_3),
inference(splitRight,[status(thm)],[c_2102]) ).
tff(c_4242,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_4228,c_77]) ).
tff(c_4260,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_4242]) ).
tff(c_4261,plain,
product(e_4,e_2,e_3),
inference(splitRight,[status(thm)],[c_1335]) ).
tff(c_4613,plain,
! [X_168] :
( product(e_3,e_2,X_168)
| ~ product(e_2,X_168,e_4) ),
inference(resolution,[status(thm)],[c_4261,c_52]) ).
tff(c_4278,plain,
! [W_23] :
( equalish(W_23,e_4)
| ~ product(W_23,e_2,e_3) ),
inference(resolution,[status(thm)],[c_4261,c_48]) ).
tff(c_4620,plain,
( equalish(e_3,e_4)
| ~ product(e_2,e_3,e_4) ),
inference(resolution,[status(thm)],[c_4613,c_4278]) ).
tff(c_4652,plain,
~ product(e_2,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_34,c_4620]) ).
tff(c_18,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_2,plain,
! [X_1,Y_2] :
( product(e_4,X_1,Y_2)
| product(e_3,X_1,Y_2)
| product(e_2,X_1,Y_2)
| product(e_1,X_1,Y_2)
| ~ group_element(Y_2)
| ~ group_element(X_1) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_4262,plain,
~ product(e_4,e_1,e_3),
inference(splitRight,[status(thm)],[c_1335]) ).
tff(c_4283,plain,
( product(e_3,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_2,c_4262]) ).
tff(c_4286,plain,
( product(e_3,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_14,c_4283]) ).
tff(c_5061,plain,
product(e_1,e_1,e_3),
inference(splitLeft,[status(thm)],[c_4286]) ).
tff(c_63,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_125]) ).
tff(c_66,plain,
! [W_39,X_27] :
( equalish(W_39,X_27)
| ~ product(X_27,X_27,W_39) ),
inference(resolution,[status(thm)],[c_50,c_63]) ).
tff(c_5076,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_5061,c_66]) ).
tff(c_5093,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_5076]) ).
tff(c_5094,plain,
( product(e_2,e_1,e_3)
| product(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_4286]) ).
tff(c_5195,plain,
product(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_5094]) ).
tff(c_5215,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_5195,c_57]) ).
tff(c_5233,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_5215]) ).
tff(c_5234,plain,
product(e_2,e_1,e_3),
inference(splitRight,[status(thm)],[c_5094]) ).
tff(c_5389,plain,
! [X_185] :
( product(e_3,e_1,X_185)
| ~ product(e_1,X_185,e_2) ),
inference(resolution,[status(thm)],[c_5234,c_52]) ).
tff(c_5420,plain,
( equalish(e_3,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[c_5389,c_77]) ).
tff(c_5452,plain,
~ product(e_1,e_1,e_2),
inference(negUnitSimplification,[status(thm)],[c_30,c_5420]) ).
tff(c_5235,plain,
~ product(e_3,e_1,e_3),
inference(splitRight,[status(thm)],[c_5094]) ).
tff(c_5432,plain,
~ product(e_1,e_3,e_2),
inference(resolution,[status(thm)],[c_5389,c_5235]) ).
tff(c_4276,plain,
! [X_29] :
( product(e_3,e_2,X_29)
| ~ product(e_2,X_29,e_4) ),
inference(resolution,[status(thm)],[c_4261,c_52]) ).
tff(c_8,plain,
! [Y_10,X_12,Z1_9,Z2_11] :
( ~ product(Y_10,X_12,Z1_9)
| ~ product(Z2_11,Y_10,X_12)
| product(Z1_9,Y_10,Z2_11) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_5579,plain,
! [Z2_189] :
( ~ product(Z2_189,e_2,e_1)
| product(e_3,e_2,Z2_189) ),
inference(resolution,[status(thm)],[c_5234,c_8]) ).
tff(c_5602,plain,
( product(e_3,e_2,e_3)
| ~ product(e_2,e_1,e_4) ),
inference(resolution,[status(thm)],[c_4276,c_5579]) ).
tff(c_5650,plain,
~ product(e_2,e_1,e_4),
inference(splitLeft,[status(thm)],[c_5602]) ).
tff(c_32,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_4638,plain,
( equalish(e_3,e_2)
| ~ product(e_2,e_2,e_4) ),
inference(resolution,[status(thm)],[c_4613,c_77]) ).
tff(c_4663,plain,
~ product(e_2,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_32,c_4638]) ).
tff(c_46,plain,
! [W_20,Z_22,X_19,Y_21] :
( equalish(W_20,Z_22)
| ~ product(X_19,Z_22,Y_21)
| ~ product(X_19,W_20,Y_21) ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_4669,plain,
! [W_20,X_168] :
( equalish(W_20,e_2)
| ~ product(e_3,W_20,X_168)
| ~ product(e_2,X_168,e_4) ),
inference(resolution,[status(thm)],[c_4613,c_46]) ).
tff(c_5402,plain,
! [X_185] :
( equalish(e_1,e_2)
| ~ product(e_2,X_185,e_4)
| ~ product(e_1,X_185,e_2) ),
inference(resolution,[status(thm)],[c_5389,c_4669]) ).
tff(c_5626,plain,
! [X_190] :
( ~ product(e_2,X_190,e_4)
| ~ product(e_1,X_190,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_18,c_5402]) ).
tff(c_5634,plain,
( ~ product(e_1,e_4,e_2)
| product(e_2,e_3,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_4,c_5626]) ).
tff(c_5644,plain,
( ~ product(e_1,e_4,e_2)
| product(e_2,e_3,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_16,c_5634]) ).
tff(c_5645,plain,
( ~ product(e_1,e_4,e_2)
| product(e_2,e_1,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_4663,c_4652,c_5644]) ).
tff(c_5749,plain,
~ product(e_1,e_4,e_2),
inference(negUnitSimplification,[status(thm)],[c_5650,c_5645]) ).
tff(c_5752,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_4,c_5749]) ).
tff(c_5755,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_12,c_5752]) ).
tff(c_5756,plain,
product(e_1,e_2,e_2),
inference(negUnitSimplification,[status(thm)],[c_5452,c_5432,c_5755]) ).
tff(c_5771,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_5756,c_77]) ).
tff(c_5791,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_5771]) ).
tff(c_5792,plain,
product(e_3,e_2,e_3),
inference(splitRight,[status(thm)],[c_5602]) ).
tff(c_4277,plain,
! [X_6] :
( ~ product(e_3,e_2,X_6)
| product(e_2,X_6,e_4) ),
inference(resolution,[status(thm)],[c_4261,c_6]) ).
tff(c_5934,plain,
product(e_2,e_3,e_4),
inference(resolution,[status(thm)],[c_5792,c_4277]) ).
tff(c_5967,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4652,c_5934]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14 % 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 : n019.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 22:25:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.32/2.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.32/2.66
% 7.32/2.66 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.32/2.70
% 7.32/2.70 Inference rules
% 7.32/2.70 ----------------------
% 7.32/2.70 #Ref : 0
% 7.32/2.70 #Sup : 1068
% 7.32/2.70 #Fact : 0
% 7.32/2.70 #Define : 0
% 7.32/2.70 #Split : 8
% 7.32/2.70 #Chain : 0
% 7.32/2.70 #Close : 0
% 7.32/2.70
% 7.32/2.70 Ordering : KBO
% 7.32/2.70
% 7.32/2.70 Simplification rules
% 7.32/2.70 ----------------------
% 7.32/2.70 #Subsume : 167
% 7.32/2.70 #Demod : 1119
% 7.32/2.70 #Tautology : 374
% 7.32/2.70 #SimpNegUnit : 451
% 7.32/2.70 #BackRed : 0
% 7.32/2.70
% 7.32/2.70 #Partial instantiations: 0
% 7.32/2.70 #Strategies tried : 1
% 7.32/2.70
% 7.32/2.70 Timing (in seconds)
% 7.32/2.70 ----------------------
% 7.32/2.71 Preprocessing : 0.46
% 7.32/2.71 Parsing : 0.25
% 7.32/2.71 CNF conversion : 0.03
% 7.32/2.71 Main loop : 1.17
% 7.32/2.71 Inferencing : 0.36
% 7.32/2.71 Reduction : 0.32
% 7.32/2.71 Demodulation : 0.20
% 7.32/2.71 BG Simplification : 0.05
% 7.32/2.71 Subsumption : 0.38
% 7.32/2.71 Abstraction : 0.03
% 7.32/2.71 MUC search : 0.00
% 7.32/2.71 Cooper : 0.00
% 7.32/2.71 Total : 1.70
% 7.32/2.71 Index Insertion : 0.00
% 7.32/2.71 Index Deletion : 0.00
% 7.32/2.71 Index Matching : 0.00
% 7.32/2.71 BG Taut test : 0.00
%------------------------------------------------------------------------------