TSTP Solution File: GRP126-4.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP126-4.004 : 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/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 : n021.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 10:40:00 EDT 2023
% Result : Unsatisfiable 8.44s 2.99s
% Output : CNFRefutation 8.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 31
% Syntax : Number of formulae : 164 ( 78 unt; 7 typ; 0 def)
% Number of atoms : 321 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 288 ( 124 ~; 164 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 105 (; 105 !; 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_101,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_87,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_89,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_99,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_81,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_83,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_74,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_77,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_43,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_141,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_93,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_76,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_115,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_95,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_131,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [Y,X,Z2,Z1] :
( product(Y,X,Z2)
| ~ product(Z1,Z2,Y)
| ~ product(X,Y,Z1) ),
file(unknown,unknown) ).
tff(f_97,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_139,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_57,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_149,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,Y) ),
file(unknown,unknown) ).
tff(f_91,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_65,axiom,
! [X,Y,Z1,Z2] :
( product(X,Y,Z1)
| ~ product(Z1,Z2,Y)
| ~ product(Y,X,Z2) ),
file(unknown,unknown) ).
tff(f_75,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(c_40,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_26,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_28,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_38,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_20,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_22,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_10,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_16,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_106,plain,
! [X_68,Y_69] :
( product(e_4,X_68,Y_69)
| product(e_3,X_68,Y_69)
| product(e_2,X_68,Y_69)
| product(e_1,X_68,Y_69)
| ~ group_element(Y_69)
| ~ group_element(X_68) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_50,plain,
! [X_27] : product(X_27,X_27,X_27),
inference(cnfTransformation,[status(thm)],[f_141]) ).
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_123]) ).
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_128,plain,
! [Y_69] :
( equalish(Y_69,e_4)
| product(e_3,e_4,Y_69)
| product(e_2,e_4,Y_69)
| product(e_1,e_4,Y_69)
| ~ group_element(Y_69)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_106,c_66]) ).
tff(c_148,plain,
! [Y_69] :
( equalish(Y_69,e_4)
| product(e_3,e_4,Y_69)
| product(e_2,e_4,Y_69)
| product(e_1,e_4,Y_69)
| ~ group_element(Y_69) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_128]) ).
tff(c_32,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_14,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_76]) ).
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_115]) ).
tff(c_34,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_861,plain,
! [Y_86] :
( equalish(Y_86,e_4)
| product(e_3,e_4,Y_86)
| product(e_2,e_4,Y_86)
| product(e_1,e_4,Y_86)
| ~ group_element(Y_86) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_128]) ).
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_131]) ).
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_885,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_2,e_4,e_3)
| product(e_1,e_4,e_3)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_861,c_57]) ).
tff(c_906,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_2,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_885]) ).
tff(c_907,plain,
( product(e_2,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_40,c_906]) ).
tff(c_909,plain,
product(e_1,e_4,e_3),
inference(splitLeft,[status(thm)],[c_907]) ).
tff(c_8,plain,
! [X_10,Y_9,Z1_12,Z2_11] :
( ~ product(X_10,Y_9,Z1_12)
| ~ product(Z1_12,Z2_11,Y_9)
| product(Y_9,X_10,Z2_11) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1128,plain,
! [Z2_95] :
( ~ product(e_3,Z2_95,e_4)
| product(e_4,e_1,Z2_95) ),
inference(resolution,[status(thm)],[c_909,c_8]) ).
tff(c_1156,plain,
( equalish(e_1,e_4)
| ~ product(e_3,e_4,e_4) ),
inference(resolution,[status(thm)],[c_1128,c_57]) ).
tff(c_1176,plain,
~ product(e_3,e_4,e_4),
inference(negUnitSimplification,[status(thm)],[c_22,c_1156]) ).
tff(c_1189,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_42,c_1176]) ).
tff(c_1201,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_16,c_1189]) ).
tff(c_2983,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_1201]) ).
tff(c_3288,plain,
! [Z2_159] :
( ~ product(e_1,Z2_159,e_4)
| product(e_4,e_3,Z2_159) ),
inference(resolution,[status(thm)],[c_2983,c_8]) ).
tff(c_36,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_97]) ).
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_139]) ).
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_1148,plain,
( equalish(e_4,e_1)
| ~ product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_1128,c_77]) ).
tff(c_1171,plain,
~ product(e_3,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_36,c_1148]) ).
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_57]) ).
tff(c_1192,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_1176]) ).
tff(c_1204,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_14,c_16,c_1192]) ).
tff(c_1205,plain,
( product(e_3,e_3,e_4)
| product(e_3,e_2,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_1171,c_1204]) ).
tff(c_1369,plain,
product(e_3,e_2,e_4),
inference(splitLeft,[status(thm)],[c_1205]) ).
tff(c_52,plain,
! [Z1_30,Z2_31,Y_29,X_28] :
( product(Z1_30,Z2_31,Y_29)
| ~ product(Y_29,X_28,Z2_31)
| ~ product(X_28,Y_29,Z1_30) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_1006,plain,
! [Z1_30] :
( product(Z1_30,e_3,e_1)
| ~ product(e_4,e_1,Z1_30) ),
inference(resolution,[status(thm)],[c_909,c_52]) ).
tff(c_1159,plain,
! [Z2_95] :
( product(Z2_95,e_3,e_1)
| ~ product(e_3,Z2_95,e_4) ),
inference(resolution,[status(thm)],[c_1128,c_1006]) ).
tff(c_1388,plain,
product(e_2,e_3,e_1),
inference(resolution,[status(thm)],[c_1369,c_1159]) ).
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_139]) ).
tff(c_1426,plain,
! [W_23] :
( equalish(W_23,e_2)
| ~ product(W_23,e_3,e_1) ),
inference(resolution,[status(thm)],[c_1388,c_48]) ).
tff(c_3317,plain,
( equalish(e_4,e_2)
| ~ product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[c_3288,c_1426]) ).
tff(c_3375,plain,
~ product(e_1,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_38,c_3317]) ).
tff(c_30,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_6,plain,
! [Y_6,X_5,Z2_8,Z1_7] :
( ~ product(Y_6,X_5,Z2_8)
| ~ product(Z1_7,Z2_8,Y_6)
| product(X_5,Y_6,Z1_7) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_1007,plain,
! [Z1_7] :
( ~ product(Z1_7,e_3,e_1)
| product(e_4,e_1,Z1_7) ),
inference(resolution,[status(thm)],[c_909,c_6]) ).
tff(c_1418,plain,
product(e_4,e_1,e_2),
inference(resolution,[status(thm)],[c_1388,c_1007]) ).
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_131]) ).
tff(c_1462,plain,
! [W_20] :
( equalish(W_20,e_1)
| ~ product(e_4,W_20,e_2) ),
inference(resolution,[status(thm)],[c_1418,c_46]) ).
tff(c_3313,plain,
( equalish(e_3,e_1)
| ~ product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[c_3288,c_1462]) ).
tff(c_3372,plain,
~ product(e_1,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_30,c_3313]) ).
tff(c_3344,plain,
( equalish(e_4,e_3)
| ~ product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[c_3288,c_77]) ).
tff(c_3394,plain,
~ product(e_1,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_40,c_3344]) ).
tff(c_3016,plain,
! [Z1_30] :
( product(Z1_30,e_1,e_3)
| ~ product(e_4,e_3,Z1_30) ),
inference(resolution,[status(thm)],[c_2983,c_52]) ).
tff(c_3611,plain,
! [Z2_164] :
( product(Z2_164,e_1,e_3)
| ~ product(e_1,Z2_164,e_4) ),
inference(resolution,[status(thm)],[c_3288,c_3016]) ).
tff(c_3618,plain,
( product(e_4,e_1,e_3)
| 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_3611]) ).
tff(c_3627,plain,
( product(e_4,e_1,e_3)
| 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_3618]) ).
tff(c_3628,plain,
product(e_4,e_1,e_3),
inference(negUnitSimplification,[status(thm)],[c_3375,c_3372,c_3394,c_3627]) ).
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_123]) ).
tff(c_1461,plain,
! [W_17] :
( equalish(W_17,e_2)
| ~ product(e_4,e_1,W_17) ),
inference(resolution,[status(thm)],[c_1418,c_44]) ).
tff(c_3649,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_3628,c_1461]) ).
tff(c_3690,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_3649]) ).
tff(c_3692,plain,
~ product(e_3,e_4,e_1),
inference(splitRight,[status(thm)],[c_1201]) ).
tff(c_3695,plain,
( equalish(e_1,e_4)
| product(e_2,e_4,e_1)
| product(e_1,e_4,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_148,c_3692]) ).
tff(c_3701,plain,
( equalish(e_1,e_4)
| product(e_2,e_4,e_1)
| product(e_1,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_3695]) ).
tff(c_3702,plain,
( product(e_2,e_4,e_1)
| product(e_1,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_22,c_3701]) ).
tff(c_4337,plain,
product(e_1,e_4,e_1),
inference(splitLeft,[status(thm)],[c_3702]) ).
tff(c_1009,plain,
! [W_17] :
( equalish(W_17,e_3)
| ~ product(e_1,e_4,W_17) ),
inference(resolution,[status(thm)],[c_909,c_44]) ).
tff(c_4350,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_4337,c_1009]) ).
tff(c_4383,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_4350]) ).
tff(c_4384,plain,
product(e_2,e_4,e_1),
inference(splitRight,[status(thm)],[c_3702]) ).
tff(c_1428,plain,
! [W_20] :
( equalish(W_20,e_3)
| ~ product(e_2,W_20,e_1) ),
inference(resolution,[status(thm)],[c_1388,c_46]) ).
tff(c_4401,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_4384,c_1428]) ).
tff(c_4429,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_4401]) ).
tff(c_4430,plain,
product(e_3,e_3,e_4),
inference(splitRight,[status(thm)],[c_1205]) ).
tff(c_4450,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_4430,c_66]) ).
tff(c_4471,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_4450]) ).
tff(c_4472,plain,
product(e_2,e_4,e_3),
inference(splitRight,[status(thm)],[c_907]) ).
tff(c_4706,plain,
! [Z2_183] :
( ~ product(e_3,Z2_183,e_4)
| product(e_4,e_2,Z2_183) ),
inference(resolution,[status(thm)],[c_4472,c_8]) ).
tff(c_4724,plain,
( equalish(e_4,e_2)
| ~ product(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[c_4706,c_77]) ).
tff(c_4743,plain,
~ product(e_3,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_38,c_4724]) ).
tff(c_4732,plain,
( equalish(e_2,e_4)
| ~ product(e_3,e_4,e_4) ),
inference(resolution,[status(thm)],[c_4706,c_57]) ).
tff(c_4748,plain,
~ product(e_3,e_4,e_4),
inference(negUnitSimplification,[status(thm)],[c_28,c_4732]) ).
tff(c_4764,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_4748]) ).
tff(c_4776,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_14,c_16,c_4764]) ).
tff(c_4777,plain,
( product(e_3,e_3,e_4)
| product(e_3,e_1,e_4) ),
inference(negUnitSimplification,[status(thm)],[c_4743,c_4776]) ).
tff(c_4984,plain,
product(e_3,e_1,e_4),
inference(splitLeft,[status(thm)],[c_4777]) ).
tff(c_4487,plain,
! [Z1_30] :
( product(Z1_30,e_3,e_2)
| ~ product(e_4,e_2,Z1_30) ),
inference(resolution,[status(thm)],[c_4472,c_52]) ).
tff(c_4735,plain,
! [Z2_183] :
( product(Z2_183,e_3,e_2)
| ~ product(e_3,Z2_183,e_4) ),
inference(resolution,[status(thm)],[c_4706,c_4487]) ).
tff(c_4999,plain,
product(e_1,e_3,e_2),
inference(resolution,[status(thm)],[c_4984,c_4735]) ).
tff(c_4488,plain,
! [Z1_7] :
( ~ product(Z1_7,e_3,e_2)
| product(e_4,e_2,Z1_7) ),
inference(resolution,[status(thm)],[c_4472,c_6]) ).
tff(c_5020,plain,
product(e_4,e_2,e_1),
inference(resolution,[status(thm)],[c_4999,c_4488]) ).
tff(c_5780,plain,
! [Z2_212] :
( ~ product(e_1,Z2_212,e_2)
| product(e_2,e_4,Z2_212) ),
inference(resolution,[status(thm)],[c_5020,c_8]) ).
tff(c_5816,plain,
( equalish(e_2,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(resolution,[status(thm)],[c_5780,c_77]) ).
tff(c_5854,plain,
~ product(e_1,e_4,e_2),
inference(negUnitSimplification,[status(thm)],[c_28,c_5816]) ).
tff(c_12,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_4473,plain,
~ product(e_1,e_4,e_3),
inference(splitRight,[status(thm)],[c_907]) ).
tff(c_4590,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_3)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_4,c_4473]) ).
tff(c_4593,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_14,c_4590]) ).
tff(c_7005,plain,
product(e_1,e_1,e_3),
inference(splitLeft,[status(thm)],[c_4593]) ).
tff(c_7026,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_7005,c_66]) ).
tff(c_7053,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_7026]) ).
tff(c_7054,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_4593]) ).
tff(c_7056,plain,
product(e_1,e_3,e_3),
inference(splitLeft,[status(thm)],[c_7054]) ).
tff(c_5025,plain,
! [W_17] :
( equalish(W_17,e_2)
| ~ product(e_1,e_3,W_17) ),
inference(resolution,[status(thm)],[c_4999,c_44]) ).
tff(c_7065,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_7056,c_5025]) ).
tff(c_7097,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_7065]) ).
tff(c_7098,plain,
product(e_1,e_2,e_3),
inference(splitRight,[status(thm)],[c_7054]) ).
tff(c_7338,plain,
! [Z2_255] :
( ~ product(e_3,Z2_255,e_2)
| product(e_2,e_1,Z2_255) ),
inference(resolution,[status(thm)],[c_7098,c_8]) ).
tff(c_7346,plain,
( product(e_2,e_1,e_4)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_1,e_4,e_2)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_148,c_7338]) ).
tff(c_7370,plain,
( product(e_2,e_1,e_4)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_7346]) ).
tff(c_7371,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_4,e_2) ),
inference(negUnitSimplification,[status(thm)],[c_5854,c_28,c_7370]) ).
tff(c_7471,plain,
product(e_2,e_4,e_2),
inference(splitLeft,[status(thm)],[c_7371]) ).
tff(c_4490,plain,
! [W_17] :
( equalish(W_17,e_3)
| ~ product(e_2,e_4,W_17) ),
inference(resolution,[status(thm)],[c_4472,c_44]) ).
tff(c_7491,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_7471,c_4490]) ).
tff(c_7534,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_7491]) ).
tff(c_7536,plain,
~ product(e_2,e_4,e_2),
inference(splitRight,[status(thm)],[c_7371]) ).
tff(c_7535,plain,
product(e_2,e_1,e_4),
inference(splitRight,[status(thm)],[c_7371]) ).
tff(c_4740,plain,
! [Z1_7,Z2_183] :
( ~ product(Z1_7,Z2_183,e_4)
| product(e_2,e_4,Z1_7)
| ~ product(e_3,Z2_183,e_4) ),
inference(resolution,[status(thm)],[c_4706,c_6]) ).
tff(c_7587,plain,
( product(e_2,e_4,e_2)
| ~ product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_7535,c_4740]) ).
tff(c_7624,plain,
product(e_2,e_4,e_2),
inference(demodulation,[status(thm),theory(equality)],[c_4984,c_7587]) ).
tff(c_7626,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7536,c_7624]) ).
tff(c_7627,plain,
product(e_3,e_3,e_4),
inference(splitRight,[status(thm)],[c_4777]) ).
tff(c_7643,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_7627,c_66]) ).
tff(c_7657,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_7643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP126-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % 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
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 22:25:06 EDT 2023
% 0.14/0.34 % CPUTime :
% 8.44/2.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.84/3.01
% 8.84/3.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.84/3.07
% 8.84/3.07 Inference rules
% 8.84/3.07 ----------------------
% 8.84/3.07 #Ref : 0
% 8.84/3.07 #Sup : 1392
% 8.84/3.07 #Fact : 0
% 8.84/3.07 #Define : 0
% 8.84/3.07 #Split : 9
% 8.84/3.07 #Chain : 0
% 8.84/3.07 #Close : 0
% 8.84/3.07
% 8.84/3.07 Ordering : KBO
% 8.84/3.07
% 8.84/3.07 Simplification rules
% 8.84/3.07 ----------------------
% 8.84/3.07 #Subsume : 209
% 8.84/3.07 #Demod : 1587
% 8.84/3.07 #Tautology : 539
% 8.84/3.07 #SimpNegUnit : 515
% 8.84/3.07 #BackRed : 0
% 8.84/3.07
% 8.84/3.07 #Partial instantiations: 0
% 8.84/3.07 #Strategies tried : 1
% 8.84/3.07
% 8.84/3.07 Timing (in seconds)
% 8.84/3.07 ----------------------
% 8.84/3.07 Preprocessing : 0.47
% 8.84/3.07 Parsing : 0.26
% 8.84/3.07 CNF conversion : 0.03
% 8.84/3.07 Main loop : 1.52
% 8.84/3.07 Inferencing : 0.48
% 8.84/3.07 Reduction : 0.45
% 8.84/3.07 Demodulation : 0.29
% 8.84/3.07 BG Simplification : 0.05
% 8.84/3.07 Subsumption : 0.46
% 8.84/3.07 Abstraction : 0.05
% 8.84/3.07 MUC search : 0.00
% 8.84/3.07 Cooper : 0.00
% 8.84/3.07 Total : 2.08
% 8.84/3.07 Index Insertion : 0.00
% 8.84/3.07 Index Deletion : 0.00
% 8.84/3.07 Index Matching : 0.00
% 8.84/3.07 BG Taut test : 0.00
%------------------------------------------------------------------------------