TSTP Solution File: GRP124-6.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP124-6.004 : 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 : n010.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 8.93s 3.17s
% Output : CNFRefutation 9.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 145 ( 72 unt; 8 typ; 0 def)
% Number of atoms : 284 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 246 ( 99 ~; 147 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 95 (; 95 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product2 > product1 > 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(product1,type,
product1: ( $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(product2,type,
product2: ( $i * $i * $i ) > $o ).
tff(f_49,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_43,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_57,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_45,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_31,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_33,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product1(X,Y,e_1)
| product1(X,Y,e_2)
| product1(X,Y,e_3)
| product1(X,Y,e_4) ),
file(unknown,unknown) ).
tff(f_97,axiom,
! [X] : product1(X,X,X),
file(unknown,unknown) ).
tff(f_87,axiom,
! [X,W,Y,Z] :
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_55,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_32,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_95,axiom,
! [W,Y,X,Z] :
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_53,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_37,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_39,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_30,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_51,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_145,axiom,
! [X,Y,Z1,Z2] :
( ~ product1(X,Y,Z1)
| ~ product1(Z1,X,Z2)
| product2(Z2,Y,X) ),
file(unknown,unknown) ).
tff(f_137,axiom,
! [X] : product2(X,X,X),
file(unknown,unknown) ).
tff(f_119,axiom,
! [X,Y,W,Z] :
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_47,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_127,axiom,
! [X,W,Y,Z] :
( ~ product2(X,W,Y)
| ~ product2(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(c_24,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_18,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_32,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_20,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_4,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_8,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_169,plain,
! [X_86,Y_87] :
( product1(X_86,Y_87,e_4)
| product1(X_86,Y_87,e_3)
| product1(X_86,Y_87,e_2)
| product1(X_86,Y_87,e_1)
| ~ group_element(Y_87)
| ~ group_element(X_86) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_42,plain,
! [X_15] : product1(X_15,X_15,X_15),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_107,plain,
! [W_68,Z_69,X_70,Y_71] :
( equalish(W_68,Z_69)
| ~ product1(X_70,Z_69,Y_71)
| ~ product1(X_70,W_68,Y_71) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_110,plain,
! [W_68,X_15] :
( equalish(W_68,X_15)
| ~ product1(X_15,W_68,X_15) ),
inference(resolution,[status(thm)],[c_42,c_107]) ).
tff(c_175,plain,
! [Y_87] :
( equalish(Y_87,e_4)
| product1(e_4,Y_87,e_3)
| product1(e_4,Y_87,e_2)
| product1(e_4,Y_87,e_1)
| ~ group_element(Y_87)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_169,c_110]) ).
tff(c_193,plain,
! [Y_87] :
( equalish(Y_87,e_4)
| product1(e_4,Y_87,e_3)
| product1(e_4,Y_87,e_2)
| product1(e_4,Y_87,e_1)
| ~ group_element(Y_87) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_175]) ).
tff(c_30,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_6,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_40,plain,
! [W_11,Z_14,Y_12,X_13] :
( equalish(W_11,Z_14)
| ~ product1(Z_14,Y_12,X_13)
| ~ product1(W_11,Y_12,X_13) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_7217,plain,
! [W_306,X_307,Y_308] :
( equalish(W_306,X_307)
| ~ product1(W_306,Y_308,e_4)
| product1(X_307,Y_308,e_3)
| product1(X_307,Y_308,e_2)
| product1(X_307,Y_308,e_1)
| ~ group_element(Y_308)
| ~ group_element(X_307) ),
inference(resolution,[status(thm)],[c_169,c_40]) ).
tff(c_7222,plain,
! [X_307] :
( equalish(e_4,X_307)
| product1(X_307,e_4,e_3)
| product1(X_307,e_4,e_2)
| product1(X_307,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_307) ),
inference(resolution,[status(thm)],[c_42,c_7217]) ).
tff(c_7504,plain,
! [X_324] :
( equalish(e_4,X_324)
| product1(X_324,e_4,e_3)
| product1(X_324,e_4,e_2)
| product1(X_324,e_4,e_1)
| ~ group_element(X_324) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_7222]) ).
tff(c_7524,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_7504,c_110]) ).
tff(c_7554,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_7524]) ).
tff(c_7555,plain,
( product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_7554]) ).
tff(c_7563,plain,
product1(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_7555]) ).
tff(c_34,plain,
! [X_1,Y_2] :
( product1(X_1,Y_2,e_4)
| product1(X_1,Y_2,e_3)
| product1(X_1,Y_2,e_2)
| product1(X_1,Y_2,e_1)
| ~ group_element(Y_2)
| ~ group_element(X_1) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_28,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_12,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_14,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_2,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_26,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_97,plain,
! [W_62,Z_63,Y_64,X_65] :
( equalish(W_62,Z_63)
| ~ product1(Z_63,Y_64,X_65)
| ~ product1(W_62,Y_64,X_65) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_100,plain,
! [W_62,X_15] :
( equalish(W_62,X_15)
| ~ product1(W_62,X_15,X_15) ),
inference(resolution,[status(thm)],[c_42,c_97]) ).
tff(c_181,plain,
! [X_86] :
( equalish(X_86,e_4)
| product1(X_86,e_4,e_3)
| product1(X_86,e_4,e_2)
| product1(X_86,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_86) ),
inference(resolution,[status(thm)],[c_169,c_100]) ).
tff(c_6471,plain,
! [X_276] :
( equalish(X_276,e_4)
| product1(X_276,e_4,e_3)
| product1(X_276,e_4,e_2)
| product1(X_276,e_4,e_1)
| ~ group_element(X_276) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_181]) ).
tff(c_6492,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_6471,c_110]) ).
tff(c_6525,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6492]) ).
tff(c_6526,plain,
( product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_32,c_6525]) ).
tff(c_6534,plain,
product1(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_6526]) ).
tff(c_54,plain,
! [Z2_34,Y_32,X_31,Z1_33] :
( product2(Z2_34,Y_32,X_31)
| ~ product1(Z1_33,X_31,Z2_34)
| ~ product1(X_31,Y_32,Z1_33) ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_6625,plain,
! [Y_280] :
( product2(e_1,Y_280,e_4)
| ~ product1(e_4,Y_280,e_3) ),
inference(resolution,[status(thm)],[c_6534,c_54]) ).
tff(c_52,plain,
! [X_30] : product2(X_30,X_30,X_30),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_57,plain,
! [W_37,Z_38,X_39,Y_40] :
( equalish(W_37,Z_38)
| ~ product2(X_39,Y_40,Z_38)
| ~ product2(X_39,Y_40,W_37) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_60,plain,
! [W_37,X_30] :
( equalish(W_37,X_30)
| ~ product2(X_30,X_30,W_37) ),
inference(resolution,[status(thm)],[c_52,c_57]) ).
tff(c_6648,plain,
( equalish(e_4,e_1)
| ~ product1(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[c_6625,c_60]) ).
tff(c_6675,plain,
~ product1(e_4,e_1,e_3),
inference(negUnitSimplification,[status(thm)],[c_28,c_6648]) ).
tff(c_6713,plain,
( equalish(e_1,e_4)
| product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_193,c_6675]) ).
tff(c_6720,plain,
( equalish(e_1,e_4)
| product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6713]) ).
tff(c_6721,plain,
( product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_14,c_6720]) ).
tff(c_6850,plain,
product1(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_6721]) ).
tff(c_221,plain,
! [Y_93] :
( equalish(Y_93,e_4)
| product1(e_4,Y_93,e_3)
| product1(e_4,Y_93,e_2)
| product1(e_4,Y_93,e_1)
| ~ group_element(Y_93) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_175]) ).
tff(c_229,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_221,c_100]) ).
tff(c_242,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_229]) ).
tff(c_243,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_32,c_242]) ).
tff(c_291,plain,
product1(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_243]) ).
tff(c_38,plain,
! [W_8,Z_10,X_7,Y_9] :
( equalish(W_8,Z_10)
| ~ product1(X_7,Z_10,Y_9)
| ~ product1(X_7,W_8,Y_9) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_301,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product1(e_4,W_8,e_1) ),
inference(resolution,[status(thm)],[c_291,c_38]) ).
tff(c_6857,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_6850,c_301]) ).
tff(c_6880,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_6857]) ).
tff(c_6881,plain,
product1(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_6721]) ).
tff(c_22,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_348,plain,
! [Y_102] :
( product2(e_1,Y_102,e_3)
| ~ product1(e_3,Y_102,e_4) ),
inference(resolution,[status(thm)],[c_291,c_54]) ).
tff(c_362,plain,
( equalish(e_3,e_1)
| ~ product1(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_348,c_60]) ).
tff(c_379,plain,
~ product1(e_3,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_22,c_362]) ).
tff(c_390,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_34,c_379]) ).
tff(c_393,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2,c_390]) ).
tff(c_458,plain,
product1(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_393]) ).
tff(c_475,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_458,c_100]) ).
tff(c_485,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_475]) ).
tff(c_486,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_393]) ).
tff(c_488,plain,
product1(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_486]) ).
tff(c_117,plain,
! [Z2_74,Y_75,X_76,Z1_77] :
( product2(Z2_74,Y_75,X_76)
| ~ product1(Z1_77,X_76,Z2_74)
| ~ product1(X_76,Y_75,Z1_77) ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_121,plain,
! [X_78,Y_79] :
( product2(X_78,Y_79,X_78)
| ~ product1(X_78,Y_79,X_78) ),
inference(resolution,[status(thm)],[c_42,c_117]) ).
tff(c_48,plain,
! [W_23,Z_25,X_22,Y_24] :
( equalish(W_23,Z_25)
| ~ product2(X_22,Z_25,Y_24)
| ~ product2(X_22,W_23,Y_24) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_201,plain,
! [W_88,Y_89,X_90] :
( equalish(W_88,Y_89)
| ~ product2(X_90,W_88,X_90)
| ~ product1(X_90,Y_89,X_90) ),
inference(resolution,[status(thm)],[c_121,c_48]) ).
tff(c_207,plain,
! [X_30,Y_89] :
( equalish(X_30,Y_89)
| ~ product1(X_30,Y_89,X_30) ),
inference(resolution,[status(thm)],[c_52,c_201]) ).
tff(c_532,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_488,c_207]) ).
tff(c_547,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_532]) ).
tff(c_548,plain,
product1(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_486]) ).
tff(c_560,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product1(W_11,e_1,e_2) ),
inference(resolution,[status(thm)],[c_548,c_40]) ).
tff(c_6889,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_6881,c_560]) ).
tff(c_6909,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_6889]) ).
tff(c_6910,plain,
product1(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_6526]) ).
tff(c_559,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product1(e_3,W_8,e_2) ),
inference(resolution,[status(thm)],[c_548,c_38]) ).
tff(c_6918,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_6910,c_559]) ).
tff(c_6938,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_6918]) ).
tff(c_6939,plain,
product1(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_243]) ).
tff(c_7007,plain,
! [Y_290] :
( product2(e_2,Y_290,e_3)
| ~ product1(e_3,Y_290,e_4) ),
inference(resolution,[status(thm)],[c_6939,c_54]) ).
tff(c_7021,plain,
( equalish(e_3,e_2)
| ~ product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[c_7007,c_60]) ).
tff(c_7038,plain,
~ product1(e_3,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_24,c_7021]) ).
tff(c_7049,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_34,c_7038]) ).
tff(c_7052,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_7049]) ).
tff(c_7172,plain,
product1(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_7052]) ).
tff(c_7188,plain,
! [W_8] :
( equalish(W_8,e_2)
| ~ product1(e_3,W_8,e_1) ),
inference(resolution,[status(thm)],[c_7172,c_38]) ).
tff(c_7566,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_7563,c_7188]) ).
tff(c_7580,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_7566]) ).
tff(c_7581,plain,
product1(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_7555]) ).
tff(c_7667,plain,
! [Y_331] :
( product2(e_2,Y_331,e_4)
| ~ product1(e_4,Y_331,e_3) ),
inference(resolution,[status(thm)],[c_7581,c_54]) ).
tff(c_7688,plain,
( equalish(e_4,e_2)
| ~ product1(e_4,e_2,e_3) ),
inference(resolution,[status(thm)],[c_7667,c_60]) ).
tff(c_7712,plain,
~ product1(e_4,e_2,e_3),
inference(negUnitSimplification,[status(thm)],[c_30,c_7688]) ).
tff(c_7735,plain,
( equalish(e_2,e_4)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_193,c_7712]) ).
tff(c_7738,plain,
( equalish(e_2,e_4)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_7735]) ).
tff(c_7739,plain,
( product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_20,c_7738]) ).
tff(c_7791,plain,
product1(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_7739]) ).
tff(c_7189,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product1(W_11,e_2,e_1) ),
inference(resolution,[status(thm)],[c_7172,c_40]) ).
tff(c_7815,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_7791,c_7189]) ).
tff(c_7829,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_7815]) ).
tff(c_7830,plain,
product1(e_4,e_2,e_2),
inference(splitRight,[status(thm)],[c_7739]) ).
tff(c_6950,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product1(e_4,W_8,e_2) ),
inference(resolution,[status(thm)],[c_6939,c_38]) ).
tff(c_7834,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_7830,c_6950]) ).
tff(c_7851,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_7834]) ).
tff(c_7852,plain,
( product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_7052]) ).
tff(c_7918,plain,
product1(e_3,e_2,e_3),
inference(splitLeft,[status(thm)],[c_7852]) ).
tff(c_7923,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_7918,c_207]) ).
tff(c_7942,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_7923]) ).
tff(c_7943,plain,
product1(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_7852]) ).
tff(c_7953,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_7943,c_100]) ).
tff(c_7967,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_7953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP124-6.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14 % 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 : n010.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 21:51:58 EDT 2023
% 0.14/0.35 % CPUTime :
% 8.93/3.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.38/3.19
% 9.38/3.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.53/3.24
% 9.53/3.24 Inference rules
% 9.53/3.24 ----------------------
% 9.53/3.24 #Ref : 0
% 9.53/3.24 #Sup : 1487
% 9.53/3.24 #Fact : 0
% 9.53/3.24 #Define : 0
% 9.53/3.24 #Split : 31
% 9.53/3.24 #Chain : 0
% 9.53/3.24 #Close : 0
% 9.53/3.24
% 9.53/3.24 Ordering : KBO
% 9.53/3.24
% 9.53/3.24 Simplification rules
% 9.53/3.24 ----------------------
% 9.53/3.24 #Subsume : 206
% 9.53/3.24 #Demod : 1237
% 9.53/3.24 #Tautology : 484
% 9.53/3.24 #SimpNegUnit : 660
% 9.53/3.24 #BackRed : 0
% 9.53/3.24
% 9.53/3.24 #Partial instantiations: 0
% 9.53/3.24 #Strategies tried : 1
% 9.53/3.24
% 9.53/3.24 Timing (in seconds)
% 9.53/3.24 ----------------------
% 9.53/3.24 Preprocessing : 0.47
% 9.53/3.24 Parsing : 0.26
% 9.53/3.24 CNF conversion : 0.02
% 9.53/3.24 Main loop : 1.60
% 9.53/3.24 Inferencing : 0.54
% 9.53/3.24 Reduction : 0.46
% 9.53/3.24 Demodulation : 0.26
% 9.53/3.24 BG Simplification : 0.04
% 9.53/3.24 Subsumption : 0.48
% 9.53/3.24 Abstraction : 0.05
% 9.53/3.24 MUC search : 0.00
% 9.53/3.24 Cooper : 0.00
% 9.53/3.24 Total : 2.14
% 9.53/3.24 Index Insertion : 0.00
% 9.53/3.24 Index Deletion : 0.00
% 9.53/3.24 Index Matching : 0.00
% 9.53/3.24 BG Taut test : 0.00
%------------------------------------------------------------------------------