TSTP Solution File: GRP123-6.003 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP123-6.003 : 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/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 : n029.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 10:39:54 EDT 2023
% Result : Unsatisfiable 4.71s 2.06s
% Output : CNFRefutation 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 69 ( 27 unt; 7 typ; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 149 ( 66 ~; 83 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 77 (; 77 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product2 > product1 > equalish > group_element > #nlpp > 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_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_34,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_36,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_30,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_32,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product1(X,Y,e_1)
| product1(X,Y,e_2)
| product1(X,Y,e_3) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [X] : product1(X,X,X),
file(unknown,unknown) ).
tff(f_80,axiom,
! [W,Y,X,Z] :
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_42,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_38,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_40,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_44,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_31,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X,W,Y,Z] :
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_128,axiom,
! [X,Y,Z1,Z2] :
( ~ product1(X,Y,Z1)
| ~ product1(Z1,Y,Z2)
| product2(Z2,X,Y) ),
file(unknown,unknown) ).
tff(f_94,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product2(X,Y,e_1)
| product2(X,Y,e_2)
| product2(X,Y,e_3) ),
file(unknown,unknown) ).
tff(f_120,axiom,
! [X] : product2(X,X,X),
file(unknown,unknown) ).
tff(f_102,axiom,
! [X,Y,W,Z] :
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(c_8,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_10,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_2,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_6,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_190,plain,
! [X_88,Y_89] :
( product1(X_88,Y_89,e_3)
| product1(X_88,Y_89,e_2)
| product1(X_88,Y_89,e_1)
| ~ group_element(Y_89)
| ~ group_element(X_88) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_28,plain,
! [X_15] : product1(X_15,X_15,X_15),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_73,plain,
! [W_56,Z_57,Y_58,X_59] :
( equalish(W_56,Z_57)
| ~ product1(Z_57,Y_58,X_59)
| ~ product1(W_56,Y_58,X_59) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_76,plain,
! [W_56,X_15] :
( equalish(W_56,X_15)
| ~ product1(W_56,X_15,X_15) ),
inference(resolution,[status(thm)],[c_28,c_73]) ).
tff(c_202,plain,
! [X_88] :
( equalish(X_88,e_3)
| product1(X_88,e_3,e_2)
| product1(X_88,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_88) ),
inference(resolution,[status(thm)],[c_190,c_76]) ).
tff(c_216,plain,
! [X_88] :
( equalish(X_88,e_3)
| product1(X_88,e_3,e_2)
| product1(X_88,e_3,e_1)
| ~ group_element(X_88) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_202]) ).
tff(c_16,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_12,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_14,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_18,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_4,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_756,plain,
! [X_119] :
( equalish(X_119,e_3)
| product1(X_119,e_3,e_2)
| product1(X_119,e_3,e_1)
| ~ group_element(X_119) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_202]) ).
tff(c_53,plain,
! [W_44,Z_45,X_46,Y_47] :
( equalish(W_44,Z_45)
| ~ product1(X_46,Z_45,Y_47)
| ~ product1(X_46,W_44,Y_47) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_56,plain,
! [W_44,X_15] :
( equalish(W_44,X_15)
| ~ product1(X_15,W_44,X_15) ),
inference(resolution,[status(thm)],[c_28,c_53]) ).
tff(c_772,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product1(e_2,e_3,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_756,c_56]) ).
tff(c_788,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_772]) ).
tff(c_789,plain,
product1(e_2,e_3,e_1),
inference(negUnitSimplification,[status(thm)],[c_14,c_18,c_788]) ).
tff(c_40,plain,
! [Z2_34,X_31,Y_32,Z1_33] :
( product2(Z2_34,X_31,Y_32)
| ~ product1(Z1_33,Y_32,Z2_34)
| ~ product1(X_31,Y_32,Z1_33) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_875,plain,
! [X_123] :
( product2(e_1,X_123,e_3)
| ~ product1(X_123,e_3,e_2) ),
inference(resolution,[status(thm)],[c_789,c_40]) ).
tff(c_107,plain,
! [X_78,Y_79] :
( product2(X_78,Y_79,e_3)
| product2(X_78,Y_79,e_2)
| product2(X_78,Y_79,e_1)
| ~ group_element(Y_79)
| ~ group_element(X_78) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_38,plain,
! [X_30] : product2(X_30,X_30,X_30),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_77,plain,
! [W_60,Z_61,X_62,Y_63] :
( equalish(W_60,Z_61)
| ~ product2(X_62,Y_63,Z_61)
| ~ product2(X_62,Y_63,W_60) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_80,plain,
! [W_60,X_30] :
( equalish(W_60,X_30)
| ~ product2(X_30,X_30,W_60) ),
inference(resolution,[status(thm)],[c_38,c_77]) ).
tff(c_248,plain,
! [Y_95] :
( equalish(e_3,Y_95)
| product2(Y_95,Y_95,e_2)
| product2(Y_95,Y_95,e_1)
| ~ group_element(Y_95) ),
inference(resolution,[status(thm)],[c_107,c_80]) ).
tff(c_103,plain,
! [Z2_74,X_75,Y_76,Z1_77] :
( product2(Z2_74,X_75,Y_76)
| ~ product1(Z1_77,Y_76,Z2_74)
| ~ product1(X_75,Y_76,Z1_77) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_136,plain,
! [X_80,X_81] :
( product2(X_80,X_81,X_80)
| ~ product1(X_81,X_80,X_80) ),
inference(resolution,[status(thm)],[c_28,c_103]) ).
tff(c_32,plain,
! [W_20,Z_21,X_18,Y_19] :
( equalish(W_20,Z_21)
| ~ product2(X_18,Y_19,Z_21)
| ~ product2(X_18,Y_19,W_20) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_157,plain,
! [W_20,X_80,X_81] :
( equalish(W_20,X_80)
| ~ product2(X_80,X_81,W_20)
| ~ product1(X_81,X_80,X_80) ),
inference(resolution,[status(thm)],[c_136,c_32]) ).
tff(c_255,plain,
! [Y_95] :
( equalish(e_2,Y_95)
| ~ product1(Y_95,Y_95,Y_95)
| equalish(e_3,Y_95)
| product2(Y_95,Y_95,e_1)
| ~ group_element(Y_95) ),
inference(resolution,[status(thm)],[c_248,c_157]) ).
tff(c_293,plain,
! [Y_96] :
( equalish(e_2,Y_96)
| equalish(e_3,Y_96)
| product2(Y_96,Y_96,e_1)
| ~ group_element(Y_96) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_255]) ).
tff(c_327,plain,
! [W_20,Y_96] :
( equalish(W_20,e_1)
| ~ product2(Y_96,Y_96,W_20)
| equalish(e_2,Y_96)
| equalish(e_3,Y_96)
| ~ group_element(Y_96) ),
inference(resolution,[status(thm)],[c_293,c_32]) ).
tff(c_879,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_1)
| ~ group_element(e_1)
| ~ product1(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[c_875,c_327]) ).
tff(c_902,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_1)
| ~ product1(e_1,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_879]) ).
tff(c_903,plain,
~ product1(e_1,e_3,e_2),
inference(negUnitSimplification,[status(thm)],[c_16,c_12,c_902]) ).
tff(c_922,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_216,c_903]) ).
tff(c_925,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_922]) ).
tff(c_926,plain,
product1(e_1,e_3,e_1),
inference(negUnitSimplification,[status(thm)],[c_10,c_925]) ).
tff(c_26,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_80]) ).
tff(c_807,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product1(W_11,e_3,e_1) ),
inference(resolution,[status(thm)],[c_789,c_26]) ).
tff(c_957,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_926,c_807]) ).
tff(c_974,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_957]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP123-6.003 : TPTP v8.1.2. Released v1.2.0.
% 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
% 0.17/0.35 % Computer : n029.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 3 22:20:23 EDT 2023
% 0.17/0.35 % CPUTime :
% 4.71/2.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.71/2.07
% 4.71/2.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.95/2.11
% 4.95/2.11 Inference rules
% 4.95/2.11 ----------------------
% 4.95/2.11 #Ref : 0
% 4.95/2.11 #Sup : 181
% 4.95/2.11 #Fact : 0
% 4.95/2.11 #Define : 0
% 4.95/2.11 #Split : 0
% 4.95/2.11 #Chain : 0
% 4.95/2.11 #Close : 0
% 4.95/2.11
% 4.95/2.11 Ordering : KBO
% 4.95/2.11
% 4.95/2.11 Simplification rules
% 4.95/2.11 ----------------------
% 4.95/2.11 #Subsume : 21
% 4.95/2.11 #Demod : 126
% 4.95/2.11 #Tautology : 60
% 4.95/2.11 #SimpNegUnit : 59
% 4.95/2.11 #BackRed : 0
% 4.95/2.11
% 4.95/2.11 #Partial instantiations: 0
% 4.95/2.11 #Strategies tried : 1
% 4.95/2.11
% 4.95/2.11 Timing (in seconds)
% 4.95/2.11 ----------------------
% 4.95/2.12 Preprocessing : 0.45
% 4.95/2.12 Parsing : 0.24
% 4.95/2.12 CNF conversion : 0.03
% 4.95/2.12 Main loop : 0.58
% 4.95/2.12 Inferencing : 0.23
% 4.95/2.12 Reduction : 0.15
% 4.95/2.12 Demodulation : 0.09
% 4.95/2.12 BG Simplification : 0.03
% 4.95/2.12 Subsumption : 0.15
% 4.95/2.12 Abstraction : 0.02
% 4.95/2.12 MUC search : 0.00
% 4.95/2.12 Cooper : 0.00
% 4.95/2.12 Total : 1.09
% 4.95/2.12 Index Insertion : 0.00
% 4.95/2.12 Index Deletion : 0.00
% 4.95/2.12 Index Matching : 0.00
% 4.95/2.12 BG Taut test : 0.00
%------------------------------------------------------------------------------