TSTP Solution File: GRP124-3.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP124-3.004 : 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/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 : 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 10:39:56 EDT 2023
% Result : Unsatisfiable 9.98s 3.41s
% Output : CNFRefutation 10.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 40
% Syntax : Number of formulae : 235 ( 121 unt; 11 typ; 0 def)
% Number of atoms : 489 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 453 ( 188 ~; 265 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 133 (; 133 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > next > greater > equalish > cycle > group_element > #nlpp > e_4 > e_3 > e_2 > e_1 > e_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(cycle,type,
cycle: ( $i * $i ) > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(next,type,
next: ( $i * $i ) > $o ).
tff(e_0,type,
e_0: $i ).
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_140,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_142,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_148,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_129,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_128,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_168,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_194,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_152,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_130,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_184,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_154,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_134,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_150,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_127,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_192,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_222,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_136,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_144,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_39,axiom,
greater(e_1,e_0),
file(unknown,unknown) ).
tff(f_38,axiom,
next(e_3,e_4),
file(unknown,unknown) ).
tff(f_126,axiom,
! [X,Y,Z,X1] :
( ~ cycle(X,Y)
| ~ product(X,e_1,Z)
| ~ greater(Y,e_0)
| ~ next(X,X1)
| equalish(Z,X1) ),
file(unknown,unknown) ).
tff(f_40,axiom,
greater(e_2,e_0),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X] :
( ~ group_element(X)
| cycle(X,e_0)
| cycle(X,e_1)
| cycle(X,e_2)
| cycle(X,e_3) ),
file(unknown,unknown) ).
tff(f_41,axiom,
greater(e_3,e_0),
file(unknown,unknown) ).
tff(f_48,axiom,
greater(e_4,e_3),
file(unknown,unknown) ).
tff(f_112,axiom,
! [X,Y] :
( ~ cycle(X,e_0)
| ~ product(X,e_1,Y)
| ~ greater(Y,X) ),
file(unknown,unknown) ).
tff(f_132,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_138,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_208,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(c_60,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_62,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_68,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_148]) ).
tff(c_48,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_46,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_76,plain,
! [X_21,Y_22] :
( product(X_21,Y_22,e_4)
| product(X_21,Y_22,e_3)
| product(X_21,Y_22,e_2)
| product(X_21,Y_22,e_1)
| ~ group_element(Y_22)
| ~ group_element(X_21) ),
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_84,plain,
! [X_35] : product(X_35,X_35,X_35),
inference(cnfTransformation,[status(thm)],[f_194]) ).
tff(c_72,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_50,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_353,plain,
! [X_132,Y_133] :
( product(X_132,Y_133,e_4)
| product(X_132,Y_133,e_3)
| product(X_132,Y_133,e_2)
| product(X_132,Y_133,e_1)
| ~ group_element(Y_133)
| ~ group_element(X_132) ),
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_101,plain,
! [W_55,Z_56,X_57,Y_58] :
( equalish(W_55,Z_56)
| ~ product(X_57,Z_56,Y_58)
| ~ product(X_57,W_55,Y_58) ),
inference(cnfTransformation,[status(thm)],[f_184]) ).
tff(c_104,plain,
! [W_55,X_35] :
( equalish(W_55,X_35)
| ~ product(X_35,W_55,X_35) ),
inference(resolution,[status(thm)],[c_84,c_101]) ).
tff(c_371,plain,
! [Y_133] :
( equalish(Y_133,e_4)
| product(e_4,Y_133,e_3)
| product(e_4,Y_133,e_2)
| product(e_4,Y_133,e_1)
| ~ group_element(Y_133)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_353,c_104]) ).
tff(c_7472,plain,
! [Y_553] :
( equalish(Y_553,e_4)
| product(e_4,Y_553,e_3)
| product(e_4,Y_553,e_2)
| product(e_4,Y_553,e_1)
| ~ group_element(Y_553) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_371]) ).
tff(c_74,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_54,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_70,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_44,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_80,plain,
! [W_28,Z_30,X_27,Y_29] :
( equalish(W_28,Z_30)
| ~ product(X_27,Z_30,Y_29)
| ~ product(X_27,W_28,Y_29) ),
inference(cnfTransformation,[status(thm)],[f_184]) ).
tff(c_5552,plain,
! [W_487,Y_488,X_489] :
( equalish(W_487,Y_488)
| ~ product(X_489,W_487,e_4)
| product(X_489,Y_488,e_3)
| product(X_489,Y_488,e_2)
| product(X_489,Y_488,e_1)
| ~ group_element(Y_488)
| ~ group_element(X_489) ),
inference(resolution,[status(thm)],[c_353,c_80]) ).
tff(c_5557,plain,
! [Y_488] :
( equalish(e_4,Y_488)
| product(e_4,Y_488,e_3)
| product(e_4,Y_488,e_2)
| product(e_4,Y_488,e_1)
| ~ group_element(Y_488)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_84,c_5552]) ).
tff(c_6049,plain,
! [Y_507] :
( equalish(e_4,Y_507)
| product(e_4,Y_507,e_3)
| product(e_4,Y_507,e_2)
| product(e_4,Y_507,e_1)
| ~ group_element(Y_507) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_5557]) ).
tff(c_213,plain,
! [W_93,Z_94,Y_95,X_96] :
( equalish(W_93,Z_94)
| ~ product(Z_94,Y_95,X_96)
| ~ product(W_93,Y_95,X_96) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_216,plain,
! [W_93,X_35] :
( equalish(W_93,X_35)
| ~ product(W_93,X_35,X_35) ),
inference(resolution,[status(thm)],[c_84,c_213]) ).
tff(c_361,plain,
! [X_132] :
( equalish(X_132,e_4)
| product(X_132,e_4,e_3)
| product(X_132,e_4,e_2)
| product(X_132,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_132) ),
inference(resolution,[status(thm)],[c_353,c_216]) ).
tff(c_5513,plain,
! [X_486] :
( equalish(X_486,e_4)
| product(X_486,e_4,e_3)
| product(X_486,e_4,e_2)
| product(X_486,e_4,e_1)
| ~ group_element(X_486) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_361]) ).
tff(c_5531,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_5513,c_104]) ).
tff(c_5547,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_48,c_5531]) ).
tff(c_5548,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_68,c_74,c_5547]) ).
tff(c_5551,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_5548]) ).
tff(c_320,plain,
! [Z1_121,Y2_119,X2_122,Z2_124,X1_123,Y1_120] :
( equalish(Y1_120,Y2_119)
| ~ product(Z2_124,X2_122,Y2_119)
| ~ product(Z2_124,X1_123,Y1_120)
| ~ product(X2_122,Y2_119,Z1_121)
| ~ product(X1_123,Y1_120,Z1_121) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_323,plain,
! [Y1_120,X_35,X1_123,Z1_121] :
( equalish(Y1_120,X_35)
| ~ product(X_35,X1_123,Y1_120)
| ~ product(X_35,X_35,Z1_121)
| ~ product(X1_123,Y1_120,Z1_121) ),
inference(resolution,[status(thm)],[c_84,c_320]) ).
tff(c_5565,plain,
! [Z1_121] :
( equalish(e_1,e_3)
| ~ product(e_3,e_3,Z1_121)
| ~ product(e_4,e_1,Z1_121) ),
inference(resolution,[status(thm)],[c_5551,c_323]) ).
tff(c_5581,plain,
! [Z1_121] :
( ~ product(e_3,e_3,Z1_121)
| ~ product(e_4,e_1,Z1_121) ),
inference(negUnitSimplification,[status(thm)],[c_54,c_5565]) ).
tff(c_6055,plain,
( ~ product(e_3,e_3,e_3)
| equalish(e_4,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_6049,c_5581]) ).
tff(c_6088,plain,
( equalish(e_4,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_84,c_6055]) ).
tff(c_6089,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_70,c_6088]) ).
tff(c_7191,plain,
product(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_6089]) ).
tff(c_7207,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_7191,c_216]) ).
tff(c_7233,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70,c_7207]) ).
tff(c_7234,plain,
product(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_6089]) ).
tff(c_56,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_6067,plain,
( equalish(e_4,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_6049,c_216]) ).
tff(c_6098,plain,
( equalish(e_4,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_6067]) ).
tff(c_6099,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_74,c_6098]) ).
tff(c_6111,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_6099]) ).
tff(c_6127,plain,
! [Z1_121] :
( equalish(e_1,e_4)
| ~ product(e_4,e_4,Z1_121)
| ~ product(e_3,e_1,Z1_121) ),
inference(resolution,[status(thm)],[c_6111,c_323]) ).
tff(c_6219,plain,
! [Z1_514] :
( ~ product(e_4,e_4,Z1_514)
| ~ product(e_3,e_1,Z1_514) ),
inference(negUnitSimplification,[status(thm)],[c_56,c_6127]) ).
tff(c_6291,plain,
~ product(e_3,e_1,e_4),
inference(resolution,[status(thm)],[c_84,c_6219]) ).
tff(c_6294,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_76,c_6291]) ).
tff(c_6297,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_44,c_6294]) ).
tff(c_6666,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_6297]) ).
tff(c_5586,plain,
! [W_28] :
( equalish(W_28,e_4)
| ~ product(e_3,W_28,e_1) ),
inference(resolution,[status(thm)],[c_5551,c_80]) ).
tff(c_6759,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_6666,c_5586]) ).
tff(c_6802,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_6759]) ).
tff(c_6803,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_6297]) ).
tff(c_6805,plain,
product(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_6803]) ).
tff(c_64,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_10,plain,
greater(e_1,e_0),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_8,plain,
next(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_234,plain,
! [Z_103,X1_104,X_105,Y_106] :
( equalish(Z_103,X1_104)
| ~ next(X_105,X1_104)
| ~ greater(Y_106,e_0)
| ~ product(X_105,e_1,Z_103)
| ~ cycle(X_105,Y_106) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_246,plain,
! [Z_103,Y_106] :
( equalish(Z_103,e_4)
| ~ greater(Y_106,e_0)
| ~ product(e_3,e_1,Z_103)
| ~ cycle(e_3,Y_106) ),
inference(resolution,[status(thm)],[c_8,c_234]) ).
tff(c_421,plain,
! [Y_135] :
( ~ greater(Y_135,e_0)
| ~ cycle(e_3,Y_135) ),
inference(splitLeft,[status(thm)],[c_246]) ).
tff(c_434,plain,
~ cycle(e_3,e_1),
inference(resolution,[status(thm)],[c_10,c_421]) ).
tff(c_12,plain,
greater(e_2,e_0),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_437,plain,
~ cycle(e_3,e_2),
inference(resolution,[status(thm)],[c_12,c_421]) ).
tff(c_32,plain,
! [X_4] :
( cycle(X_4,e_3)
| cycle(X_4,e_2)
| cycle(X_4,e_1)
| cycle(X_4,e_0)
| ~ group_element(X_4) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_14,plain,
greater(e_3,e_0),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_436,plain,
~ cycle(e_3,e_3),
inference(resolution,[status(thm)],[c_14,c_421]) ).
tff(c_485,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_32,c_436]) ).
tff(c_488,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_485]) ).
tff(c_489,plain,
cycle(e_3,e_0),
inference(negUnitSimplification,[status(thm)],[c_434,c_437,c_488]) ).
tff(c_28,plain,
greater(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_40,plain,
! [Y_16,X_15] :
( ~ greater(Y_16,X_15)
| ~ product(X_15,e_1,Y_16)
| ~ cycle(X_15,e_0) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_379,plain,
! [X_132] :
( ~ greater(e_4,X_132)
| ~ cycle(X_132,e_0)
| product(X_132,e_1,e_3)
| product(X_132,e_1,e_2)
| product(X_132,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_132) ),
inference(resolution,[status(thm)],[c_353,c_40]) ).
tff(c_2686,plain,
! [X_268] :
( ~ greater(e_4,X_268)
| ~ cycle(X_268,e_0)
| product(X_268,e_1,e_3)
| product(X_268,e_1,e_2)
| product(X_268,e_1,e_1)
| ~ group_element(X_268) ),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_379]) ).
tff(c_2704,plain,
( equalish(e_1,e_3)
| ~ greater(e_4,e_3)
| ~ cycle(e_3,e_0)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_2686,c_104]) ).
tff(c_2723,plain,
( equalish(e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_489,c_28,c_2704]) ).
tff(c_2724,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_54,c_2723]) ).
tff(c_2728,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_2724]) ).
tff(c_2739,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_2728,c_216]) ).
tff(c_2760,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_64,c_2739]) ).
tff(c_2761,plain,
product(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_2724]) ).
tff(c_52,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_58,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_1397,plain,
! [X_216] :
( ~ greater(e_4,X_216)
| ~ cycle(X_216,e_0)
| product(X_216,e_1,e_3)
| product(X_216,e_1,e_2)
| product(X_216,e_1,e_1)
| ~ group_element(X_216) ),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_379]) ).
tff(c_1415,plain,
( equalish(e_1,e_3)
| ~ greater(e_4,e_3)
| ~ cycle(e_3,e_0)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_1397,c_104]) ).
tff(c_1434,plain,
( equalish(e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_489,c_28,c_1415]) ).
tff(c_1435,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_54,c_1434]) ).
tff(c_1445,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_1435]) ).
tff(c_1305,plain,
! [X_213] :
( equalish(X_213,e_4)
| product(X_213,e_4,e_3)
| product(X_213,e_4,e_2)
| product(X_213,e_4,e_1)
| ~ group_element(X_213) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_361]) ).
tff(c_1323,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_1305,c_104]) ).
tff(c_1339,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_48,c_1323]) ).
tff(c_1340,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_68,c_74,c_1339]) ).
tff(c_1343,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_1340]) ).
tff(c_1368,plain,
! [W_28] :
( equalish(W_28,e_4)
| ~ product(e_3,W_28,e_1) ),
inference(resolution,[status(thm)],[c_1343,c_80]) ).
tff(c_1448,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_1445,c_1368]) ).
tff(c_1472,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_1448]) ).
tff(c_1473,plain,
product(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_1435]) ).
tff(c_1491,plain,
! [Z1_121] :
( equalish(e_2,e_3)
| ~ product(e_3,e_3,Z1_121)
| ~ product(e_1,e_2,Z1_121) ),
inference(resolution,[status(thm)],[c_1473,c_323]) ).
tff(c_1565,plain,
! [Z1_225] :
( ~ product(e_3,e_3,Z1_225)
| ~ product(e_1,e_2,Z1_225) ),
inference(negUnitSimplification,[status(thm)],[c_60,c_1491]) ).
tff(c_1577,plain,
~ product(e_1,e_2,e_3),
inference(resolution,[status(thm)],[c_84,c_1565]) ).
tff(c_88,plain,
! [Y1_42,X1_43,X2_46,Z1_47,Z2_44,Y2_45] :
( equalish(Y1_42,Y2_45)
| ~ product(Z2_44,X2_46,Y2_45)
| ~ product(Z2_44,X1_43,Y1_42)
| ~ product(X2_46,Y2_45,Z1_47)
| ~ product(X1_43,Y1_42,Z1_47) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_1579,plain,
! [Y1_226,X1_227,Z1_228] :
( equalish(Y1_226,e_1)
| ~ product(e_3,X1_227,Y1_226)
| ~ product(e_4,e_1,Z1_228)
| ~ product(X1_227,Y1_226,Z1_228) ),
inference(resolution,[status(thm)],[c_1343,c_88]) ).
tff(c_1581,plain,
! [Z1_228] :
( equalish(e_2,e_1)
| ~ product(e_4,e_1,Z1_228)
| ~ product(e_1,e_2,Z1_228) ),
inference(resolution,[status(thm)],[c_1473,c_1579]) ).
tff(c_1615,plain,
! [Z1_229] :
( ~ product(e_4,e_1,Z1_229)
| ~ product(e_1,e_2,Z1_229) ),
inference(negUnitSimplification,[status(thm)],[c_58,c_1581]) ).
tff(c_1623,plain,
( ~ product(e_1,e_2,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_76,c_1615]) ).
tff(c_1629,plain,
( ~ product(e_1,e_2,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_50,c_44,c_1623]) ).
tff(c_2109,plain,
~ product(e_1,e_2,e_4),
inference(splitLeft,[status(thm)],[c_1629]) ).
tff(c_2112,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_76,c_2109]) ).
tff(c_2115,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_46,c_2112]) ).
tff(c_2116,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_1577,c_2115]) ).
tff(c_2117,plain,
product(e_1,e_2,e_1),
inference(splitLeft,[status(thm)],[c_2116]) ).
tff(c_2223,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_2117,c_104]) ).
tff(c_2243,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_58,c_2223]) ).
tff(c_2244,plain,
product(e_1,e_2,e_2),
inference(splitRight,[status(thm)],[c_2116]) ).
tff(c_2258,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_2244,c_216]) ).
tff(c_2280,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_2258]) ).
tff(c_2281,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_1629]) ).
tff(c_2417,plain,
product(e_4,e_1,e_3),
inference(splitLeft,[status(thm)],[c_2281]) ).
tff(c_1345,plain,
! [Z1_121] :
( equalish(e_1,e_3)
| ~ product(e_3,e_3,Z1_121)
| ~ product(e_4,e_1,Z1_121) ),
inference(resolution,[status(thm)],[c_1343,c_323]) ).
tff(c_1360,plain,
! [Z1_121] :
( ~ product(e_3,e_3,Z1_121)
| ~ product(e_4,e_1,Z1_121) ),
inference(negUnitSimplification,[status(thm)],[c_54,c_1345]) ).
tff(c_2427,plain,
~ product(e_3,e_3,e_3),
inference(resolution,[status(thm)],[c_2417,c_1360]) ).
tff(c_2456,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_84,c_2427]) ).
tff(c_2457,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(splitRight,[status(thm)],[c_2281]) ).
tff(c_2465,plain,
product(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_2457]) ).
tff(c_2486,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_2465,c_216]) ).
tff(c_2516,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70,c_2486]) ).
tff(c_2517,plain,
product(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_2457]) ).
tff(c_82,plain,
! [W_31,Z_34,Y_32,X_33] :
( equalish(W_31,Z_34)
| ~ product(Z_34,Y_32,X_33)
| ~ product(W_31,Y_32,X_33) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_1515,plain,
! [W_31] :
( equalish(W_31,e_3)
| ~ product(W_31,e_1,e_2) ),
inference(resolution,[status(thm)],[c_1473,c_82]) ).
tff(c_2580,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_2517,c_1515]) ).
tff(c_2616,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_74,c_2580]) ).
tff(c_2617,plain,
product(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_1340]) ).
tff(c_2643,plain,
! [W_28] :
( equalish(W_28,e_4)
| ~ product(e_3,W_28,e_2) ),
inference(resolution,[status(thm)],[c_2617,c_80]) ).
tff(c_2797,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_2761,c_2643]) ).
tff(c_2821,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_2797]) ).
tff(c_2822,plain,
! [Z_103] :
( equalish(Z_103,e_4)
| ~ product(e_3,e_1,Z_103) ),
inference(splitRight,[status(thm)],[c_246]) ).
tff(c_6822,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_6805,c_2822]) ).
tff(c_6864,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_68,c_6822]) ).
tff(c_6865,plain,
product(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_6803]) ).
tff(c_6298,plain,
product(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_6089]) ).
tff(c_6152,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_4,W_28,e_1) ),
inference(resolution,[status(thm)],[c_6111,c_80]) ).
tff(c_6301,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_6298,c_6152]) ).
tff(c_6330,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_6301]) ).
tff(c_6331,plain,
product(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_6089]) ).
tff(c_6419,plain,
! [W_31] :
( equalish(W_31,e_4)
| ~ product(W_31,e_1,e_2) ),
inference(resolution,[status(thm)],[c_6331,c_82]) ).
tff(c_6966,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_6865,c_6419]) ).
tff(c_7002,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_68,c_6966]) ).
tff(c_7003,plain,
product(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_6099]) ).
tff(c_7035,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_4,W_28,e_2) ),
inference(resolution,[status(thm)],[c_7003,c_80]) ).
tff(c_7240,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_7234,c_7035]) ).
tff(c_7266,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_7240]) ).
tff(c_7267,plain,
product(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_5548]) ).
tff(c_342,plain,
! [X2_129,Z2_127,Y1_128,X1_131,Y2_130,Z1_126] :
( equalish(X1_131,X2_129)
| ~ product(Z2_127,X2_129,Y2_130)
| ~ product(Z2_127,X1_131,Y1_128)
| ~ product(X2_129,Y2_130,Z1_126)
| ~ product(X1_131,Y1_128,Z1_126) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_345,plain,
! [X1_131,X_35,Y1_128,Z1_126] :
( equalish(X1_131,X_35)
| ~ product(X_35,X1_131,Y1_128)
| ~ product(X_35,X_35,Z1_126)
| ~ product(X1_131,Y1_128,Z1_126) ),
inference(resolution,[status(thm)],[c_84,c_342]) ).
tff(c_7270,plain,
! [Z1_126] :
( equalish(e_4,e_3)
| ~ product(e_3,e_3,Z1_126)
| ~ product(e_4,e_2,Z1_126) ),
inference(resolution,[status(thm)],[c_7267,c_345]) ).
tff(c_7285,plain,
! [Z1_126] :
( ~ product(e_3,e_3,Z1_126)
| ~ product(e_4,e_2,Z1_126) ),
inference(negUnitSimplification,[status(thm)],[c_74,c_7270]) ).
tff(c_7476,plain,
( ~ product(e_3,e_3,e_3)
| equalish(e_2,e_4)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_7472,c_7285]) ).
tff(c_7505,plain,
( equalish(e_2,e_4)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_46,c_84,c_7476]) ).
tff(c_7506,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_62,c_7505]) ).
tff(c_7710,plain,
product(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_7506]) ).
tff(c_7488,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_7472,c_216]) ).
tff(c_7515,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_7488]) ).
tff(c_7516,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_68,c_74,c_7515]) ).
tff(c_7572,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7516]) ).
tff(c_7603,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_4,W_28,e_1) ),
inference(resolution,[status(thm)],[c_7572,c_80]) ).
tff(c_7723,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_7710,c_7603]) ).
tff(c_7746,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_7723]) ).
tff(c_7747,plain,
product(e_4,e_2,e_2),
inference(splitRight,[status(thm)],[c_7506]) ).
tff(c_7764,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_7747,c_216]) ).
tff(c_7787,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_72,c_7764]) ).
tff(c_7788,plain,
product(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_7516]) ).
tff(c_7795,plain,
! [Z1_121] :
( equalish(e_2,e_4)
| ~ product(e_4,e_4,Z1_121)
| ~ product(e_3,e_2,Z1_121) ),
inference(resolution,[status(thm)],[c_7788,c_323]) ).
tff(c_7871,plain,
! [Z1_567] :
( ~ product(e_4,e_4,Z1_567)
| ~ product(e_3,e_2,Z1_567) ),
inference(negUnitSimplification,[status(thm)],[c_62,c_7795]) ).
tff(c_7920,plain,
~ product(e_3,e_2,e_4),
inference(resolution,[status(thm)],[c_84,c_7871]) ).
tff(c_7923,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_76,c_7920]) ).
tff(c_7926,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_46,c_7923]) ).
tff(c_8214,plain,
product(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_7926]) ).
tff(c_7937,plain,
product(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_7506]) ).
tff(c_7970,plain,
! [W_31] :
( equalish(W_31,e_4)
| ~ product(W_31,e_2,e_1) ),
inference(resolution,[status(thm)],[c_7937,c_82]) ).
tff(c_8222,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_8214,c_7970]) ).
tff(c_8251,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_68,c_8222]) ).
tff(c_8252,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_7926]) ).
tff(c_8254,plain,
product(e_3,e_2,e_3),
inference(splitLeft,[status(thm)],[c_8252]) ).
tff(c_8322,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_8254,c_104]) ).
tff(c_8356,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_8322]) ).
tff(c_8357,plain,
product(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_8252]) ).
tff(c_7293,plain,
! [W_28] :
( equalish(W_28,e_4)
| ~ product(e_3,W_28,e_2) ),
inference(resolution,[status(thm)],[c_7267,c_80]) ).
tff(c_8372,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_8357,c_7293]) ).
tff(c_8407,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62,c_8372]) ).
tff(c_8408,plain,
product(e_4,e_2,e_2),
inference(splitRight,[status(thm)],[c_7506]) ).
tff(c_7820,plain,
! [W_28] :
( equalish(W_28,e_3)
| ~ product(e_4,W_28,e_2) ),
inference(resolution,[status(thm)],[c_7788,c_80]) ).
tff(c_8413,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_8408,c_7820]) ).
tff(c_8439,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_8413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 21:59:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 9.98/3.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.26/3.46
% 10.26/3.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.33/3.54
% 10.33/3.54 Inference rules
% 10.33/3.54 ----------------------
% 10.33/3.54 #Ref : 0
% 10.33/3.54 #Sup : 1711
% 10.33/3.54 #Fact : 0
% 10.33/3.54 #Define : 0
% 10.33/3.54 #Split : 41
% 10.33/3.54 #Chain : 0
% 10.33/3.54 #Close : 0
% 10.33/3.54
% 10.33/3.54 Ordering : KBO
% 10.33/3.54
% 10.33/3.54 Simplification rules
% 10.33/3.54 ----------------------
% 10.33/3.54 #Subsume : 631
% 10.33/3.54 #Demod : 1218
% 10.33/3.54 #Tautology : 337
% 10.33/3.54 #SimpNegUnit : 455
% 10.33/3.54 #BackRed : 0
% 10.33/3.54
% 10.33/3.54 #Partial instantiations: 0
% 10.33/3.54 #Strategies tried : 1
% 10.33/3.54
% 10.33/3.54 Timing (in seconds)
% 10.33/3.54 ----------------------
% 10.33/3.54 Preprocessing : 0.50
% 10.33/3.54 Parsing : 0.28
% 10.33/3.54 CNF conversion : 0.03
% 10.33/3.55 Main loop : 1.82
% 10.33/3.55 Inferencing : 0.60
% 10.33/3.55 Reduction : 0.57
% 10.33/3.55 Demodulation : 0.37
% 10.33/3.55 BG Simplification : 0.05
% 10.33/3.55 Subsumption : 0.51
% 10.33/3.55 Abstraction : 0.05
% 10.33/3.55 MUC search : 0.00
% 10.33/3.55 Cooper : 0.00
% 10.33/3.55 Total : 2.47
% 10.33/3.55 Index Insertion : 0.00
% 10.33/3.55 Index Deletion : 0.00
% 10.33/3.55 Index Matching : 0.00
% 10.33/3.55 BG Taut test : 0.00
%------------------------------------------------------------------------------