TSTP Solution File: GRP124-9.004 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP124-9.004 : 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 : 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 10:39:57 EDT 2023
% Result : Unsatisfiable 10.82s 3.74s
% Output : CNFRefutation 10.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 33
% Syntax : Number of formulae : 234 ( 120 unt; 9 typ; 0 def)
% Number of atoms : 457 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 377 ( 145 ~; 232 |; 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 : 12 ( 5 >; 7 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 130 (; 130 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product2 > product1 > 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(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_75,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_79,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_73,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_87,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_61,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_63,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_101,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_127,axiom,
! [X] : product1(X,X,X),
file(unknown,unknown) ).
tff(f_117,axiom,
! [X,W,Y,Z] :
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_85,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_67,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_83,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_69,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_60,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_81,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_62,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_125,axiom,
! [W,Y,X,Z] :
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_175,axiom,
! [X,Y,Z1,Z2] :
( ~ product1(X,Y,Z1)
| ~ product1(Z1,X,Z2)
| product2(Z2,Y,X) ),
file(unknown,unknown) ).
tff(f_167,axiom,
! [X] : product2(X,X,X),
file(unknown,unknown) ).
tff(f_149,axiom,
! [X,Y,W,Z] :
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_77,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_157,axiom,
! [X,W,Y,Z] :
( ~ product2(X,W,Y)
| ~ product2(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_141,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product2(X,Y,e_1)
| product2(X,Y,e_2)
| product2(X,Y,e_3)
| product2(X,Y,e_4) ),
file(unknown,unknown) ).
tff(f_165,axiom,
! [W,Y,X,Z] :
( ~ product2(W,Y,X)
| ~ product2(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(c_24,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_28,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_22,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_36,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_8,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_12,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_386,plain,
! [X_105,Y_106] :
( product1(X_105,Y_106,e_4)
| product1(X_105,Y_106,e_3)
| product1(X_105,Y_106,e_2)
| product1(X_105,Y_106,e_1)
| ~ group_element(Y_106)
| ~ group_element(X_105) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_46,plain,
! [X_19] : product1(X_19,X_19,X_19),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_65,plain,
! [W_45,Z_46,X_47,Y_48] :
( equalish(W_45,Z_46)
| ~ product1(X_47,Z_46,Y_48)
| ~ product1(X_47,W_45,Y_48) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_68,plain,
! [W_45,X_19] :
( equalish(W_45,X_19)
| ~ product1(X_19,W_45,X_19) ),
inference(resolution,[status(thm)],[c_46,c_65]) ).
tff(c_408,plain,
! [Y_106] :
( equalish(Y_106,e_4)
| product1(e_4,Y_106,e_3)
| product1(e_4,Y_106,e_2)
| product1(e_4,Y_106,e_1)
| ~ group_element(Y_106)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_386,c_68]) ).
tff(c_16145,plain,
! [Y_704] :
( equalish(Y_704,e_4)
| product1(e_4,Y_704,e_3)
| product1(e_4,Y_704,e_2)
| product1(e_4,Y_704,e_1)
| ~ group_element(Y_704) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_408]) ).
tff(c_34,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_16,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_32,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_18,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_6,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_11544,plain,
! [Y_501] :
( equalish(Y_501,e_4)
| product1(e_4,Y_501,e_3)
| product1(e_4,Y_501,e_2)
| product1(e_4,Y_501,e_1)
| ~ group_element(Y_501) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_408]) ).
tff(c_30,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_10,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_81,plain,
! [W_54,Z_55,Y_56,X_57] :
( equalish(W_54,Z_55)
| ~ product1(Z_55,Y_56,X_57)
| ~ product1(W_54,Y_56,X_57) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_84,plain,
! [W_54,X_19] :
( equalish(W_54,X_19)
| ~ product1(W_54,X_19,X_19) ),
inference(resolution,[status(thm)],[c_46,c_81]) ).
tff(c_402,plain,
! [X_105] :
( equalish(X_105,e_4)
| product1(X_105,e_4,e_3)
| product1(X_105,e_4,e_2)
| product1(X_105,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_105) ),
inference(resolution,[status(thm)],[c_386,c_84]) ).
tff(c_11258,plain,
! [X_482] :
( equalish(X_482,e_4)
| product1(X_482,e_4,e_3)
| product1(X_482,e_4,e_2)
| product1(X_482,e_4,e_1)
| ~ group_element(X_482) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_402]) ).
tff(c_11281,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_11258,c_68]) ).
tff(c_11305,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_10,c_11281]) ).
tff(c_11306,plain,
( product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_36,c_11305]) ).
tff(c_11308,plain,
product1(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_11306]) ).
tff(c_58,plain,
! [Z2_38,Y_36,X_35,Z1_37] :
( product2(Z2_38,Y_36,X_35)
| ~ product1(Z1_37,X_35,Z2_38)
| ~ product1(X_35,Y_36,Z1_37) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_11378,plain,
! [Y_489] :
( product2(e_1,Y_489,e_4)
| ~ product1(e_4,Y_489,e_3) ),
inference(resolution,[status(thm)],[c_11308,c_58]) ).
tff(c_56,plain,
! [X_34] : product2(X_34,X_34,X_34),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_91,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_149]) ).
tff(c_94,plain,
! [W_60,X_34] :
( equalish(W_60,X_34)
| ~ product2(X_34,X_34,W_60) ),
inference(resolution,[status(thm)],[c_56,c_91]) ).
tff(c_11394,plain,
( equalish(e_4,e_1)
| ~ product1(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[c_11378,c_94]) ).
tff(c_11414,plain,
~ product1(e_4,e_1,e_3),
inference(negUnitSimplification,[status(thm)],[c_32,c_11394]) ).
tff(c_11550,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_11544,c_11414]) ).
tff(c_11575,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_6,c_11550]) ).
tff(c_11576,plain,
( product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_18,c_11575]) ).
tff(c_12482,plain,
product1(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_11576]) ).
tff(c_12491,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_12482,c_84]) ).
tff(c_12505,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_12491]) ).
tff(c_12506,plain,
product1(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_11576]) ).
tff(c_26,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_38,plain,
! [X_5,Y_6] :
( product1(X_5,Y_6,e_4)
| product1(X_5,Y_6,e_3)
| product1(X_5,Y_6,e_2)
| product1(X_5,Y_6,e_1)
| ~ group_element(Y_6)
| ~ group_element(X_5) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_11567,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_11544,c_84]) ).
tff(c_11592,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_10,c_11567]) ).
tff(c_11593,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_36,c_11592]) ).
tff(c_11596,plain,
product1(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_11593]) ).
tff(c_11659,plain,
! [Y_508] :
( product2(e_1,Y_508,e_3)
| ~ product1(e_3,Y_508,e_4) ),
inference(resolution,[status(thm)],[c_11596,c_58]) ).
tff(c_11676,plain,
( equalish(e_3,e_1)
| ~ product1(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_11659,c_94]) ).
tff(c_11696,plain,
~ product1(e_3,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_26,c_11676]) ).
tff(c_11707,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_38,c_11696]) ).
tff(c_11710,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_10,c_6,c_11707]) ).
tff(c_12141,plain,
product1(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_11710]) ).
tff(c_42,plain,
! [W_12,Z_14,X_11,Y_13] :
( equalish(W_12,Z_14)
| ~ product1(X_11,Z_14,Y_13)
| ~ product1(X_11,W_12,Y_13) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_11326,plain,
! [W_12] :
( equalish(W_12,e_4)
| ~ product1(e_3,W_12,e_1) ),
inference(resolution,[status(thm)],[c_11308,c_42]) ).
tff(c_12144,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_12141,c_11326]) ).
tff(c_12161,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_12144]) ).
tff(c_12162,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_11710]) ).
tff(c_12200,plain,
product1(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_12162]) ).
tff(c_121,plain,
! [Z2_78,Y_79,X_80,Z1_81] :
( product2(Z2_78,Y_79,X_80)
| ~ product1(Z1_81,X_80,Z2_78)
| ~ product1(X_80,Y_79,Z1_81) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_125,plain,
! [X_82,Y_83] :
( product2(X_82,Y_83,X_82)
| ~ product1(X_82,Y_83,X_82) ),
inference(resolution,[status(thm)],[c_46,c_121]) ).
tff(c_52,plain,
! [W_27,Z_29,X_26,Y_28] :
( equalish(W_27,Z_29)
| ~ product2(X_26,Z_29,Y_28)
| ~ product2(X_26,W_27,Y_28) ),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_163,plain,
! [W_87,Y_88,X_89] :
( equalish(W_87,Y_88)
| ~ product2(X_89,W_87,X_89)
| ~ product1(X_89,Y_88,X_89) ),
inference(resolution,[status(thm)],[c_125,c_52]) ).
tff(c_169,plain,
! [X_34,Y_88] :
( equalish(X_34,Y_88)
| ~ product1(X_34,Y_88,X_34) ),
inference(resolution,[status(thm)],[c_56,c_163]) ).
tff(c_12207,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_12200,c_169]) ).
tff(c_12229,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_12207]) ).
tff(c_12230,plain,
product1(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_12162]) ).
tff(c_11727,plain,
product1(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_11576]) ).
tff(c_11614,plain,
! [W_12] :
( equalish(W_12,e_3)
| ~ product1(e_4,W_12,e_1) ),
inference(resolution,[status(thm)],[c_11596,c_42]) ).
tff(c_11730,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_11727,c_11614]) ).
tff(c_11747,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_11730]) ).
tff(c_11748,plain,
product1(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_11576]) ).
tff(c_44,plain,
! [W_15,Z_18,Y_16,X_17] :
( equalish(W_15,Z_18)
| ~ product1(Z_18,Y_16,X_17)
| ~ product1(W_15,Y_16,X_17) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_11783,plain,
! [W_15] :
( equalish(W_15,e_4)
| ~ product1(W_15,e_1,e_2) ),
inference(resolution,[status(thm)],[c_11748,c_44]) ).
tff(c_12292,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_12230,c_11783]) ).
tff(c_12309,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_12292]) ).
tff(c_12310,plain,
product1(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_11593]) ).
tff(c_12339,plain,
! [W_12] :
( equalish(W_12,e_3)
| ~ product1(e_4,W_12,e_2) ),
inference(resolution,[status(thm)],[c_12310,c_42]) ).
tff(c_12568,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_12506,c_12339]) ).
tff(c_12582,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_12568]) ).
tff(c_12583,plain,
product1(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_11306]) ).
tff(c_12655,plain,
! [Y_559] :
( product2(e_2,Y_559,e_4)
| ~ product1(e_4,Y_559,e_3) ),
inference(resolution,[status(thm)],[c_12583,c_58]) ).
tff(c_12671,plain,
( equalish(e_4,e_2)
| ~ product1(e_4,e_2,e_3) ),
inference(resolution,[status(thm)],[c_12655,c_94]) ).
tff(c_12691,plain,
~ product1(e_4,e_2,e_3),
inference(negUnitSimplification,[status(thm)],[c_34,c_12671]) ).
tff(c_16163,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_16145,c_12691]) ).
tff(c_16201,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_8,c_16163]) ).
tff(c_16202,plain,
( product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_24,c_16201]) ).
tff(c_16295,plain,
product1(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_16202]) ).
tff(c_13706,plain,
! [W_604,Y_605,X_606] :
( equalish(W_604,Y_605)
| ~ product1(X_606,W_604,e_4)
| product1(X_606,Y_605,e_3)
| product1(X_606,Y_605,e_2)
| product1(X_606,Y_605,e_1)
| ~ group_element(Y_605)
| ~ group_element(X_606) ),
inference(resolution,[status(thm)],[c_386,c_42]) ).
tff(c_13711,plain,
! [Y_605] :
( equalish(e_4,Y_605)
| product1(e_4,Y_605,e_3)
| product1(e_4,Y_605,e_2)
| product1(e_4,Y_605,e_1)
| ~ group_element(Y_605)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_46,c_13706]) ).
tff(c_14520,plain,
! [Y_639] :
( equalish(e_4,Y_639)
| product1(e_4,Y_639,e_3)
| product1(e_4,Y_639,e_2)
| product1(e_4,Y_639,e_1)
| ~ group_element(Y_639) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_13711]) ).
tff(c_14538,plain,
( equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_14520,c_12691]) ).
tff(c_14576,plain,
( equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_14538]) ).
tff(c_14577,plain,
( product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_34,c_14576]) ).
tff(c_14598,plain,
product1(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_14577]) ).
tff(c_187,plain,
! [X_97,Y_98] :
( product2(X_97,Y_98,e_4)
| product2(X_97,Y_98,e_3)
| product2(X_97,Y_98,e_2)
| product2(X_97,Y_98,e_1)
| ~ group_element(Y_98)
| ~ group_element(X_97) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_61,plain,
! [W_41,Z_42,X_43,Y_44] :
( equalish(W_41,Z_42)
| ~ product2(X_43,Z_42,Y_44)
| ~ product2(X_43,W_41,Y_44) ),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_64,plain,
! [W_41,X_34] :
( equalish(W_41,X_34)
| ~ product2(X_34,W_41,X_34) ),
inference(resolution,[status(thm)],[c_56,c_61]) ).
tff(c_210,plain,
! [Y_98] :
( equalish(Y_98,e_4)
| product2(e_4,Y_98,e_3)
| product2(e_4,Y_98,e_2)
| product2(e_4,Y_98,e_1)
| ~ group_element(Y_98)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_187,c_64]) ).
tff(c_13016,plain,
! [Y_574] :
( equalish(Y_574,e_4)
| product2(e_4,Y_574,e_3)
| product2(e_4,Y_574,e_2)
| product2(e_4,Y_574,e_1)
| ~ group_element(Y_574) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_210]) ).
tff(c_101,plain,
! [W_66,Z_67,Y_68,X_69] :
( equalish(W_66,Z_67)
| ~ product2(Z_67,Y_68,X_69)
| ~ product2(W_66,Y_68,X_69) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_104,plain,
! [W_66,X_34] :
( equalish(W_66,X_34)
| ~ product2(W_66,X_34,X_34) ),
inference(resolution,[status(thm)],[c_56,c_101]) ).
tff(c_13026,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product2(e_4,e_3,e_2)
| product2(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_13016,c_104]) ).
tff(c_13048,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product2(e_4,e_3,e_2)
| product2(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_13026]) ).
tff(c_13049,plain,
( product2(e_4,e_3,e_2)
| product2(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_36,c_13048]) ).
tff(c_13057,plain,
product2(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_13049]) ).
tff(c_50,plain,
! [W_24,Z_25,X_22,Y_23] :
( equalish(W_24,Z_25)
| ~ product2(X_22,Y_23,Z_25)
| ~ product2(X_22,Y_23,W_24) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_150,plain,
! [W_24,X_82,Y_83] :
( equalish(W_24,X_82)
| ~ product2(X_82,Y_83,W_24)
| ~ product1(X_82,Y_83,X_82) ),
inference(resolution,[status(thm)],[c_125,c_50]) ).
tff(c_13061,plain,
( equalish(e_1,e_4)
| ~ product1(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[c_13057,c_150]) ).
tff(c_13076,plain,
~ product1(e_4,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_18,c_13061]) ).
tff(c_13102,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_38,c_13076]) ).
tff(c_13105,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_10,c_13102]) ).
tff(c_13168,plain,
product1(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_13105]) ).
tff(c_13239,plain,
! [Y_587] :
( product2(e_1,Y_587,e_3)
| ~ product1(e_3,Y_587,e_4) ),
inference(resolution,[status(thm)],[c_13168,c_58]) ).
tff(c_13255,plain,
( equalish(e_3,e_1)
| ~ product1(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_13239,c_94]) ).
tff(c_13276,plain,
~ product1(e_3,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_26,c_13255]) ).
tff(c_13287,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_38,c_13276]) ).
tff(c_13290,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_10,c_6,c_13287]) ).
tff(c_13425,plain,
product1(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_13290]) ).
tff(c_13434,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_13425,c_84]) ).
tff(c_13448,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_13434]) ).
tff(c_13449,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_13290]) ).
tff(c_13496,plain,
product1(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_13449]) ).
tff(c_13501,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_13496,c_169]) ).
tff(c_13520,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_13501]) ).
tff(c_13521,plain,
product1(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_13449]) ).
tff(c_12602,plain,
! [W_12] :
( equalish(W_12,e_4)
| ~ product1(e_3,W_12,e_2) ),
inference(resolution,[status(thm)],[c_12583,c_42]) ).
tff(c_13567,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_13521,c_12602]) ).
tff(c_13584,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_13567]) ).
tff(c_13585,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_13105]) ).
tff(c_13644,plain,
product1(e_4,e_3,e_3),
inference(splitLeft,[status(thm)],[c_13585]) ).
tff(c_13656,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_13644,c_84]) ).
tff(c_13671,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_13656]) ).
tff(c_13672,plain,
product1(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_13585]) ).
tff(c_13744,plain,
! [Y_609] :
( product2(e_2,Y_609,e_3)
| ~ product1(e_3,Y_609,e_4) ),
inference(resolution,[status(thm)],[c_13672,c_58]) ).
tff(c_13763,plain,
( equalish(e_3,e_2)
| ~ product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[c_13744,c_94]) ).
tff(c_13787,plain,
~ product1(e_3,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_28,c_13763]) ).
tff(c_13798,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_38,c_13787]) ).
tff(c_13801,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_10,c_8,c_13798]) ).
tff(c_13975,plain,
product1(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_13801]) ).
tff(c_13993,plain,
! [W_15] :
( equalish(W_15,e_3)
| ~ product1(W_15,e_2,e_1) ),
inference(resolution,[status(thm)],[c_13975,c_44]) ).
tff(c_14601,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_14598,c_13993]) ).
tff(c_14617,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_14601]) ).
tff(c_14618,plain,
product1(e_4,e_2,e_2),
inference(splitRight,[status(thm)],[c_14577]) ).
tff(c_13691,plain,
! [W_12] :
( equalish(W_12,e_3)
| ~ product1(e_4,W_12,e_2) ),
inference(resolution,[status(thm)],[c_13672,c_42]) ).
tff(c_14624,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_14618,c_13691]) ).
tff(c_14645,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_14624]) ).
tff(c_14646,plain,
( product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_13801]) ).
tff(c_14805,plain,
product1(e_3,e_2,e_3),
inference(splitLeft,[status(thm)],[c_14646]) ).
tff(c_14882,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_14805,c_169]) ).
tff(c_14904,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_14882]) ).
tff(c_14905,plain,
product1(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_14646]) ).
tff(c_14911,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_14905,c_12602]) ).
tff(c_14931,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_14911]) ).
tff(c_14932,plain,
product2(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_13049]) ).
tff(c_14937,plain,
( equalish(e_2,e_4)
| ~ product1(e_4,e_3,e_4) ),
inference(resolution,[status(thm)],[c_14932,c_150]) ).
tff(c_14952,plain,
~ product1(e_4,e_3,e_4),
inference(negUnitSimplification,[status(thm)],[c_24,c_14937]) ).
tff(c_14978,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_38,c_14952]) ).
tff(c_14981,plain,
( product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_10,c_14978]) ).
tff(c_15044,plain,
product1(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_14981]) ).
tff(c_15115,plain,
! [Y_659] :
( product2(e_1,Y_659,e_3)
| ~ product1(e_3,Y_659,e_4) ),
inference(resolution,[status(thm)],[c_15044,c_58]) ).
tff(c_15131,plain,
( equalish(e_3,e_1)
| ~ product1(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[c_15115,c_94]) ).
tff(c_15152,plain,
~ product1(e_3,e_1,e_4),
inference(negUnitSimplification,[status(thm)],[c_26,c_15131]) ).
tff(c_15163,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_38,c_15152]) ).
tff(c_15166,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_10,c_6,c_15163]) ).
tff(c_15301,plain,
product1(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_15166]) ).
tff(c_15310,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_15301,c_84]) ).
tff(c_15324,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_15310]) ).
tff(c_15325,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_15166]) ).
tff(c_15372,plain,
product1(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_15325]) ).
tff(c_15377,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_15372,c_169]) ).
tff(c_15396,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_15377]) ).
tff(c_15397,plain,
product1(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_15325]) ).
tff(c_15444,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_15397,c_12602]) ).
tff(c_15462,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_15444]) ).
tff(c_15463,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_14981]) ).
tff(c_15522,plain,
product1(e_4,e_3,e_3),
inference(splitLeft,[status(thm)],[c_15463]) ).
tff(c_15534,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_15522,c_84]) ).
tff(c_15549,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_15534]) ).
tff(c_15550,plain,
product1(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_15463]) ).
tff(c_15622,plain,
! [Y_681] :
( product2(e_2,Y_681,e_3)
| ~ product1(e_3,Y_681,e_4) ),
inference(resolution,[status(thm)],[c_15550,c_58]) ).
tff(c_15641,plain,
( equalish(e_3,e_2)
| ~ product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[c_15622,c_94]) ).
tff(c_15665,plain,
~ product1(e_3,e_2,e_4),
inference(negUnitSimplification,[status(thm)],[c_28,c_15641]) ).
tff(c_15676,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_38,c_15665]) ).
tff(c_15679,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_10,c_8,c_15676]) ).
tff(c_15853,plain,
product1(e_3,e_2,e_1),
inference(splitLeft,[status(thm)],[c_15679]) ).
tff(c_15871,plain,
! [W_15] :
( equalish(W_15,e_3)
| ~ product1(W_15,e_2,e_1) ),
inference(resolution,[status(thm)],[c_15853,c_44]) ).
tff(c_16298,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_16295,c_15871]) ).
tff(c_16314,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_16298]) ).
tff(c_16315,plain,
product1(e_4,e_2,e_2),
inference(splitRight,[status(thm)],[c_16202]) ).
tff(c_15569,plain,
! [W_12] :
( equalish(W_12,e_3)
| ~ product1(e_4,W_12,e_2) ),
inference(resolution,[status(thm)],[c_15550,c_42]) ).
tff(c_16321,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_16315,c_15569]) ).
tff(c_16342,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_16321]) ).
tff(c_16343,plain,
( product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_15679]) ).
tff(c_16386,plain,
product1(e_3,e_2,e_3),
inference(splitLeft,[status(thm)],[c_16343]) ).
tff(c_16393,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_16386,c_169]) ).
tff(c_16415,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_16393]) ).
tff(c_16416,plain,
product1(e_3,e_2,e_2),
inference(splitRight,[status(thm)],[c_16343]) ).
tff(c_16422,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_16416,c_12602]) ).
tff(c_16443,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_16422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 22:01:46 EDT 2023
% 0.14/0.36 % CPUTime :
% 10.82/3.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.82/3.77
% 10.82/3.77 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.82/3.82
% 10.82/3.82 Inference rules
% 10.82/3.82 ----------------------
% 10.82/3.82 #Ref : 0
% 10.82/3.82 #Sup : 3091
% 10.82/3.82 #Fact : 0
% 10.82/3.82 #Define : 0
% 10.82/3.82 #Split : 77
% 10.82/3.82 #Chain : 0
% 10.82/3.82 #Close : 0
% 10.82/3.82
% 10.82/3.82 Ordering : KBO
% 10.82/3.82
% 10.82/3.82 Simplification rules
% 10.82/3.82 ----------------------
% 10.82/3.82 #Subsume : 512
% 10.82/3.82 #Demod : 2477
% 10.82/3.82 #Tautology : 908
% 10.82/3.82 #SimpNegUnit : 1376
% 10.82/3.82 #BackRed : 0
% 10.82/3.82
% 10.82/3.82 #Partial instantiations: 0
% 10.82/3.82 #Strategies tried : 1
% 10.82/3.82
% 10.82/3.82 Timing (in seconds)
% 10.82/3.82 ----------------------
% 10.82/3.83 Preprocessing : 0.48
% 10.82/3.83 Parsing : 0.27
% 10.82/3.83 CNF conversion : 0.03
% 10.82/3.83 Main loop : 2.15
% 10.82/3.83 Inferencing : 0.69
% 10.82/3.83 Reduction : 0.66
% 10.82/3.83 Demodulation : 0.38
% 10.82/3.83 BG Simplification : 0.05
% 10.82/3.83 Subsumption : 0.64
% 10.82/3.83 Abstraction : 0.06
% 10.82/3.83 MUC search : 0.00
% 10.82/3.83 Cooper : 0.00
% 10.82/3.83 Total : 2.73
% 10.82/3.83 Index Insertion : 0.00
% 10.82/3.83 Index Deletion : 0.00
% 10.82/3.83 Index Matching : 0.00
% 10.82/3.83 BG Taut test : 0.00
%------------------------------------------------------------------------------