TSTP Solution File: GRP127-1.004 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP127-1.004 : 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 : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:40:00 EDT 2023
% Result : Unsatisfiable 6.88s 2.66s
% Output : CNFRefutation 7.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 27
% Syntax : Number of formulae : 178 ( 90 unt; 7 typ; 0 def)
% Number of atoms : 392 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 333 ( 112 ~; 221 |; 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 : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 102 (; 102 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > equalish > group_element > #nlpp > e_4 > e_3 > e_2 > e_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(e_4,type,
e_4: $i ).
tff(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_46,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_48,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_58,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_40,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_60,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_42,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_50,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_44,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_56,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_33,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_36,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_35,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_54,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_74,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_100,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_98,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_90,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_108,axiom,
! [Y,X,Z1,Z2] :
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| product(Z2,Y,X) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_34,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(c_18,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_20,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_30,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_12,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_32,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_14,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_22,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_16,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_28,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_2,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_8,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_6,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_26,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_80,plain,
! [X_44,Y_45] :
( product(X_44,Y_45,e_4)
| product(X_44,Y_45,e_3)
| product(X_44,Y_45,e_2)
| product(X_44,Y_45,e_1)
| ~ group_element(Y_45)
| ~ group_element(X_44) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_42,plain,
! [X_15] : product(X_15,X_15,X_15),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_55,plain,
! [W_27,Z_28,Y_29,X_30] :
( equalish(W_27,Z_28)
| ~ product(Z_28,Y_29,X_30)
| ~ product(W_27,Y_29,X_30) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_58,plain,
! [W_27,X_15] :
( equalish(W_27,X_15)
| ~ product(W_27,X_15,X_15) ),
inference(resolution,[status(thm)],[c_42,c_55]) ).
tff(c_92,plain,
! [X_44] :
( equalish(X_44,e_4)
| product(X_44,e_4,e_3)
| product(X_44,e_4,e_2)
| product(X_44,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X_44) ),
inference(resolution,[status(thm)],[c_80,c_58]) ).
tff(c_123,plain,
! [X_48] :
( equalish(X_48,e_4)
| product(X_48,e_4,e_3)
| product(X_48,e_4,e_2)
| product(X_48,e_4,e_1)
| ~ group_element(X_48) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_92]) ).
tff(c_46,plain,
! [W_21,Z_22,X_23,Y_24] :
( equalish(W_21,Z_22)
| ~ product(X_23,Z_22,Y_24)
| ~ product(X_23,W_21,Y_24) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_49,plain,
! [W_21,X_15] :
( equalish(W_21,X_15)
| ~ product(X_15,W_21,X_15) ),
inference(resolution,[status(thm)],[c_42,c_46]) ).
tff(c_140,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_123,c_49]) ).
tff(c_156,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_6,c_140]) ).
tff(c_157,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_32,c_156]) ).
tff(c_159,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_157]) ).
tff(c_44,plain,
! [Z2_19,Y_16,X_17,Z1_18] :
( product(Z2_19,Y_16,X_17)
| ~ product(Z1_18,Y_16,Z2_19)
| ~ product(Y_16,X_17,Z1_18) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_2387,plain,
! [Y_117,X_118,X_119] :
( product(e_4,Y_117,X_118)
| ~ product(Y_117,X_118,X_119)
| product(X_119,Y_117,e_3)
| product(X_119,Y_117,e_2)
| product(X_119,Y_117,e_1)
| ~ group_element(Y_117)
| ~ group_element(X_119) ),
inference(resolution,[status(thm)],[c_80,c_44]) ).
tff(c_2411,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_159,c_2387]) ).
tff(c_2453,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_2411]) ).
tff(c_2574,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_2453]) ).
tff(c_2589,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_2574,c_49]) ).
tff(c_2606,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_2589]) ).
tff(c_2607,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_2453]) ).
tff(c_2609,plain,
product(e_4,e_3,e_4),
inference(splitLeft,[status(thm)],[c_2607]) ).
tff(c_1059,plain,
! [Y_83,X_84,X_85] :
( product(e_4,Y_83,X_84)
| ~ product(Y_83,X_84,X_85)
| product(X_85,Y_83,e_3)
| product(X_85,Y_83,e_2)
| product(X_85,Y_83,e_1)
| ~ group_element(Y_83)
| ~ group_element(X_85) ),
inference(resolution,[status(thm)],[c_80,c_44]) ).
tff(c_1083,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_159,c_1059]) ).
tff(c_1125,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_1083]) ).
tff(c_1308,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_1125]) ).
tff(c_98,plain,
! [Y_45] :
( equalish(Y_45,e_4)
| product(e_4,Y_45,e_3)
| product(e_4,Y_45,e_2)
| product(e_4,Y_45,e_1)
| ~ group_element(Y_45)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_80,c_49]) ).
tff(c_236,plain,
! [Y_56] :
( equalish(Y_56,e_4)
| product(e_4,Y_56,e_3)
| product(e_4,Y_56,e_2)
| product(e_4,Y_56,e_1)
| ~ group_element(Y_56) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_98]) ).
tff(c_253,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_236,c_58]) ).
tff(c_271,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_6,c_253]) ).
tff(c_272,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_32,c_271]) ).
tff(c_275,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_272]) ).
tff(c_40,plain,
! [W_11,Z_14,Y_12,X_13] :
( equalish(W_11,Z_14)
| ~ product(Z_14,Y_12,X_13)
| ~ product(W_11,Y_12,X_13) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_343,plain,
! [W_11] :
( equalish(W_11,e_4)
| ~ product(W_11,e_3,e_1) ),
inference(resolution,[status(thm)],[c_275,c_40]) ).
tff(c_1313,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_1308,c_343]) ).
tff(c_1335,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_1313]) ).
tff(c_1336,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_1125]) ).
tff(c_1406,plain,
product(e_4,e_3,e_4),
inference(splitLeft,[status(thm)],[c_1336]) ).
tff(c_36,plain,
! [W_5,Z_6,X_3,Y_4] :
( equalish(W_5,Z_6)
| ~ product(X_3,Y_4,Z_6)
| ~ product(X_3,Y_4,W_5) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_342,plain,
! [W_5] :
( equalish(W_5,e_1)
| ~ product(e_4,e_3,W_5) ),
inference(resolution,[status(thm)],[c_275,c_36]) ).
tff(c_1415,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_1406,c_342]) ).
tff(c_1443,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1415]) ).
tff(c_1444,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_1336]) ).
tff(c_1597,plain,
product(e_1,e_3,e_2),
inference(splitLeft,[status(thm)],[c_1444]) ).
tff(c_4,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_169,plain,
! [X_17] :
( product(e_1,e_4,X_17)
| ~ product(e_4,X_17,e_3) ),
inference(resolution,[status(thm)],[c_159,c_44]) ).
tff(c_792,plain,
! [Y_73] :
( product(e_1,e_4,Y_73)
| equalish(Y_73,e_4)
| product(e_4,Y_73,e_2)
| product(e_4,Y_73,e_1)
| ~ group_element(Y_73) ),
inference(resolution,[status(thm)],[c_236,c_169]) ).
tff(c_810,plain,
( equalish(e_4,e_2)
| product(e_1,e_4,e_2)
| equalish(e_2,e_4)
| product(e_4,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_792,c_58]) ).
tff(c_831,plain,
( equalish(e_4,e_2)
| product(e_1,e_4,e_2)
| equalish(e_2,e_4)
| product(e_4,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_810]) ).
tff(c_832,plain,
( product(e_1,e_4,e_2)
| product(e_4,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_20,c_30,c_831]) ).
tff(c_845,plain,
product(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_832]) ).
tff(c_38,plain,
! [W_8,Z_10,X_7,Y_9] :
( equalish(W_8,Z_10)
| ~ product(X_7,Z_10,Y_9)
| ~ product(X_7,W_8,Y_9) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_344,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product(e_4,W_8,e_1) ),
inference(resolution,[status(thm)],[c_275,c_38]) ).
tff(c_848,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_845,c_344]) ).
tff(c_862,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_848]) ).
tff(c_863,plain,
product(e_1,e_4,e_2),
inference(splitRight,[status(thm)],[c_832]) ).
tff(c_955,plain,
! [W_8] :
( equalish(W_8,e_4)
| ~ product(e_1,W_8,e_2) ),
inference(resolution,[status(thm)],[c_863,c_38]) ).
tff(c_1602,plain,
equalish(e_3,e_4),
inference(resolution,[status(thm)],[c_1597,c_955]) ).
tff(c_1619,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_1602]) ).
tff(c_1620,plain,
product(e_1,e_3,e_3),
inference(splitRight,[status(thm)],[c_1444]) ).
tff(c_1632,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_1620,c_58]) ).
tff(c_1649,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_1632]) ).
tff(c_1650,plain,
product(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_272]) ).
tff(c_1667,plain,
! [W_5] :
( equalish(W_5,e_2)
| ~ product(e_4,e_3,W_5) ),
inference(resolution,[status(thm)],[c_1650,c_36]) ).
tff(c_2759,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_2609,c_1667]) ).
tff(c_2786,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_2759]) ).
tff(c_2787,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_2607]) ).
tff(c_2796,plain,
product(e_1,e_3,e_2),
inference(splitLeft,[status(thm)],[c_2787]) ).
tff(c_1668,plain,
! [W_11] :
( equalish(W_11,e_4)
| ~ product(W_11,e_3,e_2) ),
inference(resolution,[status(thm)],[c_1650,c_40]) ).
tff(c_2944,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_2796,c_1668]) ).
tff(c_2961,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_2944]) ).
tff(c_2962,plain,
product(e_1,e_3,e_3),
inference(splitRight,[status(thm)],[c_2787]) ).
tff(c_2974,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_2962,c_58]) ).
tff(c_2991,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_2974]) ).
tff(c_2992,plain,
product(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_157]) ).
tff(c_4113,plain,
! [Y_169,X_170,X_171] :
( product(e_4,Y_169,X_170)
| ~ product(Y_169,X_170,X_171)
| product(X_171,Y_169,e_3)
| product(X_171,Y_169,e_2)
| product(X_171,Y_169,e_1)
| ~ group_element(Y_169)
| ~ group_element(X_171) ),
inference(resolution,[status(thm)],[c_80,c_44]) ).
tff(c_4137,plain,
( product(e_4,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_2992,c_4113]) ).
tff(c_4181,plain,
( product(e_4,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_4137]) ).
tff(c_4310,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_4181]) ).
tff(c_4537,plain,
! [X_180] :
( product(e_1,e_3,X_180)
| ~ product(e_3,X_180,e_2) ),
inference(resolution,[status(thm)],[c_4310,c_44]) ).
tff(c_4557,plain,
product(e_1,e_3,e_4),
inference(resolution,[status(thm)],[c_2992,c_4537]) ).
tff(c_101,plain,
! [Y_45,X_17,X_44] :
( product(e_4,Y_45,X_17)
| ~ product(Y_45,X_17,X_44)
| product(X_44,Y_45,e_3)
| product(X_44,Y_45,e_2)
| product(X_44,Y_45,e_1)
| ~ group_element(Y_45)
| ~ group_element(X_44) ),
inference(resolution,[status(thm)],[c_80,c_44]) ).
tff(c_4600,plain,
( 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_4557,c_101]) ).
tff(c_4617,plain,
( 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_8,c_2,c_4600]) ).
tff(c_5526,plain,
product(e_4,e_1,e_1),
inference(splitLeft,[status(thm)],[c_4617]) ).
tff(c_3012,plain,
! [W_127,X_128,Y_129] :
( equalish(W_127,e_4)
| ~ product(X_128,Y_129,W_127)
| product(X_128,Y_129,e_3)
| product(X_128,Y_129,e_2)
| product(X_128,Y_129,e_1)
| ~ group_element(Y_129)
| ~ group_element(X_128) ),
inference(resolution,[status(thm)],[c_80,c_36]) ).
tff(c_3070,plain,
! [X_133] :
( equalish(X_133,e_4)
| product(X_133,X_133,e_3)
| product(X_133,X_133,e_2)
| product(X_133,X_133,e_1)
| ~ group_element(X_133) ),
inference(resolution,[status(thm)],[c_42,c_3012]) ).
tff(c_66,plain,
! [W_34,Z_35,X_36,Y_37] :
( equalish(W_34,Z_35)
| ~ product(X_36,Y_37,Z_35)
| ~ product(X_36,Y_37,W_34) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_69,plain,
! [W_34,X_15] :
( equalish(W_34,X_15)
| ~ product(X_15,X_15,W_34) ),
inference(resolution,[status(thm)],[c_42,c_66]) ).
tff(c_3121,plain,
! [X_134] :
( equalish(e_3,X_134)
| equalish(X_134,e_4)
| product(X_134,X_134,e_2)
| product(X_134,X_134,e_1)
| ~ group_element(X_134) ),
inference(resolution,[status(thm)],[c_3070,c_69]) ).
tff(c_3181,plain,
! [X_135] :
( equalish(e_2,X_135)
| equalish(e_3,X_135)
| equalish(X_135,e_4)
| product(X_135,X_135,e_1)
| ~ group_element(X_135) ),
inference(resolution,[status(thm)],[c_3121,c_69]) ).
tff(c_3219,plain,
! [W_11,X_135] :
( equalish(W_11,X_135)
| ~ product(W_11,X_135,e_1)
| equalish(e_2,X_135)
| equalish(e_3,X_135)
| equalish(X_135,e_4)
| ~ group_element(X_135) ),
inference(resolution,[status(thm)],[c_3181,c_40]) ).
tff(c_5533,plain,
( equalish(e_4,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_1,e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_5526,c_3219]) ).
tff(c_5559,plain,
( equalish(e_4,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_1,e_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5533]) ).
tff(c_5561,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_22,c_16,c_28,c_5559]) ).
tff(c_5562,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_4617]) ).
tff(c_5571,plain,
product(e_4,e_1,e_3),
inference(splitLeft,[status(thm)],[c_5562]) ).
tff(c_3002,plain,
! [X_17] :
( product(e_2,e_4,X_17)
| ~ product(e_4,X_17,e_3) ),
inference(resolution,[status(thm)],[c_2992,c_44]) ).
tff(c_5596,plain,
product(e_2,e_4,e_1),
inference(resolution,[status(thm)],[c_5571,c_3002]) ).
tff(c_4340,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product(e_2,W_8,e_1) ),
inference(resolution,[status(thm)],[c_4310,c_38]) ).
tff(c_5610,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_5596,c_4340]) ).
tff(c_5633,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_5610]) ).
tff(c_5634,plain,
product(e_4,e_1,e_2),
inference(splitRight,[status(thm)],[c_5562]) ).
tff(c_3301,plain,
! [W_138,Y_139,X_140] :
( equalish(W_138,Y_139)
| ~ product(X_140,W_138,e_4)
| product(X_140,Y_139,e_3)
| product(X_140,Y_139,e_2)
| product(X_140,Y_139,e_1)
| ~ group_element(Y_139)
| ~ group_element(X_140) ),
inference(resolution,[status(thm)],[c_80,c_38]) ).
tff(c_3306,plain,
! [Y_139] :
( equalish(e_4,Y_139)
| product(e_4,Y_139,e_3)
| product(e_4,Y_139,e_2)
| product(e_4,Y_139,e_1)
| ~ group_element(Y_139)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_42,c_3301]) ).
tff(c_3456,plain,
! [Y_146] :
( equalish(e_4,Y_146)
| product(e_4,Y_146,e_3)
| product(e_4,Y_146,e_2)
| product(e_4,Y_146,e_1)
| ~ group_element(Y_146) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_3306]) ).
tff(c_3735,plain,
! [Y_158] :
( product(e_2,e_4,Y_158)
| equalish(e_4,Y_158)
| product(e_4,Y_158,e_2)
| product(e_4,Y_158,e_1)
| ~ group_element(Y_158) ),
inference(resolution,[status(thm)],[c_3456,c_3002]) ).
tff(c_3757,plain,
( product(e_2,e_4,e_2)
| equalish(e_4,e_2)
| product(e_4,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_3735,c_58]) ).
tff(c_3782,plain,
( product(e_2,e_4,e_2)
| equalish(e_4,e_2)
| product(e_4,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3757]) ).
tff(c_3783,plain,
( product(e_2,e_4,e_2)
| product(e_4,e_2,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_3782]) ).
tff(c_3786,plain,
product(e_4,e_2,e_1),
inference(splitLeft,[status(thm)],[c_3783]) ).
tff(c_3473,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_3456,c_58]) ).
tff(c_3491,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_6,c_3473]) ).
tff(c_3492,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_3491]) ).
tff(c_3495,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_3492]) ).
tff(c_3520,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product(e_4,W_8,e_1) ),
inference(resolution,[status(thm)],[c_3495,c_38]) ).
tff(c_3792,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_3786,c_3520]) ).
tff(c_3813,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_3792]) ).
tff(c_3814,plain,
product(e_2,e_4,e_2),
inference(splitRight,[status(thm)],[c_3783]) ).
tff(c_3004,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_4,e_2) ),
inference(resolution,[status(thm)],[c_2992,c_40]) ).
tff(c_3820,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_3814,c_3004]) ).
tff(c_3841,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_3820]) ).
tff(c_3842,plain,
product(e_4,e_3,e_2),
inference(splitRight,[status(thm)],[c_3492]) ).
tff(c_3871,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product(e_4,W_8,e_2) ),
inference(resolution,[status(thm)],[c_3842,c_38]) ).
tff(c_5898,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_5634,c_3871]) ).
tff(c_5918,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_5898]) ).
tff(c_5919,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_4181]) ).
tff(c_5921,plain,
product(e_4,e_3,e_4),
inference(splitLeft,[status(thm)],[c_5919]) ).
tff(c_3869,plain,
! [W_5] :
( equalish(W_5,e_2)
| ~ product(e_4,e_3,W_5) ),
inference(resolution,[status(thm)],[c_3842,c_36]) ).
tff(c_6064,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_5921,c_3869]) ).
tff(c_6090,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_6064]) ).
tff(c_6091,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_5919]) ).
tff(c_6100,plain,
product(e_2,e_3,e_2),
inference(splitLeft,[status(thm)],[c_6091]) ).
tff(c_3870,plain,
! [W_11] :
( equalish(W_11,e_4)
| ~ product(W_11,e_3,e_2) ),
inference(resolution,[status(thm)],[c_3842,c_40]) ).
tff(c_6105,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_6100,c_3870]) ).
tff(c_6127,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_6105]) ).
tff(c_6128,plain,
product(e_2,e_3,e_3),
inference(splitRight,[status(thm)],[c_6091]) ).
tff(c_6140,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_6128,c_58]) ).
tff(c_6157,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_6140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP127-1.004 : TPTP v8.1.2. Released v1.2.0.
% 0.08/0.15 % 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
% 0.16/0.38 % Computer : n031.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Thu Aug 3 22:18:45 EDT 2023
% 0.16/0.38 % CPUTime :
% 6.88/2.66 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.88/2.70
% 6.88/2.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.25/2.75
% 7.25/2.75 Inference rules
% 7.25/2.75 ----------------------
% 7.25/2.75 #Ref : 0
% 7.25/2.75 #Sup : 1117
% 7.25/2.75 #Fact : 4
% 7.25/2.75 #Define : 0
% 7.25/2.75 #Split : 20
% 7.25/2.75 #Chain : 0
% 7.25/2.75 #Close : 0
% 7.25/2.75
% 7.25/2.75 Ordering : KBO
% 7.25/2.75
% 7.25/2.75 Simplification rules
% 7.25/2.75 ----------------------
% 7.25/2.75 #Subsume : 129
% 7.25/2.75 #Demod : 1079
% 7.25/2.75 #Tautology : 429
% 7.25/2.75 #SimpNegUnit : 433
% 7.25/2.75 #BackRed : 0
% 7.25/2.75
% 7.25/2.75 #Partial instantiations: 0
% 7.25/2.75 #Strategies tried : 1
% 7.25/2.75
% 7.25/2.75 Timing (in seconds)
% 7.25/2.75 ----------------------
% 7.25/2.75 Preprocessing : 0.45
% 7.25/2.75 Parsing : 0.24
% 7.25/2.75 CNF conversion : 0.02
% 7.25/2.75 Main loop : 1.15
% 7.25/2.75 Inferencing : 0.40
% 7.25/2.75 Reduction : 0.34
% 7.25/2.75 Demodulation : 0.21
% 7.25/2.75 BG Simplification : 0.04
% 7.25/2.75 Subsumption : 0.30
% 7.25/2.75 Abstraction : 0.04
% 7.25/2.75 MUC search : 0.00
% 7.25/2.75 Cooper : 0.00
% 7.25/2.75 Total : 1.69
% 7.25/2.75 Index Insertion : 0.00
% 7.25/2.75 Index Deletion : 0.00
% 7.25/2.75 Index Matching : 0.00
% 7.25/2.75 BG Taut test : 0.00
%------------------------------------------------------------------------------