TSTP Solution File: GRP126-1.004 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP126-1.004 : 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/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 : n004.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 10:39:58 EDT 2023
% Result : Unsatisfiable 6.94s 2.70s
% Output : CNFRefutation 7.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 28
% Syntax : Number of formulae : 158 ( 85 unt; 7 typ; 0 def)
% Number of atoms : 314 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 252 ( 89 ~; 163 |; 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 : 83 (; 83 !; 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_58,axiom,
~ equalish(e_4,e_3),
file(unknown,unknown) ).
tff(f_50,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_44,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_40,axiom,
~ equalish(e_1,e_4),
file(unknown,unknown) ).
tff(f_38,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_54,axiom,
~ equalish(e_4,e_1),
file(unknown,unknown) ).
tff(f_56,axiom,
~ equalish(e_4,e_2),
file(unknown,unknown) ).
tff(f_31,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_34,axiom,
group_element(e_4),
file(unknown,unknown) ).
tff(f_72,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_98,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_96,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_33,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_46,axiom,
~ equalish(e_2,e_4),
file(unknown,unknown) ).
tff(f_32,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_48,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_52,axiom,
~ equalish(e_3,e_4),
file(unknown,unknown) ).
tff(f_88,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_106,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,Y) ),
file(unknown,unknown) ).
tff(f_80,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_42,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(c_32,plain,
~ equalish(e_4,e_3),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_24,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_18,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_14,plain,
~ equalish(e_1,e_4),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_12,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_28,plain,
~ equalish(e_4,e_1),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_30,plain,
~ equalish(e_4,e_2),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_2,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_8,plain,
group_element(e_4),
inference(cnfTransformation,[status(thm)],[f_34]) ).
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_72]) ).
tff(c_42,plain,
! [X_15] : product(X_15,X_15,X_15),
inference(cnfTransformation,[status(thm)],[f_98]) ).
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_96]) ).
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_106,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(X_44) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_92]) ).
tff(c_6,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_34,plain,
! [X_1,Y_2] :
( product(X_1,Y_2,e_4)
| product(X_1,Y_2,e_3)
| product(X_1,Y_2,e_2)
| product(X_1,Y_2,e_1)
| ~ group_element(Y_2)
| ~ group_element(X_1) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_20,plain,
~ equalish(e_2,e_4),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_4,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_22,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_26,plain,
~ equalish(e_3,e_4),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_121,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_88]) ).
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_138,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_121,c_49]) ).
tff(c_153,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_138]) ).
tff(c_154,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_32,c_153]) ).
tff(c_156,plain,
product(e_3,e_4,e_1),
inference(splitLeft,[status(thm)],[c_154]) ).
tff(c_44,plain,
! [Z1_18,Z2_19,Y_17,X_16] :
( product(Z1_18,Z2_19,Y_17)
| ~ product(Y_17,X_16,Z2_19)
| ~ product(X_16,Y_17,Z1_18) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_239,plain,
! [Z1_53] :
( product(Z1_53,e_1,e_3)
| ~ product(e_4,e_3,Z1_53) ),
inference(resolution,[status(thm)],[c_156,c_44]) ).
tff(c_242,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_34,c_239]) ).
tff(c_245,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6,c_242]) ).
tff(c_1130,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_245]) ).
tff(c_201,plain,
! [Z1_18] :
( product(Z1_18,e_1,e_3)
| ~ product(e_4,e_3,Z1_18) ),
inference(resolution,[status(thm)],[c_156,c_44]) ).
tff(c_1147,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_1130,c_201]) ).
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_80]) ).
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_1220,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_1147,c_69]) ).
tff(c_1236,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_1220]) ).
tff(c_1237,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_245]) ).
tff(c_1239,plain,
product(e_4,e_1,e_3),
inference(splitLeft,[status(thm)],[c_1237]) ).
tff(c_16,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_1452,plain,
! [Z1_84] :
( product(Z1_84,e_3,e_4)
| ~ product(e_1,e_4,Z1_84) ),
inference(resolution,[status(thm)],[c_1239,c_44]) ).
tff(c_1461,plain,
( product(e_3,e_3,e_4)
| equalish(e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_106,c_1452]) ).
tff(c_1475,plain,
( product(e_3,e_3,e_4)
| equalish(e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1461]) ).
tff(c_1476,plain,
( product(e_3,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_14,c_1475]) ).
tff(c_1540,plain,
product(e_1,e_4,e_1),
inference(splitLeft,[status(thm)],[c_1476]) ).
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_80]) ).
tff(c_246,plain,
! [W_54,X_55,Y_56] :
( equalish(W_54,e_4)
| ~ product(X_55,Y_56,W_54)
| product(X_55,Y_56,e_3)
| product(X_55,Y_56,e_2)
| product(X_55,Y_56,e_1)
| ~ group_element(Y_56)
| ~ group_element(X_55) ),
inference(resolution,[status(thm)],[c_80,c_36]) ).
tff(c_388,plain,
! [X_60] :
( equalish(X_60,e_4)
| product(X_60,X_60,e_3)
| product(X_60,X_60,e_2)
| product(X_60,X_60,e_1)
| ~ group_element(X_60) ),
inference(resolution,[status(thm)],[c_42,c_246]) ).
tff(c_473,plain,
! [X_62] :
( equalish(e_3,X_62)
| equalish(X_62,e_4)
| product(X_62,X_62,e_2)
| product(X_62,X_62,e_1)
| ~ group_element(X_62) ),
inference(resolution,[status(thm)],[c_388,c_69]) ).
tff(c_513,plain,
! [X_63] :
( equalish(e_2,X_63)
| equalish(e_3,X_63)
| equalish(X_63,e_4)
| product(X_63,X_63,e_1)
| ~ group_element(X_63) ),
inference(resolution,[status(thm)],[c_473,c_69]) ).
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_88]) ).
tff(c_568,plain,
! [W_8,X_63] :
( equalish(W_8,X_63)
| ~ product(X_63,W_8,e_1)
| equalish(e_2,X_63)
| equalish(e_3,X_63)
| equalish(X_63,e_4)
| ~ group_element(X_63) ),
inference(resolution,[status(thm)],[c_513,c_38]) ).
tff(c_1545,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_1540,c_568]) ).
tff(c_1565,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_1545]) ).
tff(c_1567,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_22,c_16,c_28,c_1565]) ).
tff(c_1568,plain,
( product(e_1,e_4,e_2)
| product(e_3,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_1476]) ).
tff(c_1678,plain,
product(e_3,e_3,e_4),
inference(splitLeft,[status(thm)],[c_1568]) ).
tff(c_1691,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_1678,c_69]) ).
tff(c_1712,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_1691]) ).
tff(c_1713,plain,
product(e_1,e_4,e_2),
inference(splitRight,[status(thm)],[c_1568]) ).
tff(c_2084,plain,
! [Z1_99] :
( product(Z1_99,e_2,e_1)
| ~ product(e_4,e_1,Z1_99) ),
inference(resolution,[status(thm)],[c_1713,c_44]) ).
tff(c_2093,plain,
product(e_3,e_2,e_1),
inference(resolution,[status(thm)],[c_1239,c_2084]) ).
tff(c_204,plain,
! [W_8] :
( equalish(W_8,e_4)
| ~ product(e_3,W_8,e_1) ),
inference(resolution,[status(thm)],[c_156,c_38]) ).
tff(c_2112,plain,
equalish(e_2,e_4),
inference(resolution,[status(thm)],[c_2093,c_204]) ).
tff(c_2139,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_2112]) ).
tff(c_2140,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_1237]) ).
tff(c_2202,plain,
product(e_4,e_3,e_2),
inference(splitLeft,[status(thm)],[c_2140]) ).
tff(c_2219,plain,
product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[c_2202,c_201]) ).
tff(c_2316,plain,
! [W_106] :
( equalish(W_106,e_1)
| ~ product(e_2,W_106,e_3) ),
inference(resolution,[status(thm)],[c_2219,c_38]) ).
tff(c_2353,plain,
( equalish(e_4,e_1)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_106,c_2316]) ).
tff(c_2382,plain,
( equalish(e_4,e_1)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2353]) ).
tff(c_2383,plain,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_20,c_28,c_2382]) ).
tff(c_2768,plain,
product(e_2,e_4,e_1),
inference(splitLeft,[status(thm)],[c_2383]) ).
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_96]) ).
tff(c_203,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_4,e_1) ),
inference(resolution,[status(thm)],[c_156,c_40]) ).
tff(c_2775,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_2768,c_203]) ).
tff(c_2794,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_2775]) ).
tff(c_2795,plain,
product(e_2,e_4,e_2),
inference(splitRight,[status(thm)],[c_2383]) ).
tff(c_2885,plain,
equalish(e_4,e_2),
inference(resolution,[status(thm)],[c_2795,c_49]) ).
tff(c_2901,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_2885]) ).
tff(c_2902,plain,
product(e_4,e_3,e_3),
inference(splitRight,[status(thm)],[c_2140]) ).
tff(c_2914,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_2902,c_58]) ).
tff(c_2929,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_2914]) ).
tff(c_2930,plain,
product(e_3,e_4,e_2),
inference(splitRight,[status(thm)],[c_154]) ).
tff(c_3038,plain,
! [Z1_126] :
( product(Z1_126,e_2,e_3)
| ~ product(e_4,e_3,Z1_126) ),
inference(resolution,[status(thm)],[c_2930,c_44]) ).
tff(c_3041,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[c_34,c_3038]) ).
tff(c_3044,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6,c_3041]) ).
tff(c_3873,plain,
product(e_4,e_3,e_1),
inference(splitLeft,[status(thm)],[c_3044]) ).
tff(c_2976,plain,
! [Z1_18] :
( product(Z1_18,e_2,e_3)
| ~ product(e_4,e_3,Z1_18) ),
inference(resolution,[status(thm)],[c_2930,c_44]) ).
tff(c_3946,plain,
product(e_1,e_2,e_3),
inference(resolution,[status(thm)],[c_3873,c_2976]) ).
tff(c_4079,plain,
! [W_152] :
( equalish(W_152,e_2)
| ~ product(e_1,W_152,e_3) ),
inference(resolution,[status(thm)],[c_3946,c_38]) ).
tff(c_4104,plain,
( equalish(e_4,e_2)
| equalish(e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_106,c_4079]) ).
tff(c_4125,plain,
( equalish(e_4,e_2)
| equalish(e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4104]) ).
tff(c_4126,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_14,c_30,c_4125]) ).
tff(c_4532,plain,
product(e_1,e_4,e_1),
inference(splitLeft,[status(thm)],[c_4126]) ).
tff(c_4545,plain,
equalish(e_4,e_1),
inference(resolution,[status(thm)],[c_4532,c_49]) ).
tff(c_4561,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_4545]) ).
tff(c_4562,plain,
product(e_1,e_4,e_2),
inference(splitRight,[status(thm)],[c_4126]) ).
tff(c_2978,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_4,e_2) ),
inference(resolution,[status(thm)],[c_2930,c_40]) ).
tff(c_4639,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_4562,c_2978]) ).
tff(c_4658,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_4639]) ).
tff(c_4659,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3) ),
inference(splitRight,[status(thm)],[c_3044]) ).
tff(c_4661,plain,
product(e_4,e_2,e_3),
inference(splitLeft,[status(thm)],[c_4659]) ).
tff(c_4867,plain,
! [Z1_170] :
( product(Z1_170,e_3,e_4)
| ~ product(e_2,e_4,Z1_170) ),
inference(resolution,[status(thm)],[c_4661,c_44]) ).
tff(c_4884,plain,
( product(e_3,e_3,e_4)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_106,c_4867]) ).
tff(c_4906,plain,
( product(e_3,e_3,e_4)
| equalish(e_2,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4884]) ).
tff(c_4907,plain,
( product(e_3,e_3,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_20,c_4906]) ).
tff(c_4971,plain,
product(e_2,e_4,e_1),
inference(splitLeft,[status(thm)],[c_4907]) ).
tff(c_5373,plain,
! [Z1_183] :
( product(Z1_183,e_1,e_2)
| ~ product(e_4,e_2,Z1_183) ),
inference(resolution,[status(thm)],[c_4971,c_44]) ).
tff(c_5382,plain,
product(e_3,e_1,e_2),
inference(resolution,[status(thm)],[c_4661,c_5373]) ).
tff(c_2979,plain,
! [W_8] :
( equalish(W_8,e_4)
| ~ product(e_3,W_8,e_2) ),
inference(resolution,[status(thm)],[c_2930,c_38]) ).
tff(c_5395,plain,
equalish(e_1,e_4),
inference(resolution,[status(thm)],[c_5382,c_2979]) ).
tff(c_5414,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_5395]) ).
tff(c_5415,plain,
( product(e_2,e_4,e_2)
| product(e_3,e_3,e_4) ),
inference(splitRight,[status(thm)],[c_4907]) ).
tff(c_5518,plain,
product(e_3,e_3,e_4),
inference(splitLeft,[status(thm)],[c_5415]) ).
tff(c_5531,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_5518,c_69]) ).
tff(c_5552,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_5531]) ).
tff(c_5553,plain,
product(e_2,e_4,e_2),
inference(splitRight,[status(thm)],[c_5415]) ).
tff(c_5567,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_5553,c_2978]) ).
tff(c_5587,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_5567]) ).
tff(c_5588,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_4659]) ).
tff(c_5650,plain,
product(e_4,e_3,e_2),
inference(splitLeft,[status(thm)],[c_5588]) ).
tff(c_5663,plain,
product(e_2,e_2,e_3),
inference(resolution,[status(thm)],[c_5650,c_2976]) ).
tff(c_5680,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_5663,c_69]) ).
tff(c_5696,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_5680]) ).
tff(c_5697,plain,
product(e_4,e_3,e_3),
inference(splitRight,[status(thm)],[c_5588]) ).
tff(c_5810,plain,
equalish(e_4,e_3),
inference(resolution,[status(thm)],[c_5697,c_58]) ).
tff(c_5825,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_5810]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP126-1.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % 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
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 3 21:51:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 6.94/2.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.94/2.71
% 6.94/2.71 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.22/2.76
% 7.22/2.76 Inference rules
% 7.22/2.76 ----------------------
% 7.22/2.76 #Ref : 0
% 7.22/2.76 #Sup : 1060
% 7.22/2.76 #Fact : 0
% 7.22/2.76 #Define : 0
% 7.22/2.76 #Split : 13
% 7.22/2.76 #Chain : 0
% 7.22/2.76 #Close : 0
% 7.22/2.76
% 7.22/2.76 Ordering : KBO
% 7.22/2.76
% 7.22/2.76 Simplification rules
% 7.22/2.76 ----------------------
% 7.22/2.76 #Subsume : 80
% 7.22/2.76 #Demod : 1173
% 7.22/2.76 #Tautology : 489
% 7.22/2.76 #SimpNegUnit : 421
% 7.22/2.76 #BackRed : 0
% 7.22/2.76
% 7.22/2.76 #Partial instantiations: 0
% 7.22/2.76 #Strategies tried : 1
% 7.22/2.76
% 7.22/2.76 Timing (in seconds)
% 7.22/2.76 ----------------------
% 7.22/2.77 Preprocessing : 0.47
% 7.22/2.77 Parsing : 0.27
% 7.22/2.77 CNF conversion : 0.02
% 7.22/2.77 Main loop : 1.21
% 7.22/2.77 Inferencing : 0.41
% 7.22/2.77 Reduction : 0.34
% 7.22/2.77 Demodulation : 0.21
% 7.22/2.77 BG Simplification : 0.04
% 7.22/2.77 Subsumption : 0.35
% 7.22/2.77 Abstraction : 0.04
% 7.22/2.77 MUC search : 0.00
% 7.22/2.77 Cooper : 0.00
% 7.22/2.77 Total : 1.76
% 7.22/2.77 Index Insertion : 0.00
% 7.22/2.77 Index Deletion : 0.00
% 7.22/2.77 Index Matching : 0.00
% 7.22/2.77 BG Taut test : 0.00
%------------------------------------------------------------------------------