TSTP Solution File: GRP133-1.003 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP133-1.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : 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 10:40:14 EDT 2023
% Result : Unsatisfiable 9.90s 3.33s
% Output : CNFRefutation 9.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 20
% Syntax : Number of formulae : 207 ( 95 unt; 6 typ; 0 def)
% Number of atoms : 456 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 390 ( 135 ~; 255 |; 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 : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 109 (; 109 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > equalish > group_element > #nlpp > e_3 > e_2 > e_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_40,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_34,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_28,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_30,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_42,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_38,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_36,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_29,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3) ),
file(unknown,unknown) ).
tff(f_86,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,X) ),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_32,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(c_16,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_10,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_2,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_6,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_18,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_14,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_12,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_4,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_20,plain,
! [X_1,Y_2] :
( 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_54]) ).
tff(c_33,plain,
! [X_35,Y_36] :
( product(X_35,Y_36,e_3)
| product(X_35,Y_36,e_2)
| product(X_35,Y_36,e_1)
| ~ group_element(Y_36)
| ~ group_element(X_35) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_28,plain,
! [Z1_17,Z2_18,X_15,Y_16] :
( product(Z1_17,Z2_18,X_15)
| ~ product(Y_16,X_15,Z2_18)
| ~ product(X_15,Y_16,Z1_17) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_59,plain,
! [Z1_46,Y_47,X_48] :
( product(Z1_46,e_3,Y_47)
| ~ product(Y_47,X_48,Z1_46)
| product(X_48,Y_47,e_2)
| product(X_48,Y_47,e_1)
| ~ group_element(Y_47)
| ~ group_element(X_48) ),
inference(resolution,[status(thm)],[c_33,c_28]) ).
tff(c_62,plain,
! [X_1,Y_2] :
( product(e_3,e_3,X_1)
| product(Y_2,X_1,e_2)
| product(Y_2,X_1,e_1)
| product(X_1,Y_2,e_2)
| product(X_1,Y_2,e_1)
| ~ group_element(Y_2)
| ~ group_element(X_1) ),
inference(resolution,[status(thm)],[c_20,c_59]) ).
tff(c_150,plain,
! [Y_51] :
( product(e_3,e_3,Y_51)
| product(Y_51,Y_51,e_1)
| ~ group_element(Y_51)
| product(Y_51,Y_51,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_62]) ).
tff(c_24,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_70]) ).
tff(c_45,plain,
! [W_8,Y_36,X_35] :
( equalish(W_8,Y_36)
| ~ product(X_35,W_8,e_3)
| product(X_35,Y_36,e_2)
| product(X_35,Y_36,e_1)
| ~ group_element(Y_36)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_33,c_24]) ).
tff(c_157,plain,
! [Y_36] :
( equalish(e_3,Y_36)
| product(e_3,Y_36,e_2)
| product(e_3,Y_36,e_1)
| ~ group_element(Y_36)
| product(e_3,e_3,e_1)
| ~ group_element(e_3)
| product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[c_150,c_45]) ).
tff(c_189,plain,
! [Y_36] :
( equalish(e_3,Y_36)
| product(e_3,Y_36,e_2)
| product(e_3,Y_36,e_1)
| ~ group_element(Y_36)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_157]) ).
tff(c_3101,plain,
product(e_3,e_3,e_2),
inference(splitLeft,[status(thm)],[c_189]) ).
tff(c_3622,plain,
! [Z1_148] :
( product(Z1_148,e_2,e_3)
| ~ product(e_3,e_3,Z1_148) ),
inference(resolution,[status(thm)],[c_3101,c_28]) ).
tff(c_3660,plain,
product(e_2,e_2,e_3),
inference(resolution,[status(thm)],[c_3101,c_3622]) ).
tff(c_26,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_78]) ).
tff(c_43,plain,
! [W_11,X_35,Y_36] :
( equalish(W_11,X_35)
| ~ product(W_11,Y_36,e_3)
| product(X_35,Y_36,e_2)
| product(X_35,Y_36,e_1)
| ~ group_element(Y_36)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_33,c_26]) ).
tff(c_3769,plain,
! [X_35] :
( equalish(e_2,X_35)
| product(X_35,e_2,e_2)
| product(X_35,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_3660,c_43]) ).
tff(c_5463,plain,
! [X_167] :
( equalish(e_2,X_167)
| product(X_167,e_2,e_2)
| product(X_167,e_2,e_1)
| ~ group_element(X_167) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3769]) ).
tff(c_3325,plain,
! [W_8] :
( equalish(W_8,e_3)
| ~ product(e_3,W_8,e_2) ),
inference(resolution,[status(thm)],[c_3101,c_24]) ).
tff(c_5478,plain,
( equalish(e_2,e_3)
| product(e_3,e_2,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_5463,c_3325]) ).
tff(c_5541,plain,
( equalish(e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_5478]) ).
tff(c_5542,plain,
product(e_3,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_14,c_5541]) ).
tff(c_42,plain,
! [Z1_17,Y_36,X_35] :
( product(Z1_17,e_3,Y_36)
| ~ product(Y_36,X_35,Z1_17)
| product(X_35,Y_36,e_2)
| product(X_35,Y_36,e_1)
| ~ group_element(Y_36)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_33,c_28]) ).
tff(c_5618,plain,
( product(e_1,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_5542,c_42]) ).
tff(c_5667,plain,
( product(e_1,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_5618]) ).
tff(c_6509,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_5667]) ).
tff(c_5672,plain,
! [Z1_17] :
( product(Z1_17,e_1,e_2)
| ~ product(e_2,e_3,Z1_17) ),
inference(resolution,[status(thm)],[c_5542,c_28]) ).
tff(c_6543,plain,
product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[c_6509,c_5672]) ).
tff(c_75,plain,
! [Y_2] :
( product(e_3,e_3,Y_2)
| product(Y_2,Y_2,e_1)
| ~ group_element(Y_2)
| product(Y_2,Y_2,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_62]) ).
tff(c_1663,plain,
! [Z1_100,Y_101] :
( product(Z1_100,e_2,Y_101)
| ~ product(Y_101,Y_101,Z1_100)
| product(e_3,e_3,Y_101)
| product(Y_101,Y_101,e_1)
| ~ group_element(Y_101) ),
inference(resolution,[status(thm)],[c_150,c_28]) ).
tff(c_1719,plain,
! [Y_102] :
( product(e_2,e_2,Y_102)
| product(e_3,e_3,Y_102)
| product(Y_102,Y_102,e_1)
| ~ group_element(Y_102) ),
inference(resolution,[status(thm)],[c_75,c_1663]) ).
tff(c_22,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_62]) ).
tff(c_1808,plain,
! [W_5,Y_102] :
( equalish(W_5,Y_102)
| ~ product(e_3,e_3,W_5)
| product(e_2,e_2,Y_102)
| product(Y_102,Y_102,e_1)
| ~ group_element(Y_102) ),
inference(resolution,[status(thm)],[c_1719,c_22]) ).
tff(c_3291,plain,
! [Y_102] :
( equalish(e_2,Y_102)
| product(e_2,e_2,Y_102)
| product(Y_102,Y_102,e_1)
| ~ group_element(Y_102) ),
inference(resolution,[status(thm)],[c_3101,c_1808]) ).
tff(c_5676,plain,
! [W_168] :
( equalish(W_168,e_3)
| ~ product(W_168,e_2,e_1) ),
inference(resolution,[status(thm)],[c_5542,c_26]) ).
tff(c_5687,plain,
( equalish(e_2,e_3)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_3291,c_5676]) ).
tff(c_5718,plain,
( equalish(e_2,e_3)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5687]) ).
tff(c_5719,plain,
product(e_1,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_12,c_14,c_5718]) ).
tff(c_5950,plain,
! [W_5] :
( equalish(W_5,e_1)
| ~ product(e_1,e_1,W_5) ),
inference(resolution,[status(thm)],[c_5719,c_22]) ).
tff(c_6597,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_6543,c_5950]) ).
tff(c_6641,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_6597]) ).
tff(c_6642,plain,
( product(e_2,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_5667]) ).
tff(c_6798,plain,
product(e_1,e_3,e_3),
inference(splitLeft,[status(thm)],[c_6642]) ).
tff(c_6814,plain,
( product(e_3,e_3,e_1)
| 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_6798,c_42]) ).
tff(c_6859,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2,c_6814]) ).
tff(c_7044,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_6859]) ).
tff(c_5949,plain,
! [W_11] :
( equalish(W_11,e_1)
| ~ product(W_11,e_1,e_1) ),
inference(resolution,[status(thm)],[c_5719,c_26]) ).
tff(c_7051,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_7044,c_5949]) ).
tff(c_7096,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_7051]) ).
tff(c_7097,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_3,e_1) ),
inference(splitRight,[status(thm)],[c_6859]) ).
tff(c_7258,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7097]) ).
tff(c_5675,plain,
! [W_8] :
( equalish(W_8,e_2)
| ~ product(e_3,W_8,e_1) ),
inference(resolution,[status(thm)],[c_5542,c_24]) ).
tff(c_7265,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_7258,c_5675]) ).
tff(c_7344,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_7265]) ).
tff(c_7345,plain,
product(e_3,e_1,e_2),
inference(splitRight,[status(thm)],[c_7097]) ).
tff(c_7605,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_7345,c_3325]) ).
tff(c_7661,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_7605]) ).
tff(c_7662,plain,
product(e_2,e_3,e_2),
inference(splitRight,[status(thm)],[c_6642]) ).
tff(c_3323,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_3,e_2) ),
inference(resolution,[status(thm)],[c_3101,c_26]) ).
tff(c_7678,plain,
equalish(e_2,e_3),
inference(resolution,[status(thm)],[c_7662,c_3323]) ).
tff(c_7731,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_7678]) ).
tff(c_7732,plain,
! [Y_36] :
( product(e_3,e_3,e_1)
| equalish(e_3,Y_36)
| product(e_3,Y_36,e_2)
| product(e_3,Y_36,e_1)
| ~ group_element(Y_36) ),
inference(splitRight,[status(thm)],[c_189]) ).
tff(c_14578,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7732]) ).
tff(c_14918,plain,
! [Z1_288] :
( product(Z1_288,e_1,e_3)
| ~ product(e_3,e_3,Z1_288) ),
inference(resolution,[status(thm)],[c_14578,c_28]) ).
tff(c_14956,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_14578,c_14918]) ).
tff(c_8,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_8201,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_7732]) ).
tff(c_8639,plain,
! [Z1_210] :
( product(Z1_210,e_1,e_3)
| ~ product(e_3,e_3,Z1_210) ),
inference(resolution,[status(thm)],[c_8201,c_28]) ).
tff(c_8677,plain,
product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[c_8201,c_8639]) ).
tff(c_8717,plain,
! [X_35] :
( equalish(e_1,X_35)
| product(X_35,e_1,e_2)
| product(X_35,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_8677,c_43]) ).
tff(c_8755,plain,
! [X_35] :
( equalish(e_1,X_35)
| product(X_35,e_1,e_2)
| product(X_35,e_1,e_1)
| ~ group_element(X_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8717]) ).
tff(c_10636,plain,
! [X_226] :
( equalish(e_1,X_226)
| product(X_226,e_1,e_2)
| product(X_226,e_1,e_1)
| ~ group_element(X_226) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8717]) ).
tff(c_7733,plain,
~ product(e_3,e_3,e_2),
inference(splitRight,[status(thm)],[c_189]) ).
tff(c_7762,plain,
( product(e_2,e_2,e_1)
| ~ group_element(e_2)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[c_75,c_7733]) ).
tff(c_7795,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_7762]) ).
tff(c_7799,plain,
product(e_2,e_2,e_2),
inference(splitLeft,[status(thm)],[c_7795]) ).
tff(c_7973,plain,
! [W_8] :
( equalish(W_8,e_2)
| ~ product(e_2,W_8,e_2) ),
inference(resolution,[status(thm)],[c_7799,c_24]) ).
tff(c_10651,plain,
( equalish(e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_10636,c_7973]) ).
tff(c_10716,plain,
( equalish(e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10651]) ).
tff(c_10717,plain,
product(e_2,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_8,c_10716]) ).
tff(c_10875,plain,
( product(e_1,e_3,e_2)
| 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_10717,c_42]) ).
tff(c_10904,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4,c_10875]) ).
tff(c_11114,plain,
product(e_1,e_2,e_1),
inference(splitLeft,[status(thm)],[c_10904]) ).
tff(c_10909,plain,
! [Z1_17] :
( product(Z1_17,e_1,e_1)
| ~ product(e_1,e_2,Z1_17) ),
inference(resolution,[status(thm)],[c_10717,c_28]) ).
tff(c_11137,plain,
product(e_1,e_1,e_1),
inference(resolution,[status(thm)],[c_11114,c_10909]) ).
tff(c_10910,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product(W_11,e_1,e_1) ),
inference(resolution,[status(thm)],[c_10717,c_26]) ).
tff(c_11167,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_11137,c_10910]) ).
tff(c_11204,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_11167]) ).
tff(c_11205,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(splitRight,[status(thm)],[c_10904]) ).
tff(c_11312,plain,
product(e_1,e_3,e_2),
inference(splitLeft,[status(thm)],[c_11205]) ).
tff(c_11665,plain,
! [Z1_240] :
( product(Z1_240,e_2,e_3)
| ~ product(e_3,e_1,Z1_240) ),
inference(resolution,[status(thm)],[c_11312,c_28]) ).
tff(c_11668,plain,
( product(e_2,e_2,e_3)
| equalish(e_1,e_3)
| product(e_3,e_1,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_8755,c_11665]) ).
tff(c_11692,plain,
( product(e_2,e_2,e_3)
| equalish(e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_11668]) ).
tff(c_11693,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_1,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_11692]) ).
tff(c_11709,plain,
product(e_3,e_1,e_1),
inference(splitLeft,[status(thm)],[c_11693]) ).
tff(c_11714,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_11709,c_10910]) ).
tff(c_11751,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_11714]) ).
tff(c_11752,plain,
product(e_2,e_2,e_3),
inference(splitRight,[status(thm)],[c_11693]) ).
tff(c_7972,plain,
! [W_5] :
( equalish(W_5,e_2)
| ~ product(e_2,e_2,W_5) ),
inference(resolution,[status(thm)],[c_7799,c_22]) ).
tff(c_11860,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_11752,c_7972]) ).
tff(c_11895,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_11860]) ).
tff(c_11896,plain,
product(e_1,e_2,e_2),
inference(splitRight,[status(thm)],[c_11205]) ).
tff(c_7971,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product(W_11,e_2,e_2) ),
inference(resolution,[status(thm)],[c_7799,c_26]) ).
tff(c_11908,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_11896,c_7971]) ).
tff(c_11949,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_11908]) ).
tff(c_11951,plain,
~ product(e_3,e_3,e_1),
inference(splitRight,[status(thm)],[c_7732]) ).
tff(c_11969,plain,
( product(e_1,e_1,e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[c_75,c_11951]) ).
tff(c_11987,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11969]) ).
tff(c_12089,plain,
product(e_1,e_1,e_2),
inference(splitLeft,[status(thm)],[c_11987]) ).
tff(c_1818,plain,
! [W_5,Y_102] :
( equalish(W_5,e_1)
| ~ product(Y_102,Y_102,W_5)
| product(e_2,e_2,Y_102)
| product(e_3,e_3,Y_102)
| ~ group_element(Y_102) ),
inference(resolution,[status(thm)],[c_1719,c_22]) ).
tff(c_12099,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_3,e_3,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_12089,c_1818]) ).
tff(c_12138,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_3,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12099]) ).
tff(c_12139,plain,
product(e_2,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_11951,c_12,c_12138]) ).
tff(c_12175,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_12139,c_7972]) ).
tff(c_12206,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_12175]) ).
tff(c_12208,plain,
~ product(e_1,e_1,e_2),
inference(splitRight,[status(thm)],[c_11987]) ).
tff(c_12524,plain,
! [Y_255] :
( equalish(e_3,Y_255)
| product(e_3,Y_255,e_2)
| product(e_3,Y_255,e_1)
| ~ group_element(Y_255) ),
inference(splitRight,[status(thm)],[c_7732]) ).
tff(c_12533,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_12524,c_7971]) ).
tff(c_12621,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_12533]) ).
tff(c_12622,plain,
product(e_3,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_18,c_12621]) ).
tff(c_12736,plain,
( product(e_1,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_12622,c_42]) ).
tff(c_12777,plain,
( product(e_1,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_12736]) ).
tff(c_13631,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_12777]) ).
tff(c_12782,plain,
! [Z1_17] :
( product(Z1_17,e_1,e_2)
| ~ product(e_2,e_3,Z1_17) ),
inference(resolution,[status(thm)],[c_12622,c_28]) ).
tff(c_13635,plain,
product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[c_13631,c_12782]) ).
tff(c_13670,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12208,c_13635]) ).
tff(c_13672,plain,
~ product(e_2,e_3,e_1),
inference(splitRight,[status(thm)],[c_12777]) ).
tff(c_46,plain,
! [W_37,X_38,Y_39] :
( equalish(W_37,X_38)
| ~ product(W_37,Y_39,e_3)
| product(X_38,Y_39,e_2)
| product(X_38,Y_39,e_1)
| ~ group_element(Y_39)
| ~ group_element(X_38) ),
inference(resolution,[status(thm)],[c_33,c_26]) ).
tff(c_49,plain,
! [X_1,X_38,Y_2] :
( equalish(X_1,X_38)
| product(X_38,Y_2,e_2)
| product(X_38,Y_2,e_1)
| ~ group_element(X_38)
| product(X_1,Y_2,e_2)
| product(X_1,Y_2,e_1)
| ~ group_element(Y_2)
| ~ group_element(X_1) ),
inference(resolution,[status(thm)],[c_20,c_46]) ).
tff(c_1819,plain,
! [W_8,Y_102] :
( equalish(W_8,Y_102)
| ~ product(Y_102,W_8,e_1)
| product(e_2,e_2,Y_102)
| product(e_3,e_3,Y_102)
| ~ group_element(Y_102) ),
inference(resolution,[status(thm)],[c_1719,c_24]) ).
tff(c_12726,plain,
( equalish(e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_3,e_3)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_12622,c_1819]) ).
tff(c_12757,plain,
( equalish(e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_3,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_12726]) ).
tff(c_12758,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_3,e_3) ),
inference(negUnitSimplification,[status(thm)],[c_14,c_12757]) ).
tff(c_13102,plain,
product(e_3,e_3,e_3),
inference(splitLeft,[status(thm)],[c_12758]) ).
tff(c_13297,plain,
! [W_264] :
( equalish(W_264,e_3)
| ~ product(e_3,e_3,W_264) ),
inference(resolution,[status(thm)],[c_13102,c_22]) ).
tff(c_13342,plain,
! [X_38] :
( equalish(e_2,e_3)
| equalish(e_3,X_38)
| product(X_38,e_3,e_2)
| product(X_38,e_3,e_1)
| ~ group_element(X_38)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_49,c_13297]) ).
tff(c_13383,plain,
! [X_38] :
( equalish(e_2,e_3)
| equalish(e_3,X_38)
| product(X_38,e_3,e_2)
| product(X_38,e_3,e_1)
| ~ group_element(X_38)
| product(e_3,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_13342]) ).
tff(c_13676,plain,
! [X_270] :
( equalish(e_3,X_270)
| product(X_270,e_3,e_2)
| product(X_270,e_3,e_1)
| ~ group_element(X_270) ),
inference(negUnitSimplification,[status(thm)],[c_11951,c_14,c_13383]) ).
tff(c_13698,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_13676,c_7973]) ).
tff(c_13802,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_13698]) ).
tff(c_13804,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13672,c_18,c_13802]) ).
tff(c_13805,plain,
product(e_2,e_2,e_3),
inference(splitRight,[status(thm)],[c_12758]) ).
tff(c_13813,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_13805,c_7972]) ).
tff(c_13848,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_13813]) ).
tff(c_13849,plain,
product(e_2,e_2,e_1),
inference(splitRight,[status(thm)],[c_7795]) ).
tff(c_14143,plain,
! [Z1_277] :
( product(Z1_277,e_1,e_2)
| ~ product(e_2,e_2,Z1_277) ),
inference(resolution,[status(thm)],[c_13849,c_28]) ).
tff(c_14169,plain,
product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[c_13849,c_14143]) ).
tff(c_14258,plain,
! [W_5] :
( equalish(W_5,e_2)
| ~ product(e_1,e_1,W_5) ),
inference(resolution,[status(thm)],[c_14169,c_22]) ).
tff(c_14983,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[c_14956,c_14258]) ).
tff(c_15014,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_14983]) ).
tff(c_15130,plain,
! [Y_292] :
( equalish(e_3,Y_292)
| product(e_3,Y_292,e_2)
| product(e_3,Y_292,e_1)
| ~ group_element(Y_292) ),
inference(splitRight,[status(thm)],[c_7732]) ).
tff(c_14257,plain,
! [W_11] :
( equalish(W_11,e_1)
| ~ product(W_11,e_1,e_2) ),
inference(resolution,[status(thm)],[c_14169,c_26]) ).
tff(c_15139,plain,
( equalish(e_3,e_1)
| product(e_3,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_15130,c_14257]) ).
tff(c_15227,plain,
( equalish(e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15139]) ).
tff(c_15228,plain,
product(e_3,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_16,c_15227]) ).
tff(c_15344,plain,
( 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_15228,c_42]) ).
tff(c_15385,plain,
( 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_15344]) ).
tff(c_16352,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_15385]) ).
tff(c_15390,plain,
! [Z1_17] :
( product(Z1_17,e_1,e_1)
| ~ product(e_1,e_3,Z1_17) ),
inference(resolution,[status(thm)],[c_15228,c_28]) ).
tff(c_16387,plain,
product(e_1,e_1,e_1),
inference(resolution,[status(thm)],[c_16352,c_15390]) ).
tff(c_15391,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_1,e_1) ),
inference(resolution,[status(thm)],[c_15228,c_26]) ).
tff(c_16431,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_16387,c_15391]) ).
tff(c_16470,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_16431]) ).
tff(c_16471,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(splitRight,[status(thm)],[c_15385]) ).
tff(c_16475,plain,
product(e_1,e_3,e_3),
inference(splitLeft,[status(thm)],[c_16471]) ).
tff(c_15334,plain,
( equalish(e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_3,e_3)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_15228,c_1819]) ).
tff(c_15365,plain,
( equalish(e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_3,e_3) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_15334]) ).
tff(c_15366,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_3,e_3) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_15365]) ).
tff(c_15590,plain,
product(e_3,e_3,e_3),
inference(splitLeft,[status(thm)],[c_15366]) ).
tff(c_15717,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_3,e_3) ),
inference(resolution,[status(thm)],[c_15590,c_26]) ).
tff(c_16597,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_16475,c_15717]) ).
tff(c_16637,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_16597]) ).
tff(c_16638,plain,
product(e_1,e_3,e_2),
inference(splitRight,[status(thm)],[c_16471]) ).
tff(c_14259,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_1,W_8,e_2) ),
inference(resolution,[status(thm)],[c_14169,c_24]) ).
tff(c_16650,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_16638,c_14259]) ).
tff(c_16697,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_16650]) ).
tff(c_16698,plain,
product(e_2,e_2,e_3),
inference(splitRight,[status(thm)],[c_15366]) ).
tff(c_13914,plain,
! [W_5] :
( equalish(W_5,e_1)
| ~ product(e_2,e_2,W_5) ),
inference(resolution,[status(thm)],[c_13849,c_22]) ).
tff(c_16704,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[c_16698,c_13914]) ).
tff(c_16735,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16,c_16704]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP133-1.003 : 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
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 22:24:36 EDT 2023
% 0.13/0.35 % CPUTime :
% 9.90/3.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.90/3.35
% 9.90/3.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.90/3.41
% 9.90/3.41 Inference rules
% 9.90/3.41 ----------------------
% 9.90/3.41 #Ref : 0
% 9.90/3.41 #Sup : 3145
% 9.90/3.41 #Fact : 12
% 9.90/3.41 #Define : 0
% 9.90/3.41 #Split : 20
% 9.90/3.41 #Chain : 0
% 9.90/3.41 #Close : 0
% 9.90/3.41
% 9.90/3.41 Ordering : KBO
% 9.90/3.41
% 9.90/3.41 Simplification rules
% 9.90/3.41 ----------------------
% 9.90/3.41 #Subsume : 335
% 9.90/3.41 #Demod : 3651
% 9.90/3.41 #Tautology : 1261
% 9.90/3.41 #SimpNegUnit : 954
% 9.90/3.41 #BackRed : 0
% 9.90/3.41
% 9.90/3.41 #Partial instantiations: 0
% 9.90/3.41 #Strategies tried : 1
% 9.90/3.41
% 9.90/3.41 Timing (in seconds)
% 9.90/3.41 ----------------------
% 9.90/3.41 Preprocessing : 0.40
% 9.90/3.41 Parsing : 0.22
% 9.90/3.41 CNF conversion : 0.02
% 9.90/3.41 Main loop : 1.92
% 9.90/3.41 Inferencing : 0.57
% 9.90/3.41 Reduction : 0.50
% 9.90/3.41 Demodulation : 0.30
% 9.90/3.41 BG Simplification : 0.05
% 9.90/3.41 Subsumption : 0.66
% 9.90/3.41 Abstraction : 0.06
% 9.90/3.41 MUC search : 0.00
% 9.90/3.41 Cooper : 0.00
% 9.90/3.41 Total : 2.41
% 9.90/3.41 Index Insertion : 0.00
% 9.90/3.41 Index Deletion : 0.00
% 9.90/3.41 Index Matching : 0.00
% 9.90/3.41 BG Taut test : 0.00
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