TSTP Solution File: GRP128-1.003 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP128-1.003 : 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 : n017.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 10:40:06 EDT 2023
% Result : Unsatisfiable 6.14s 2.51s
% Output : CNFRefutation 6.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of formulae : 125 ( 48 unt; 6 typ; 0 def)
% Number of atoms : 296 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 285 ( 108 ~; 177 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 89 (; 89 !; 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_42,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_33,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_34,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_58,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_40,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_36,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_44,axiom,
~ equalish(e_3,e_1),
file(unknown,unknown) ).
tff(f_32,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_46,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_90,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Z1,Y,Z2)
| product(X,Z1,Z2) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_74,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_38,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(c_14,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_4,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_6,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_34]) ).
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_58]) ).
tff(c_12,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_8,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_16,plain,
~ equalish(e_3,e_1),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_2,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_18,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_46]) ).
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_58]) ).
tff(c_28,plain,
! [X_15,Z1_17,Z2_18,Y_16] :
( product(X_15,Z1_17,Z2_18)
| ~ product(Z1_17,Y_16,Z2_18)
| ~ product(X_15,Y_16,Z1_17) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_59,plain,
! [X_46,X_47,Y_48] :
( product(X_46,X_47,e_3)
| ~ product(X_46,Y_48,X_47)
| product(X_47,Y_48,e_2)
| product(X_47,Y_48,e_1)
| ~ group_element(Y_48)
| ~ group_element(X_47) ),
inference(resolution,[status(thm)],[c_33,c_28]) ).
tff(c_61,plain,
! [X_1,Y_2] :
( product(X_1,e_3,e_3)
| product(e_3,Y_2,e_2)
| product(e_3,Y_2,e_1)
| ~ group_element(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(resolution,[status(thm)],[c_20,c_59]) ).
tff(c_64,plain,
! [X_1,Y_2] :
( product(X_1,e_3,e_3)
| product(e_3,Y_2,e_2)
| product(e_3,Y_2,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(demodulation,[status(thm),theory(equality)],[c_6,c_61]) ).
tff(c_76,plain,
! [Y_2] :
( product(e_3,e_3,e_3)
| product(e_3,Y_2,e_1)
| ~ group_element(Y_2)
| ~ group_element(e_3)
| product(e_3,Y_2,e_2) ),
inference(factorization,[status(thm),theory(equality)],[c_64]) ).
tff(c_79,plain,
! [Y_2] :
( product(e_3,e_3,e_3)
| product(e_3,Y_2,e_1)
| ~ group_element(Y_2)
| product(e_3,Y_2,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_76]) ).
tff(c_158,plain,
product(e_3,e_3,e_3),
inference(splitLeft,[status(thm)],[c_79]) ).
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_82]) ).
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_166,plain,
! [X_35] :
( equalish(e_3,X_35)
| product(X_35,e_3,e_2)
| product(X_35,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_158,c_43]) ).
tff(c_186,plain,
! [X_35] :
( equalish(e_3,X_35)
| product(X_35,e_3,e_2)
| product(X_35,e_3,e_1)
| ~ group_element(X_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_166]) ).
tff(c_337,plain,
! [X_57] :
( equalish(e_3,X_57)
| product(X_57,e_3,e_2)
| product(X_57,e_3,e_1)
| ~ group_element(X_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_166]) ).
tff(c_1493,plain,
! [X_100,X_101] :
( product(X_100,X_101,e_2)
| ~ product(X_100,e_3,X_101)
| equalish(e_3,X_101)
| product(X_101,e_3,e_1)
| ~ group_element(X_101) ),
inference(resolution,[status(thm)],[c_337,c_28]) ).
tff(c_1515,plain,
! [X_35] :
( product(X_35,e_2,e_2)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_2)
| equalish(e_3,X_35)
| product(X_35,e_3,e_1)
| ~ group_element(X_35) ),
inference(resolution,[status(thm)],[c_186,c_1493]) ).
tff(c_1563,plain,
! [X_35] :
( product(X_35,e_2,e_2)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,X_35)
| product(X_35,e_3,e_1)
| ~ group_element(X_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1515]) ).
tff(c_1564,plain,
! [X_35] :
( product(X_35,e_2,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,X_35)
| product(X_35,e_3,e_1)
| ~ group_element(X_35) ),
inference(negUnitSimplification,[status(thm)],[c_18,c_1563]) ).
tff(c_1693,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_1564]) ).
tff(c_365,plain,
! [X_15,X_57] :
( product(X_15,X_57,e_2)
| ~ product(X_15,e_3,X_57)
| equalish(e_3,X_57)
| product(X_57,e_3,e_1)
| ~ group_element(X_57) ),
inference(resolution,[status(thm)],[c_337,c_28]) ).
tff(c_1697,plain,
( product(e_2,e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_1693,c_365]) ).
tff(c_1720,plain,
( product(e_2,e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1697]) ).
tff(c_1721,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_3,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_16,c_1720]) ).
tff(c_1921,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_1721]) ).
tff(c_1738,plain,
! [W_11] :
( equalish(W_11,e_2)
| ~ product(W_11,e_3,e_1) ),
inference(resolution,[status(thm)],[c_1693,c_26]) ).
tff(c_1924,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_1921,c_1738]) ).
tff(c_1948,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_1924]) ).
tff(c_1949,plain,
product(e_2,e_1,e_2),
inference(splitRight,[status(thm)],[c_1721]) ).
tff(c_2442,plain,
! [X_122] :
( product(X_122,e_2,e_2)
| ~ product(X_122,e_1,e_2) ),
inference(resolution,[status(thm)],[c_1949,c_28]) ).
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_74]) ).
tff(c_2003,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_2,W_8,e_2) ),
inference(resolution,[status(thm)],[c_1949,c_24]) ).
tff(c_2446,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[c_2442,c_2003]) ).
tff(c_2486,plain,
equalish(e_2,e_1),
inference(demodulation,[status(thm),theory(equality)],[c_1949,c_2446]) ).
tff(c_2488,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_2486]) ).
tff(c_2490,plain,
~ product(e_2,e_3,e_1),
inference(splitRight,[status(thm)],[c_1564]) ).
tff(c_2504,plain,
! [X_126] :
( product(X_126,e_2,e_2)
| equalish(e_3,X_126)
| product(X_126,e_3,e_1)
| ~ group_element(X_126) ),
inference(splitRight,[status(thm)],[c_1564]) ).
tff(c_2507,plain,
( product(e_2,e_2,e_2)
| equalish(e_3,e_2)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_2504,c_2490]) ).
tff(c_2543,plain,
( product(e_2,e_2,e_2)
| equalish(e_3,e_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2507]) ).
tff(c_2544,plain,
product(e_2,e_2,e_2),
inference(negUnitSimplification,[status(thm)],[c_18,c_2543]) ).
tff(c_191,plain,
! [W_51] :
( equalish(W_51,e_3)
| ~ product(W_51,e_3,e_3) ),
inference(resolution,[status(thm)],[c_158,c_26]) ).
tff(c_201,plain,
! [X_1] :
( equalish(X_1,e_3)
| product(X_1,e_3,e_2)
| product(X_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_1) ),
inference(resolution,[status(thm)],[c_20,c_191]) ).
tff(c_430,plain,
! [X_61] :
( equalish(X_61,e_3)
| product(X_61,e_3,e_2)
| product(X_61,e_3,e_1)
| ~ group_element(X_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_201]) ).
tff(c_464,plain,
! [W_8,X_61] :
( equalish(W_8,e_3)
| ~ product(X_61,W_8,e_2)
| equalish(X_61,e_3)
| product(X_61,e_3,e_1)
| ~ group_element(X_61) ),
inference(resolution,[status(thm)],[c_430,c_24]) ).
tff(c_2589,plain,
( equalish(e_2,e_3)
| product(e_2,e_3,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_2544,c_464]) ).
tff(c_2616,plain,
( equalish(e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2589]) ).
tff(c_2618,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2490,c_14,c_2616]) ).
tff(c_2620,plain,
~ product(e_3,e_3,e_3),
inference(splitRight,[status(thm)],[c_79]) ).
tff(c_2626,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_20,c_2620]) ).
tff(c_2632,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2626]) ).
tff(c_2696,plain,
product(e_3,e_3,e_1),
inference(splitLeft,[status(thm)],[c_2632]) ).
tff(c_2858,plain,
! [X_136] :
( product(X_136,e_3,e_1)
| ~ product(X_136,e_3,e_3) ),
inference(resolution,[status(thm)],[c_2696,c_28]) ).
tff(c_2865,plain,
! [X_1] :
( product(X_1,e_3,e_2)
| product(X_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_1) ),
inference(resolution,[status(thm)],[c_20,c_2858]) ).
tff(c_2869,plain,
! [X_1] :
( product(X_1,e_3,e_2)
| product(X_1,e_3,e_1)
| ~ group_element(X_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2865]) ).
tff(c_10,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_2619,plain,
! [Y_2] :
( product(e_3,Y_2,e_1)
| ~ group_element(Y_2)
| product(e_3,Y_2,e_2) ),
inference(splitRight,[status(thm)],[c_79]) ).
tff(c_42,plain,
! [X_15,X_35,Y_36] :
( product(X_15,X_35,e_3)
| ~ product(X_15,Y_36,X_35)
| 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_2698,plain,
( product(e_3,e_1,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_2696,c_42]) ).
tff(c_2711,plain,
( product(e_3,e_1,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_2698]) ).
tff(c_2934,plain,
product(e_1,e_3,e_1),
inference(splitLeft,[status(thm)],[c_2711]) ).
tff(c_2717,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_3,e_1) ),
inference(resolution,[status(thm)],[c_2696,c_26]) ).
tff(c_2937,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_2934,c_2717]) ).
tff(c_2953,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_2937]) ).
tff(c_2954,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_1,e_3) ),
inference(splitRight,[status(thm)],[c_2711]) ).
tff(c_2957,plain,
product(e_3,e_1,e_3),
inference(splitLeft,[status(thm)],[c_2954]) ).
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_66]) ).
tff(c_3004,plain,
! [W_140] :
( equalish(W_140,e_3)
| ~ product(e_3,e_1,W_140) ),
inference(resolution,[status(thm)],[c_2957,c_22]) ).
tff(c_3011,plain,
( equalish(e_2,e_3)
| product(e_3,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_2619,c_3004]) ).
tff(c_3036,plain,
( equalish(e_2,e_3)
| product(e_3,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3011]) ).
tff(c_3037,plain,
product(e_3,e_1,e_1),
inference(negUnitSimplification,[status(thm)],[c_14,c_3036]) ).
tff(c_2989,plain,
! [W_5] :
( equalish(W_5,e_3)
| ~ product(e_3,e_1,W_5) ),
inference(resolution,[status(thm)],[c_2957,c_22]) ).
tff(c_3059,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[c_3037,c_2989]) ).
tff(c_3078,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_3059]) ).
tff(c_3079,plain,
product(e_1,e_3,e_2),
inference(splitRight,[status(thm)],[c_2954]) ).
tff(c_3110,plain,
! [W_141] :
( equalish(W_141,e_1)
| ~ product(W_141,e_3,e_2) ),
inference(resolution,[status(thm)],[c_3079,c_26]) ).
tff(c_3550,plain,
! [X_152] :
( equalish(X_152,e_1)
| product(X_152,e_3,e_1)
| ~ group_element(X_152) ),
inference(resolution,[status(thm)],[c_2869,c_3110]) ).
tff(c_3689,plain,
! [X_155] :
( equalish(X_155,e_3)
| equalish(X_155,e_1)
| ~ group_element(X_155) ),
inference(resolution,[status(thm)],[c_3550,c_2717]) ).
tff(c_3695,plain,
( equalish(e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_3689,c_14]) ).
tff(c_3701,plain,
equalish(e_2,e_1),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3695]) ).
tff(c_3703,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_3701]) ).
tff(c_3704,plain,
product(e_3,e_3,e_2),
inference(splitRight,[status(thm)],[c_2632]) ).
tff(c_3939,plain,
! [X_162] :
( product(X_162,e_3,e_2)
| ~ product(X_162,e_3,e_3) ),
inference(resolution,[status(thm)],[c_3704,c_28]) ).
tff(c_3946,plain,
! [X_1] :
( product(X_1,e_3,e_2)
| product(X_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_1) ),
inference(resolution,[status(thm)],[c_20,c_3939]) ).
tff(c_4033,plain,
! [X_165] :
( product(X_165,e_3,e_2)
| product(X_165,e_3,e_1)
| ~ group_element(X_165) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_3946]) ).
tff(c_3726,plain,
! [W_11] :
( equalish(W_11,e_3)
| ~ product(W_11,e_3,e_2) ),
inference(resolution,[status(thm)],[c_3704,c_26]) ).
tff(c_4065,plain,
! [X_165] :
( equalish(X_165,e_3)
| product(X_165,e_3,e_1)
| ~ group_element(X_165) ),
inference(resolution,[status(thm)],[c_4033,c_3726]) ).
tff(c_3707,plain,
( product(e_3,e_2,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_3704,c_42]) ).
tff(c_3720,plain,
( product(e_3,e_2,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_3707]) ).
tff(c_4116,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_3720]) ).
tff(c_4140,plain,
! [W_167] :
( equalish(W_167,e_2)
| ~ product(W_167,e_3,e_1) ),
inference(resolution,[status(thm)],[c_4116,c_26]) ).
tff(c_4464,plain,
! [X_176] :
( equalish(X_176,e_2)
| equalish(X_176,e_3)
| ~ group_element(X_176) ),
inference(resolution,[status(thm)],[c_4065,c_4140]) ).
tff(c_4467,plain,
( equalish(e_1,e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_4464,c_10]) ).
tff(c_4473,plain,
equalish(e_1,e_2),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4467]) ).
tff(c_4475,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_4473]) ).
tff(c_4477,plain,
~ product(e_2,e_3,e_1),
inference(splitRight,[status(thm)],[c_3720]) ).
tff(c_4480,plain,
( equalish(e_2,e_3)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_4065,c_4477]) ).
tff(c_4483,plain,
equalish(e_2,e_3),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4480]) ).
tff(c_4485,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_4483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP128-1.003 : TPTP v8.1.2. Released v1.2.0.
% 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
% 0.13/0.36 % Computer : n017.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 3 21:48:36 EDT 2023
% 0.13/0.36 % CPUTime :
% 6.14/2.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.14/2.52
% 6.14/2.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.26/2.56
% 6.26/2.56 Inference rules
% 6.26/2.56 ----------------------
% 6.26/2.56 #Ref : 0
% 6.26/2.56 #Sup : 821
% 6.26/2.56 #Fact : 12
% 6.26/2.56 #Define : 0
% 6.26/2.56 #Split : 9
% 6.26/2.56 #Chain : 0
% 6.26/2.56 #Close : 0
% 6.26/2.56
% 6.26/2.56 Ordering : KBO
% 6.26/2.56
% 6.26/2.56 Simplification rules
% 6.26/2.56 ----------------------
% 6.26/2.56 #Subsume : 87
% 6.26/2.56 #Demod : 852
% 6.26/2.56 #Tautology : 280
% 6.26/2.56 #SimpNegUnit : 229
% 6.26/2.57 #BackRed : 0
% 6.26/2.57
% 6.26/2.57 #Partial instantiations: 0
% 6.26/2.57 #Strategies tried : 1
% 6.26/2.57
% 6.26/2.57 Timing (in seconds)
% 6.26/2.57 ----------------------
% 6.26/2.57 Preprocessing : 0.42
% 6.26/2.57 Parsing : 0.24
% 6.26/2.57 CNF conversion : 0.02
% 6.26/2.57 Main loop : 0.93
% 6.26/2.57 Inferencing : 0.33
% 6.26/2.57 Reduction : 0.25
% 6.26/2.57 Demodulation : 0.16
% 6.26/2.57 BG Simplification : 0.04
% 6.26/2.57 Subsumption : 0.25
% 6.26/2.57 Abstraction : 0.04
% 6.26/2.57 MUC search : 0.00
% 6.26/2.57 Cooper : 0.00
% 6.26/2.57 Total : 1.42
% 6.26/2.57 Index Insertion : 0.00
% 6.26/2.57 Index Deletion : 0.00
% 6.26/2.57 Index Matching : 0.00
% 6.26/2.57 BG Taut test : 0.00
%------------------------------------------------------------------------------