%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP132-2.002 : TPTP v9.0.0. 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 : n013.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 : Wed Apr 9 06:25:17 PM UTC 2025
% Result : Unsatisfiable 39.91s 28.20s
% Output : CNFRefutation 39.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 261 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 341 ( 141 ~; 200 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 121 ( 121 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > next > greater > equalish > group_element > #nlpp > e_2 > e_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(group_element,type,
group_element: $i > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(e_2,type,
e_2: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(next,type,
next: ( $i * $i ) > $o ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_46,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_45,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2) ),
file(unknown,unknown) ).
tff(f_84,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_48,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_112,axiom,
! [Y1,X1,Z2,Y2,X2,Z1] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(Y1,Y2) ),
file(unknown,unknown) ).
tff(f_76,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_50,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(c_10,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_8,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_16,plain,
! [X_4,Y_5] :
( product(X_4,Y_5,e_2)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_35,plain,
! [X_46,Y_47] :
( product(X_46,Y_47,e_2)
| product(X_46,Y_47,e_1)
| ~ group_element(Y_47)
| ~ group_element(X_46) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_22,plain,
! [W_14,Z_17,Y_15,X_16] :
( equalish(W_14,Z_17)
| ~ product(Z_17,Y_15,X_16)
| ~ product(W_14,Y_15,X_16) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_89,plain,
! [W_70,X_71,Y_72] :
( equalish(W_70,X_71)
| ~ product(W_70,Y_72,e_2)
| product(X_71,Y_72,e_1)
| ~ group_element(Y_72)
| ~ group_element(X_71) ),
inference(resolution,[status(thm)],[c_35,c_22]) ).
tff(c_92,plain,
! [X_4,X_71,Y_5] :
( equalish(X_4,X_71)
| product(X_71,Y_5,e_1)
| ~ group_element(X_71)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_16,c_89]) ).
tff(c_12,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_246,plain,
! [X_97,X_98,Y_99] :
( equalish(X_97,X_98)
| product(X_98,Y_99,e_1)
| ~ group_element(X_98)
| product(X_97,Y_99,e_1)
| ~ group_element(Y_99)
| ~ group_element(X_97) ),
inference(resolution,[status(thm)],[c_16,c_89]) ).
tff(c_68,plain,
! [X2_55,Z1_53,X1_54,Y1_56,Y2_52,Z2_51] :
( equalish(Y1_56,Y2_52)
| ~ product(Z2_51,X2_55,Y2_52)
| ~ product(Z2_51,X1_54,Y1_56)
| ~ product(X2_55,Y2_52,Z1_53)
| ~ product(X1_54,Y1_56,Z1_53) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_74,plain,
! [Z1_53,X_4,X1_54,Y1_56,Y_5] :
( equalish(Y1_56,e_2)
| ~ product(X_4,X1_54,Y1_56)
| ~ product(Y_5,e_2,Z1_53)
| ~ product(X1_54,Y1_56,Z1_53)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_16,c_68]) ).
tff(c_252,plain,
! [X_97,Z1_53,Y_99,X_98,Y_5] :
( equalish(e_1,e_2)
| ~ product(Y_5,e_2,Z1_53)
| ~ product(Y_99,e_1,Z1_53)
| product(X_98,Y_5,e_1)
| ~ group_element(Y_5)
| equalish(X_97,X_98)
| ~ group_element(X_98)
| product(X_97,Y_99,e_1)
| ~ group_element(Y_99)
| ~ group_element(X_97) ),
inference(resolution,[status(thm)],[c_246,c_74]) ).
tff(c_575,plain,
! [X_163,Z1_167,Y_166,X_164,Y_165] :
( ~ product(Y_166,e_2,Z1_167)
| ~ product(Y_165,e_1,Z1_167)
| product(X_163,Y_166,e_1)
| ~ group_element(Y_166)
| equalish(X_164,X_163)
| ~ group_element(X_163)
| product(X_164,Y_165,e_1)
| ~ group_element(Y_165)
| ~ group_element(X_164) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_252]) ).
tff(c_590,plain,
! [Y_165,X_163,X_4,X_164] :
( ~ product(Y_165,e_1,e_2)
| product(X_163,X_4,e_1)
| equalish(X_164,X_163)
| ~ group_element(X_163)
| product(X_164,Y_165,e_1)
| ~ group_element(Y_165)
| ~ group_element(X_164)
| product(X_4,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_16,c_575]) ).
tff(c_29978,plain,
! [Y_696,X_697,X_698,X_699] :
( ~ product(Y_696,e_1,e_2)
| product(X_697,X_698,e_1)
| equalish(X_699,X_697)
| ~ group_element(X_697)
| product(X_699,Y_696,e_1)
| ~ group_element(Y_696)
| ~ group_element(X_699)
| product(X_698,e_2,e_1)
| ~ group_element(X_698) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_590]) ).
tff(c_29981,plain,
! [X_697,X_698,X_699,X_4] :
( product(X_697,X_698,e_1)
| equalish(X_699,X_697)
| ~ group_element(X_697)
| product(X_699,X_4,e_1)
| ~ group_element(X_699)
| product(X_698,e_2,e_1)
| ~ group_element(X_698)
| product(X_4,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_16,c_29978]) ).
tff(c_29984,plain,
! [X_697,X_698,X_699,X_4] :
( product(X_697,X_698,e_1)
| equalish(X_699,X_697)
| ~ group_element(X_697)
| product(X_699,X_4,e_1)
| ~ group_element(X_699)
| product(X_698,e_2,e_1)
| ~ group_element(X_698)
| product(X_4,e_1,e_1)
| ~ group_element(X_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_29981]) ).
tff(c_38171,plain,
! [X_697,X_698] :
( product(X_697,X_698,e_1)
| equalish(e_1,X_697)
| ~ group_element(X_697)
| product(X_698,e_2,e_1)
| ~ group_element(X_698)
| ~ group_element(e_1)
| product(e_1,e_1,e_1) ),
inference(factorization,[status(thm),theory(equality)],[c_29984]) ).
tff(c_38174,plain,
! [X_697,X_698] :
( product(X_697,X_698,e_1)
| equalish(e_1,X_697)
| ~ group_element(X_697)
| product(X_698,e_2,e_1)
| ~ group_element(X_698)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_38171]) ).
tff(c_39873,plain,
product(e_1,e_1,e_1),
inference(splitLeft,[status(thm)],[c_38174]) ).
tff(c_20,plain,
! [W_11,Z_13,X_10,Y_12] :
( equalish(W_11,Z_13)
| ~ product(X_10,Z_13,Y_12)
| ~ product(X_10,W_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_300,plain,
! [W_11,Y_99,X_97,X_98] :
( equalish(W_11,Y_99)
| ~ product(X_97,W_11,e_1)
| equalish(X_97,X_98)
| product(X_98,Y_99,e_1)
| ~ group_element(X_98)
| ~ group_element(Y_99)
| ~ group_element(X_97) ),
inference(resolution,[status(thm)],[c_246,c_20]) ).
tff(c_40053,plain,
! [Y_99,X_98] :
( equalish(e_1,Y_99)
| equalish(e_1,X_98)
| product(X_98,Y_99,e_1)
| ~ group_element(X_98)
| ~ group_element(Y_99)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_39873,c_300]) ).
tff(c_40353,plain,
! [Y_99,X_98] :
( equalish(e_1,Y_99)
| equalish(e_1,X_98)
| product(X_98,Y_99,e_1)
| ~ group_element(X_98)
| ~ group_element(Y_99) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_40053]) ).
tff(c_40071,plain,
! [Y_5,Z1_53] :
( equalish(e_1,e_2)
| ~ product(Y_5,e_2,Z1_53)
| ~ product(e_1,e_1,Z1_53)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_39873,c_74]) ).
tff(c_40380,plain,
! [Y_5,Z1_53] :
( equalish(e_1,e_2)
| ~ product(Y_5,e_2,Z1_53)
| ~ product(e_1,e_1,Z1_53)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_40071]) ).
tff(c_42818,plain,
! [Y_798,Z1_799] :
( ~ product(Y_798,e_2,Z1_799)
| ~ product(e_1,e_1,Z1_799)
| product(e_1,Y_798,e_1)
| ~ group_element(Y_798) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_40380]) ).
tff(c_42821,plain,
! [X_98] :
( ~ product(e_1,e_1,e_1)
| product(e_1,X_98,e_1)
| equalish(e_1,e_2)
| equalish(e_1,X_98)
| ~ group_element(X_98)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_40353,c_42818]) ).
tff(c_43111,plain,
! [X_98] :
( product(e_1,X_98,e_1)
| equalish(e_1,e_2)
| equalish(e_1,X_98)
| ~ group_element(X_98) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_39873,c_42821]) ).
tff(c_43401,plain,
! [X_800] :
( product(e_1,X_800,e_1)
| equalish(e_1,X_800)
| ~ group_element(X_800) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_43111]) ).
tff(c_40388,plain,
! [W_11] :
( equalish(W_11,e_1)
| ~ product(e_1,W_11,e_1) ),
inference(resolution,[status(thm)],[c_39873,c_20]) ).
tff(c_44526,plain,
! [X_806] :
( equalish(X_806,e_1)
| equalish(e_1,X_806)
| ~ group_element(X_806) ),
inference(resolution,[status(thm)],[c_43401,c_40388]) ).
tff(c_14,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_44529,plain,
( equalish(e_1,e_2)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_44526,c_14]) ).
tff(c_44533,plain,
equalish(e_1,e_2),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_44529]) ).
tff(c_44535,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_44533]) ).
tff(c_44537,plain,
~ product(e_1,e_1,e_1),
inference(splitRight,[status(thm)],[c_38174]) ).
tff(c_44809,plain,
! [X_4] :
( equalish(X_4,e_1)
| product(X_4,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_92,c_44537]) ).
tff(c_45088,plain,
! [X_4] :
( equalish(X_4,e_1)
| product(X_4,e_1,e_1)
| ~ group_element(X_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_44809]) ).
tff(c_85,plain,
! [W_67,Y_68,X_69] :
( equalish(W_67,Y_68)
| ~ product(X_69,W_67,e_2)
| product(X_69,Y_68,e_1)
| ~ group_element(Y_68)
| ~ group_element(X_69) ),
inference(resolution,[status(thm)],[c_35,c_20]) ).
tff(c_88,plain,
! [Y_5,Y_68,X_4] :
( equalish(Y_5,Y_68)
| product(X_4,Y_68,e_1)
| ~ group_element(Y_68)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_16,c_85]) ).
tff(c_44815,plain,
! [Y_5] :
( equalish(Y_5,e_1)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_88,c_44537]) ).
tff(c_45094,plain,
! [Y_5] :
( equalish(Y_5,e_1)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_44815]) ).
tff(c_46911,plain,
! [Y_812] :
( equalish(Y_812,e_1)
| product(e_1,Y_812,e_1)
| ~ group_element(Y_812) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_44815]) ).
tff(c_47136,plain,
! [Y_5,Z1_53,Y_812] :
( equalish(e_1,e_2)
| ~ product(Y_5,e_2,Z1_53)
| ~ product(Y_812,e_1,Z1_53)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(e_1)
| equalish(Y_812,e_1)
| ~ group_element(Y_812) ),
inference(resolution,[status(thm)],[c_46911,c_74]) ).
tff(c_47409,plain,
! [Y_5,Z1_53,Y_812] :
( equalish(e_1,e_2)
| ~ product(Y_5,e_2,Z1_53)
| ~ product(Y_812,e_1,Z1_53)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5)
| equalish(Y_812,e_1)
| ~ group_element(Y_812) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_47136]) ).
tff(c_55137,plain,
! [Y_850,Z1_851,Y_852] :
( ~ product(Y_850,e_2,Z1_851)
| ~ product(Y_852,e_1,Z1_851)
| product(e_1,Y_850,e_1)
| ~ group_element(Y_850)
| equalish(Y_852,e_1)
| ~ group_element(Y_852) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_47409]) ).
tff(c_55140,plain,
! [Y_852] :
( ~ product(Y_852,e_1,e_1)
| product(e_1,e_1,e_1)
| ~ group_element(e_1)
| equalish(Y_852,e_1)
| ~ group_element(Y_852)
| equalish(e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_45094,c_55137]) ).
tff(c_55433,plain,
! [Y_852] :
( ~ product(Y_852,e_1,e_1)
| product(e_1,e_1,e_1)
| equalish(Y_852,e_1)
| ~ group_element(Y_852)
| equalish(e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_55140]) ).
tff(c_55740,plain,
! [Y_855] :
( ~ product(Y_855,e_1,e_1)
| equalish(Y_855,e_1)
| ~ group_element(Y_855) ),
inference(negUnitSimplification,[status(thm)],[c_14,c_44537,c_55433]) ).
tff(c_56426,plain,
! [X_856] :
( equalish(X_856,e_1)
| ~ group_element(X_856) ),
inference(resolution,[status(thm)],[c_45088,c_55740]) ).
tff(c_56429,plain,
~ group_element(e_2),
inference(resolution,[status(thm)],[c_56426,c_14]) ).
tff(c_56433,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_56429]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP132-2.002 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.11 % 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
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 7 21:27:17 EDT 2025
% 0.11/0.32 % CPUTime :
% 39.91/28.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.91/28.21
% 39.91/28.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------