%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP135-2.002 : 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 : n015.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 06:25:19 PM UTC 2025
% Result : Unsatisfiable 4.85s 2.14s
% Output : CNFRefutation 4.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 130 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 57 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 59 ( 59 !; 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_48,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_46,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_43,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_44,axiom,
group_element(e_2),
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) ),
file(unknown,unknown) ).
tff(f_90,axiom,
! [Y,X,Z1,Z2] :
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| product(Z2,Y,X) ),
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_82,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
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_1),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_12,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_8,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_10,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_44]) ).
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_58]) ).
tff(c_60,plain,
! [Z2_41,Y_42,X_43,Z1_44] :
( product(Z2_41,Y_42,X_43)
| ~ product(Z1_44,Y_42,Z2_41)
| ~ product(Y_42,X_43,Z1_44) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_95,plain,
! [Y_57,X_58,X_59] :
( product(e_2,Y_57,X_58)
| ~ product(Y_57,X_58,X_59)
| product(X_59,Y_57,e_1)
| ~ group_element(Y_57)
| ~ group_element(X_59) ),
inference(resolution,[status(thm)],[c_16,c_60]) ).
tff(c_97,plain,
! [X_4,Y_5] :
( product(e_2,X_4,Y_5)
| product(e_2,X_4,e_1)
| ~ group_element(e_2)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_16,c_95]) ).
tff(c_100,plain,
! [X_4,Y_5] :
( product(e_2,X_4,Y_5)
| product(e_2,X_4,e_1)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_97]) ).
tff(c_112,plain,
! [X_4] :
( product(X_4,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X_4)
| product(e_2,X_4,e_1) ),
inference(factorization,[status(thm),theory(equality)],[c_100]) ).
tff(c_207,plain,
! [X_62] :
( product(X_62,e_1,e_1)
| ~ group_element(X_62)
| product(e_2,X_62,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_112]) ).
tff(c_66,plain,
! [Y_5,X_43,X_4] :
( product(e_2,Y_5,X_43)
| ~ product(Y_5,X_43,X_4)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_16,c_60]) ).
tff(c_209,plain,
! [X_62] :
( product(e_1,X_62,e_1)
| ~ group_element(e_1)
| ~ group_element(X_62)
| product(e_2,X_62,e_1) ),
inference(resolution,[status(thm)],[c_207,c_66]) ).
tff(c_234,plain,
! [X_62] :
( product(e_1,X_62,e_1)
| ~ group_element(X_62)
| product(e_2,X_62,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_209]) ).
tff(c_117,plain,
! [X_4] :
( product(X_4,e_1,e_1)
| ~ group_element(X_4)
| product(e_2,X_4,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_112]) ).
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_74]) ).
tff(c_747,plain,
! [W_84,X_85] :
( equalish(W_84,e_1)
| ~ product(X_85,W_84,e_1)
| ~ group_element(X_85)
| product(e_2,X_85,e_1) ),
inference(resolution,[status(thm)],[c_207,c_20]) ).
tff(c_765,plain,
! [X_4] :
( equalish(X_4,e_1)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(X_4,e_1,e_1)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_117,c_747]) ).
tff(c_784,plain,
! [X_4] :
( equalish(X_4,e_1)
| product(e_2,e_2,e_1)
| product(X_4,e_1,e_1)
| ~ group_element(X_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_765]) ).
tff(c_962,plain,
product(e_2,e_2,e_1),
inference(splitLeft,[status(thm)],[c_784]) ).
tff(c_979,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_962,c_66]) ).
tff(c_1010,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_10,c_979]) ).
tff(c_1464,plain,
product(e_1,e_2,e_1),
inference(splitLeft,[status(thm)],[c_1010]) ).
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_82]) ).
tff(c_1017,plain,
! [W_14] :
( equalish(W_14,e_2)
| ~ product(W_14,e_2,e_1) ),
inference(resolution,[status(thm)],[c_962,c_22]) ).
tff(c_1467,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_1464,c_1017]) ).
tff(c_1489,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_1467]) ).
tff(c_1490,plain,
product(e_2,e_2,e_2),
inference(splitRight,[status(thm)],[c_1010]) ).
tff(c_18,plain,
! [W_8,Z_9,X_6,Y_7] :
( equalish(W_8,Z_9)
| ~ product(X_6,Y_7,Z_9)
| ~ product(X_6,Y_7,W_8) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_1018,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_2,e_2,W_8) ),
inference(resolution,[status(thm)],[c_962,c_18]) ).
tff(c_1499,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_1490,c_1018]) ).
tff(c_1528,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_1499]) ).
tff(c_1530,plain,
~ product(e_2,e_2,e_1),
inference(splitRight,[status(thm)],[c_784]) ).
tff(c_1551,plain,
( product(e_1,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_234,c_1530]) ).
tff(c_1580,plain,
product(e_1,e_2,e_1),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_1551]) ).
tff(c_1594,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_1580,c_66]) ).
tff(c_1619,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1594]) ).
tff(c_2355,plain,
product(e_1,e_1,e_1),
inference(splitLeft,[status(thm)],[c_1619]) ).
tff(c_1554,plain,
( product(e_2,e_1,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_117,c_1530]) ).
tff(c_1583,plain,
product(e_2,e_1,e_1),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_1554]) ).
tff(c_1858,plain,
! [W_14] :
( equalish(W_14,e_2)
| ~ product(W_14,e_1,e_1) ),
inference(resolution,[status(thm)],[c_1583,c_22]) ).
tff(c_2358,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_2355,c_1858]) ).
tff(c_2387,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_2358]) ).
tff(c_2388,plain,
product(e_2,e_1,e_2),
inference(splitRight,[status(thm)],[c_1619]) ).
tff(c_1859,plain,
! [W_8] :
( equalish(W_8,e_1)
| ~ product(e_2,e_1,W_8) ),
inference(resolution,[status(thm)],[c_1583,c_18]) ).
tff(c_2392,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_2388,c_1859]) ).
tff(c_2422,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_2392]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP135-2.002 : TPTP v9.0.0. Released v1.2.0.
% 0.11/0.13 % 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
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 21:27:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.85/2.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.85/2.15
% 4.85/2.15 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------