%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP123-2.003 : 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 : n024.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 06:25:03 PM UTC 2025
% Result : Unsatisfiable 3.81s 1.99s
% Output : CNFRefutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 100 ( 47 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 52 ( 52 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > next > greater > 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(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(e_3,type,
e_3: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(e_1,type,
e_1: $i ).
tff(f_54,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_56,axiom,
~ equalish(e_1,e_3),
file(unknown,unknown) ).
tff(f_50,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_52,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_76,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_102,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_100,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_60,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_64,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_51,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_92,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_116,axiom,
! [Y1,X1,Z2,Y2,X2,Z1] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,Y1,X1)
| ~ product(Z2,Y2,X2)
| equalish(X1,X2) ),
file(unknown,unknown) ).
tff(c_20,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_22,plain,
~ equalish(e_1,e_3),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_14,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_18,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_83,plain,
! [X_55,Y_56] :
( 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(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_40,plain,
! [X_18] : product(X_18,X_18,X_18),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_69,plain,
! [W_45,Z_46,Y_47,X_48] :
( equalish(W_45,Z_46)
| ~ product(Z_46,Y_47,X_48)
| ~ product(W_45,Y_47,X_48) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_72,plain,
! [W_45,X_18] :
( equalish(W_45,X_18)
| ~ product(W_45,X_18,X_18) ),
inference(resolution,[status(thm)],[c_40,c_69]) ).
tff(c_89,plain,
! [X_55] :
( equalish(X_55,e_3)
| product(X_55,e_3,e_2)
| product(X_55,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_55) ),
inference(resolution,[status(thm)],[c_83,c_72]) ).
tff(c_109,plain,
! [X_55] :
( equalish(X_55,e_3)
| product(X_55,e_3,e_2)
| product(X_55,e_3,e_1)
| ~ group_element(X_55) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_89]) ).
tff(c_26,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_30,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_16,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_132,plain,
! [X_59] :
( equalish(X_59,e_3)
| product(X_59,e_3,e_2)
| product(X_59,e_3,e_1)
| ~ group_element(X_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_89]) ).
tff(c_59,plain,
! [W_38,Z_39,X_40,Y_41] :
( equalish(W_38,Z_39)
| ~ product(X_40,Z_39,Y_41)
| ~ product(X_40,W_38,Y_41) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_62,plain,
! [W_38,X_18] :
( equalish(W_38,X_18)
| ~ product(X_18,W_38,X_18) ),
inference(resolution,[status(thm)],[c_40,c_59]) ).
tff(c_144,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_2,e_3,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_132,c_62]) ).
tff(c_155,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_144]) ).
tff(c_156,plain,
product(e_2,e_3,e_1),
inference(negUnitSimplification,[status(thm)],[c_26,c_30,c_155]) ).
tff(c_167,plain,
! [X2_65,Y2_60,Y1_64,X1_62,Z1_61,Z2_63] :
( equalish(X1_62,X2_65)
| ~ product(Z2_63,Y2_60,X2_65)
| ~ product(Z2_63,Y1_64,X1_62)
| ~ product(X2_65,Y2_60,Z1_61)
| ~ product(X1_62,Y1_64,Z1_61) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_480,plain,
! [X1_82,X_83,Y1_84,Z1_85] :
( equalish(X1_82,X_83)
| ~ product(X_83,Y1_84,X1_82)
| ~ product(X_83,X_83,Z1_85)
| ~ product(X1_82,Y1_84,Z1_85) ),
inference(resolution,[status(thm)],[c_40,c_167]) ).
tff(c_494,plain,
! [Z1_85] :
( equalish(e_1,e_2)
| ~ product(e_2,e_2,Z1_85)
| ~ product(e_1,e_3,Z1_85) ),
inference(resolution,[status(thm)],[c_156,c_480]) ).
tff(c_576,plain,
! [Z1_89] :
( ~ product(e_2,e_2,Z1_89)
| ~ product(e_1,e_3,Z1_89) ),
inference(negUnitSimplification,[status(thm)],[c_20,c_494]) ).
tff(c_604,plain,
~ product(e_1,e_3,e_2),
inference(resolution,[status(thm)],[c_40,c_576]) ).
tff(c_607,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_109,c_604]) ).
tff(c_610,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_607]) ).
tff(c_611,plain,
product(e_1,e_3,e_1),
inference(negUnitSimplification,[status(thm)],[c_22,c_610]) ).
tff(c_38,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_100]) ).
tff(c_165,plain,
! [W_14] :
( equalish(W_14,e_2)
| ~ product(W_14,e_3,e_1) ),
inference(resolution,[status(thm)],[c_156,c_38]) ).
tff(c_618,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[c_611,c_165]) ).
tff(c_636,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP123-2.003 : 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
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 21:18:36 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.81/1.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.81/1.99
% 3.81/1.99 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------