%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP131-2.002 : 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 : n027.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 44.03s 31.59s
% Output : CNFRefutation 44.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 224 ( 97 ~; 127 |; 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 : 93 ( 93 !; 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_47,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_46,axiom,
group_element(e_1),
file(unknown,unknown) ).
tff(f_51,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2) ),
file(unknown,unknown) ).
tff(f_49,axiom,
~ equalish(e_1,e_2),
file(unknown,unknown) ).
tff(f_85,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_99,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(f_77,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(c_10,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_8,plain,
group_element(e_1),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_14,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_51]) ).
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_61]) ).
tff(c_12,plain,
~ equalish(e_1,e_2),
inference(cnfTransformation,[status(thm)],[f_49]) ).
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_61]) ).
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_85]) ).
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_244,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_76,plain,
! [Y2_58,Z2_61,Y1_63,X2_59,X1_60,Z1_62] :
( equalish(X1_60,X2_59)
| ~ product(Z2_61,Y2_58,X2_59)
| ~ product(Z2_61,Y1_63,X1_60)
| ~ product(X2_59,Y2_58,Z1_62)
| ~ product(X1_60,Y1_63,Z1_62) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_79,plain,
! [X_4,Y1_63,Y_5,X1_60,Z1_62] :
( equalish(X1_60,e_2)
| ~ product(X_4,Y1_63,X1_60)
| ~ product(e_2,Y_5,Z1_62)
| ~ product(X1_60,Y1_63,Z1_62)
| product(X_4,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(X_4) ),
inference(resolution,[status(thm)],[c_16,c_76]) ).
tff(c_264,plain,
! [X_97,Y_99,X_98,Y_5,Z1_62] :
( equalish(e_1,e_2)
| ~ product(e_2,Y_5,Z1_62)
| ~ product(e_1,Y_99,Z1_62)
| product(X_97,Y_5,e_1)
| ~ group_element(Y_5)
| 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_244,c_79]) ).
tff(c_539,plain,
! [Z1_159,Y_161,X_158,X_160,Y_162] :
( ~ product(e_2,Y_162,Z1_159)
| ~ product(e_1,Y_161,Z1_159)
| product(X_160,Y_162,e_1)
| ~ group_element(Y_162)
| equalish(X_160,X_158)
| product(X_158,Y_161,e_1)
| ~ group_element(X_158)
| ~ group_element(Y_161)
| ~ group_element(X_160) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_264]) ).
tff(c_554,plain,
! [Y_161,X_160,Y_5,X_158] :
( ~ product(e_1,Y_161,e_2)
| product(X_160,Y_5,e_1)
| equalish(X_160,X_158)
| product(X_158,Y_161,e_1)
| ~ group_element(X_158)
| ~ group_element(Y_161)
| ~ group_element(X_160)
| product(e_2,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_16,c_539]) ).
tff(c_27056,plain,
! [Y_673,X_674,Y_675,X_676] :
( ~ product(e_1,Y_673,e_2)
| product(X_674,Y_675,e_1)
| equalish(X_674,X_676)
| product(X_676,Y_673,e_1)
| ~ group_element(X_676)
| ~ group_element(Y_673)
| ~ group_element(X_674)
| product(e_2,Y_675,e_1)
| ~ group_element(Y_675) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_554]) ).
tff(c_27059,plain,
! [X_674,Y_675,X_676,Y_5] :
( product(X_674,Y_675,e_1)
| equalish(X_674,X_676)
| product(X_676,Y_5,e_1)
| ~ group_element(X_676)
| ~ group_element(X_674)
| product(e_2,Y_675,e_1)
| ~ group_element(Y_675)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[c_16,c_27056]) ).
tff(c_27062,plain,
! [X_674,Y_675,X_676,Y_5] :
( product(X_674,Y_675,e_1)
| equalish(X_674,X_676)
| product(X_676,Y_5,e_1)
| ~ group_element(X_676)
| ~ group_element(X_674)
| product(e_2,Y_675,e_1)
| ~ group_element(Y_675)
| product(e_1,Y_5,e_1)
| ~ group_element(Y_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_27059]) ).
tff(c_36498,plain,
! [X_674,Y_675,Y_5] :
( product(X_674,Y_675,e_1)
| equalish(X_674,e_1)
| ~ group_element(e_1)
| ~ group_element(X_674)
| product(e_2,Y_675,e_1)
| ~ group_element(Y_675)
| ~ group_element(Y_5)
| product(e_1,Y_5,e_1) ),
inference(factorization,[status(thm),theory(equality)],[c_27062]) ).
tff(c_36501,plain,
! [X_674,Y_675,Y_5] :
( product(X_674,Y_675,e_1)
| equalish(X_674,e_1)
| ~ group_element(X_674)
| product(e_2,Y_675,e_1)
| ~ group_element(Y_675)
| ~ group_element(Y_5)
| product(e_1,Y_5,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_36498]) ).
tff(c_40302,plain,
! [Y_5] :
( ~ group_element(Y_5)
| product(e_1,Y_5,e_1) ),
inference(splitLeft,[status(thm)],[c_36501]) ).
tff(c_40303,plain,
! [Y_773] :
( ~ group_element(Y_773)
| product(e_1,Y_773,e_1) ),
inference(splitLeft,[status(thm)],[c_36501]) ).
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_77]) ).
tff(c_40751,plain,
! [W_774,Y_775] :
( equalish(W_774,Y_775)
| ~ product(e_1,W_774,e_1)
| ~ group_element(Y_775) ),
inference(resolution,[status(thm)],[c_40303,c_20]) ).
tff(c_41965,plain,
! [Y_778,Y_779] :
( equalish(Y_778,Y_779)
| ~ group_element(Y_779)
| ~ group_element(Y_778) ),
inference(resolution,[status(thm)],[c_40302,c_40751]) ).
tff(c_41968,plain,
( ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_41965,c_14]) ).
tff(c_41975,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_41968]) ).
tff(c_41976,plain,
! [X_674,Y_675] :
( product(X_674,Y_675,e_1)
| equalish(X_674,e_1)
| ~ group_element(X_674)
| product(e_2,Y_675,e_1)
| ~ group_element(Y_675) ),
inference(splitRight,[status(thm)],[c_36501]) ).
tff(c_41988,plain,
! [Y_675] :
( equalish(e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(Y_675)
| product(e_2,Y_675,e_1) ),
inference(factorization,[status(thm),theory(equality)],[c_41976]) ).
tff(c_41991,plain,
! [Y_675] :
( equalish(e_2,e_1)
| ~ group_element(Y_675)
| product(e_2,Y_675,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_41988]) ).
tff(c_41992,plain,
! [Y_675] :
( ~ group_element(Y_675)
| product(e_2,Y_675,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_14,c_41991]) ).
tff(c_42802,plain,
! [Y_782] :
( ~ group_element(Y_782)
| product(e_2,Y_782,e_1) ),
inference(negUnitSimplification,[status(thm)],[c_14,c_41991]) ).
tff(c_43259,plain,
! [W_783,Y_784] :
( equalish(W_783,Y_784)
| ~ product(e_2,W_783,e_1)
| ~ group_element(Y_784) ),
inference(resolution,[status(thm)],[c_42802,c_20]) ).
tff(c_44368,plain,
! [Y_790,Y_791] :
( equalish(Y_790,Y_791)
| ~ group_element(Y_791)
| ~ group_element(Y_790) ),
inference(resolution,[status(thm)],[c_41992,c_43259]) ).
tff(c_44371,plain,
( ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_44368,c_14]) ).
tff(c_44378,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_44371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP131-2.002 : TPTP v9.0.0. Released v1.2.0.
% 0.00/0.09 % 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
% 0.09/0.29 % Computer : n027.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Apr 7 21:26:35 EDT 2025
% 0.09/0.29 % CPUTime :
% 44.03/31.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.13/31.59
% 44.13/31.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------