%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP125-1.003 : 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 : n023.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 06:25:07 PM UTC 2025
% Result : Unsatisfiable 4.48s 2.15s
% Output : CNFRefutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 107 ( 44 ~; 63 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 4 ( 3 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 > 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_39,axiom,
~ equalish(e_2,e_1),
file(unknown,unknown) ).
tff(f_32,axiom,
group_element(e_2),
file(unknown,unknown) ).
tff(f_33,axiom,
group_element(e_3),
file(unknown,unknown) ).
tff(f_57,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_41,axiom,
~ equalish(e_2,e_3),
file(unknown,unknown) ).
tff(f_45,axiom,
~ equalish(e_3,e_2),
file(unknown,unknown) ).
tff(f_83,axiom,
! [X] : product(X,X,X),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_81,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,X) ),
file(unknown,unknown) ).
tff(f_65,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file(unknown,unknown) ).
tff(c_12,plain,
~ equalish(e_2,e_1),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_4,plain,
group_element(e_2),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_6,plain,
group_element(e_3),
inference(cnfTransformation,[status(thm)],[f_33]) ).
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_57]) ).
tff(c_14,plain,
~ equalish(e_2,e_3),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_18,plain,
~ equalish(e_3,e_2),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_71,plain,
! [X_46,Y_47] :
( product(X_46,Y_47,e_3)
| 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_57]) ).
tff(c_28,plain,
! [X_15] : product(X_15,X_15,X_15),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_52,plain,
! [W_34,Z_35,X_36,Y_37] :
( equalish(W_34,Z_35)
| ~ product(X_36,Z_35,Y_37)
| ~ product(X_36,W_34,Y_37) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_55,plain,
! [W_34,X_15] :
( equalish(W_34,X_15)
| ~ product(X_15,W_34,X_15) ),
inference(resolution,[status(thm)],[c_28,c_52]) ).
tff(c_80,plain,
! [Y_47] :
( equalish(Y_47,e_3)
| product(e_3,Y_47,e_2)
| product(e_3,Y_47,e_1)
| ~ group_element(Y_47)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[c_71,c_55]) ).
tff(c_107,plain,
! [Y_48] :
( equalish(Y_48,e_3)
| product(e_3,Y_48,e_2)
| product(e_3,Y_48,e_1)
| ~ group_element(Y_48) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_80]) ).
tff(c_32,plain,
! [W_21,Z_22,Y_23,X_24] :
( equalish(W_21,Z_22)
| ~ product(Z_22,Y_23,X_24)
| ~ product(W_21,Y_23,X_24) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_35,plain,
! [W_21,X_15] :
( equalish(W_21,X_15)
| ~ product(W_21,X_15,X_15) ),
inference(resolution,[status(thm)],[c_28,c_32]) ).
tff(c_124,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_3,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[c_107,c_35]) ).
tff(c_139,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_124]) ).
tff(c_140,plain,
product(e_3,e_2,e_1),
inference(negUnitSimplification,[status(thm)],[c_14,c_18,c_139]) ).
tff(c_30,plain,
! [Z1_18,Z2_19,X_16,Y_17] :
( product(Z1_18,Z2_19,X_16)
| ~ product(Y_17,X_16,Z2_19)
| ~ product(X_16,Y_17,Z1_18) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_198,plain,
! [Z1_55] :
( product(Z1_55,e_1,e_2)
| ~ product(e_2,e_3,Z1_55) ),
inference(resolution,[status(thm)],[c_140,c_30]) ).
tff(c_201,plain,
( product(e_3,e_1,e_2)
| 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_20,c_198]) ).
tff(c_204,plain,
( product(e_3,e_1,e_2)
| 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_201]) ).
tff(c_205,plain,
product(e_2,e_3,e_1),
inference(splitLeft,[status(thm)],[c_204]) ).
tff(c_150,plain,
! [Z1_18] :
( product(Z1_18,e_1,e_2)
| ~ product(e_2,e_3,Z1_18) ),
inference(resolution,[status(thm)],[c_140,c_30]) ).
tff(c_216,plain,
product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[c_205,c_150]) ).
tff(c_42,plain,
! [W_28,Z_29,X_30,Y_31] :
( equalish(W_28,Z_29)
| ~ product(X_30,Y_31,Z_29)
| ~ product(X_30,Y_31,W_28) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_45,plain,
! [W_28,X_15] :
( equalish(W_28,X_15)
| ~ product(X_15,X_15,W_28) ),
inference(resolution,[status(thm)],[c_28,c_42]) ).
tff(c_243,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[c_216,c_45]) ).
tff(c_254,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_243]) ).
tff(c_256,plain,
~ product(e_2,e_3,e_1),
inference(splitRight,[status(thm)],[c_204]) ).
tff(c_92,plain,
! [X_46] :
( equalish(X_46,e_3)
| product(X_46,e_3,e_2)
| product(X_46,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X_46) ),
inference(resolution,[status(thm)],[c_71,c_35]) ).
tff(c_1105,plain,
! [X_81] :
( equalish(X_81,e_3)
| product(X_81,e_3,e_2)
| product(X_81,e_3,e_1)
| ~ group_element(X_81) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_92]) ).
tff(c_1126,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_1105,c_55]) ).
tff(c_1159,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_4,c_1126]) ).
tff(c_1161,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_256,c_14,c_18,c_1159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : GRP125-1.003 : TPTP v9.0.0. Released v1.2.0.
% 0.12/0.12 % 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 : n023.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 21:20:39 EDT 2025
% 0.19/0.33 % CPUTime :
% 4.48/2.15 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.48/2.16
% 4.48/2.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------