%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD039-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 : n021.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 06:10:46 PM UTC 2025
% Result : Unsatisfiable 4.90s 2.21s
% Output : CNFRefutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 85 ( 46 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(additive_inverse,type,
additive_inverse: $i > $i ).
tff(defined,type,
defined: $i > $o ).
tff(multiplicative_inverse,type,
multiplicative_inverse: $i > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(f_159,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_222,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_204,axiom,
! [X,Y] :
( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) ),
file(unknown,unknown) ).
tff(f_246,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file(unknown,unknown) ).
tff(f_173,axiom,
defined(multiplicative_identity),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_252,axiom,
sum(additive_identity,multiplicative_identity,additive_identity),
file(unknown,unknown) ).
tff(f_233,axiom,
! [U,Z,X,Y,V] :
( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) ),
file(unknown,unknown) ).
tff(c_28,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_46,plain,
! [Y_65,X_64] :
( ~ defined(Y_65)
| ~ defined(X_64)
| less_or_equal(Y_65,X_64)
| less_or_equal(X_64,Y_65) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_863,plain,
! [Y_65] :
( ~ defined(Y_65)
| less_or_equal(Y_65,Y_65) ),
inference(factorization,[status(thm),theory(equality)],[c_46]) ).
tff(c_97,plain,
! [Y_95,X_96] :
( ~ less_or_equal(Y_95,X_96)
| ~ less_or_equal(X_96,Y_95)
| sum(additive_identity,X_96,Y_95) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_52,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_107,plain,
( ~ less_or_equal(multiplicative_identity,additive_identity)
| ~ less_or_equal(additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[c_97,c_52]) ).
tff(c_109,plain,
~ less_or_equal(additive_identity,multiplicative_identity),
inference(splitLeft,[status(thm)],[c_107]) ).
tff(c_34,plain,
defined(multiplicative_identity),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_127,plain,
! [Y_65] :
( ~ defined(Y_65)
| less_or_equal(Y_65,Y_65) ),
inference(factorization,[status(thm),theory(equality)],[c_46]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_58,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_214,plain,
! [V_123,Z_121,Y_122,U_119,X_120] :
( ~ sum(Y_122,Z_121,V_123)
| ~ sum(X_120,Z_121,U_119)
| ~ less_or_equal(X_120,Y_122)
| less_or_equal(U_119,V_123) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_245,plain,
! [X_124,U_125] :
( ~ sum(X_124,multiplicative_identity,U_125)
| ~ less_or_equal(X_124,additive_identity)
| less_or_equal(U_125,additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_214]) ).
tff(c_265,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_6,c_245]) ).
tff(c_281,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_265]) ).
tff(c_283,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_281]) ).
tff(c_286,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_127,c_283]) ).
tff(c_292,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_286]) ).
tff(c_294,plain,
less_or_equal(additive_identity,additive_identity),
inference(splitRight,[status(thm)],[c_281]) ).
tff(c_770,plain,
! [X_167,X_168,U_169] :
( ~ sum(X_167,X_168,U_169)
| ~ less_or_equal(X_167,additive_identity)
| less_or_equal(U_169,X_168)
| ~ defined(X_168) ),
inference(resolution,[status(thm)],[c_6,c_214]) ).
tff(c_800,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_58,c_770]) ).
tff(c_822,plain,
less_or_equal(additive_identity,multiplicative_identity),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_294,c_800]) ).
tff(c_824,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_109,c_822]) ).
tff(c_825,plain,
~ less_or_equal(multiplicative_identity,additive_identity),
inference(splitRight,[status(thm)],[c_107]) ).
tff(c_1018,plain,
! [V_201,X_198,Z_199,Y_200,U_197] :
( ~ sum(Y_200,Z_199,V_201)
| ~ sum(X_198,Z_199,U_197)
| ~ less_or_equal(X_198,Y_200)
| less_or_equal(U_197,V_201) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_1049,plain,
! [X_202,U_203] :
( ~ sum(X_202,multiplicative_identity,U_203)
| ~ less_or_equal(X_202,additive_identity)
| less_or_equal(U_203,additive_identity) ),
inference(resolution,[status(thm)],[c_58,c_1018]) ).
tff(c_1069,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_6,c_1049]) ).
tff(c_1085,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(multiplicative_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_1069]) ).
tff(c_1086,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(negUnitSimplification,[status(thm)],[c_825,c_1085]) ).
tff(c_1091,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_863,c_1086]) ).
tff(c_1097,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_1091]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : FLD039-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.10/0.12 % 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 : n021.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 18:46:43 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.90/2.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.90/2.22
% 4.90/2.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------