%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD017-3 : 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 : n002.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 06:10:40 PM UTC 2025
% Result : Unsatisfiable 5.41s 2.30s
% Output : CNFRefutation 5.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 96 ( 50 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > x > multiplicative_identity > c > b > 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(x,type,
x: $i ).
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(b,type,
b: $i ).
tff(defined,type,
defined: $i > $o ).
tff(multiplicative_inverse,type,
multiplicative_inverse: $i > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
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_253,axiom,
sum(additive_identity,a,x),
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(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
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_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_250,axiom,
defined(b),
file(unknown,unknown) ).
tff(f_254,axiom,
sum(a,b,c),
file(unknown,unknown) ).
tff(f_57,axiom,
! [W,U,Z,X,Y,V] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file(unknown,unknown) ).
tff(f_256,axiom,
~ sum(x,b,c),
file(unknown,unknown) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
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_133,plain,
! [Y_65] :
( ~ defined(Y_65)
| less_or_equal(Y_65,Y_65) ),
inference(factorization,[status(thm),theory(equality)],[c_46]) ).
tff(c_62,plain,
sum(additive_identity,a,x),
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_209,plain,
! [V_119,X_116,Y_118,Z_117,U_115] :
( ~ sum(Y_118,Z_117,V_119)
| ~ sum(X_116,Z_117,U_115)
| ~ less_or_equal(X_116,Y_118)
| less_or_equal(U_115,V_119) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_517,plain,
! [X_150,U_151] :
( ~ sum(X_150,a,U_151)
| ~ less_or_equal(X_150,additive_identity)
| less_or_equal(U_151,x) ),
inference(resolution,[status(thm)],[c_62,c_209]) ).
tff(c_558,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(x,x) ),
inference(resolution,[status(thm)],[c_62,c_517]) ).
tff(c_641,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_558]) ).
tff(c_647,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_133,c_641]) ).
tff(c_654,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_647]) ).
tff(c_656,plain,
less_or_equal(additive_identity,additive_identity),
inference(splitRight,[status(thm)],[c_558]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1268,plain,
! [X_193,X_194,U_195] :
( ~ sum(X_193,X_194,U_195)
| ~ less_or_equal(X_193,additive_identity)
| less_or_equal(U_195,X_194)
| ~ defined(X_194) ),
inference(resolution,[status(thm)],[c_6,c_209]) ).
tff(c_1340,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(x,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_62,c_1268]) ).
tff(c_1404,plain,
less_or_equal(x,a),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_656,c_1340]) ).
tff(c_540,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(a,x)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_6,c_517]) ).
tff(c_557,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(a,x) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_540]) ).
tff(c_708,plain,
less_or_equal(a,x),
inference(demodulation,[status(thm),theory(equality)],[c_656,c_557]) ).
tff(c_112,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_10,plain,
! [X_16,Y_15,Z_17] :
( ~ sum(X_16,Y_15,Z_17)
| sum(Y_15,X_16,Z_17) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_118,plain,
! [X_96,Y_95] :
( sum(X_96,additive_identity,Y_95)
| ~ less_or_equal(Y_95,X_96)
| ~ less_or_equal(X_96,Y_95) ),
inference(resolution,[status(thm)],[c_112,c_10]) ).
tff(c_56,plain,
defined(b),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_64,plain,
sum(a,b,c),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_442,plain,
! [Y_142,X_145,Z_141,V_143,W_146,U_144] :
( ~ sum(U_144,Z_141,W_146)
| ~ sum(Y_142,Z_141,V_143)
| ~ sum(X_145,Y_142,U_144)
| sum(X_145,V_143,W_146) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_892,plain,
! [Y_181,V_182,X_183] :
( ~ sum(Y_181,b,V_182)
| ~ sum(X_183,Y_181,a)
| sum(X_183,V_182,c) ),
inference(resolution,[status(thm)],[c_64,c_442]) ).
tff(c_907,plain,
! [X_183] :
( ~ sum(X_183,additive_identity,a)
| sum(X_183,b,c)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_6,c_892]) ).
tff(c_1591,plain,
! [X_203] :
( ~ sum(X_203,additive_identity,a)
| sum(X_203,b,c) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_907]) ).
tff(c_66,plain,
~ sum(x,b,c),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_1624,plain,
~ sum(x,additive_identity,a),
inference(resolution,[status(thm)],[c_1591,c_66]) ).
tff(c_1627,plain,
( ~ less_or_equal(a,x)
| ~ less_or_equal(x,a) ),
inference(resolution,[status(thm)],[c_118,c_1624]) ).
tff(c_1631,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1404,c_708,c_1627]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : FLD017-3 : 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 : n002.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 18:42:01 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.41/2.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.41/2.31
% 5.41/2.31 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------