%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD022-3 : 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 : n026.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 06:10:41 PM UTC 2025
% Result : Unsatisfiable 39.57s 26.54s
% Output : CNFRefutation 39.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 38 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 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 : 44 ( 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > u > 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(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(u,type,
u: $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_256,axiom,
~ sum(additive_identity,a,b),
file(unknown,unknown) ).
tff(f_250,axiom,
defined(b),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_251,axiom,
defined(c),
file(unknown,unknown) ).
tff(f_254,axiom,
sum(b,c,u),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
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_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_253,axiom,
sum(a,c,u),
file(unknown,unknown) ).
tff(c_66,plain,
~ sum(additive_identity,a,b),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_56,plain,
defined(b),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_8,plain,
! [X_14] :
( ~ defined(X_14)
| sum(additive_inverse(X_14),X_14,additive_identity) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_58,plain,
defined(c),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_64,plain,
sum(b,c,u),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_314,plain,
! [U_130,W_132,Y_128,V_129,Z_127,X_131] :
( ~ sum(U_130,Z_127,W_132)
| ~ sum(Y_128,Z_127,V_129)
| ~ sum(X_131,Y_128,U_130)
| sum(X_131,V_129,W_132) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2093,plain,
! [Y_212,X_213,V_214,X_215] :
( ~ sum(Y_212,X_213,V_214)
| ~ sum(X_215,Y_212,additive_identity)
| sum(X_215,V_214,X_213)
| ~ defined(X_213) ),
inference(resolution,[status(thm)],[c_6,c_314]) ).
tff(c_2163,plain,
! [X_215] :
( ~ sum(X_215,b,additive_identity)
| sum(X_215,u,c)
| ~ defined(c) ),
inference(resolution,[status(thm)],[c_64,c_2093]) ).
tff(c_2310,plain,
! [X_218] :
( ~ sum(X_218,b,additive_identity)
| sum(X_218,u,c) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_2163]) ).
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_2400,plain,
! [X_221] :
( sum(u,X_221,c)
| ~ sum(X_221,b,additive_identity) ),
inference(resolution,[status(thm)],[c_2310,c_10]) ).
tff(c_2406,plain,
( sum(u,additive_inverse(b),c)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_8,c_2400]) ).
tff(c_2410,plain,
sum(u,additive_inverse(b),c),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_2406]) ).
tff(c_2445,plain,
sum(additive_inverse(b),u,c),
inference(resolution,[status(thm)],[c_2410,c_10]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_62,plain,
sum(a,c,u),
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_73,plain,
! [X_82,Y_83,Z_84] :
( ~ sum(X_82,Y_83,Z_84)
| sum(Y_83,X_82,Z_84) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_85,plain,
sum(c,a,u),
inference(resolution,[status(thm)],[c_62,c_73]) ).
tff(c_2155,plain,
! [X_215] :
( ~ sum(X_215,c,additive_identity)
| sum(X_215,u,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_85,c_2093]) ).
tff(c_2246,plain,
! [X_216] :
( ~ sum(X_216,c,additive_identity)
| sum(X_216,u,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_2155]) ).
tff(c_4807,plain,
! [X_280] :
( sum(u,X_280,a)
| ~ sum(X_280,c,additive_identity) ),
inference(resolution,[status(thm)],[c_2246,c_10]) ).
tff(c_4813,plain,
( sum(u,additive_inverse(c),a)
| ~ defined(c) ),
inference(resolution,[status(thm)],[c_8,c_4807]) ).
tff(c_4819,plain,
sum(u,additive_inverse(c),a),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_4813]) ).
tff(c_82,plain,
! [X_14] :
( sum(X_14,additive_inverse(X_14),additive_identity)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_73]) ).
tff(c_73474,plain,
! [Y_884,X_885,V_886,X_887] :
( ~ sum(Y_884,additive_inverse(X_885),V_886)
| ~ sum(X_887,Y_884,X_885)
| sum(X_887,V_886,additive_identity)
| ~ defined(X_885) ),
inference(resolution,[status(thm)],[c_82,c_314]) ).
tff(c_73624,plain,
! [X_887] :
( ~ sum(X_887,u,c)
| sum(X_887,a,additive_identity)
| ~ defined(c) ),
inference(resolution,[status(thm)],[c_4819,c_73474]) ).
tff(c_74491,plain,
! [X_891] :
( ~ sum(X_891,u,c)
| sum(X_891,a,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_73624]) ).
tff(c_74573,plain,
sum(additive_inverse(b),a,additive_identity),
inference(resolution,[status(thm)],[c_2445,c_74491]) ).
tff(c_74809,plain,
sum(a,additive_inverse(b),additive_identity),
inference(resolution,[status(thm)],[c_74573,c_10]) ).
tff(c_2238,plain,
! [X_215,X_14] :
( ~ sum(X_215,additive_inverse(X_14),additive_identity)
| sum(X_215,additive_identity,X_14)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_2093]) ).
tff(c_75226,plain,
( sum(a,additive_identity,b)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c_74809,c_2238]) ).
tff(c_75282,plain,
sum(a,additive_identity,b),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_75226]) ).
tff(c_75519,plain,
sum(additive_identity,a,b),
inference(resolution,[status(thm)],[c_75282,c_10]) ).
tff(c_75581,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66,c_75519]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : FLD022-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.02/0.09 % 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 : n026.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 18:42:53 EDT 2025
% 0.09/0.29 % CPUTime :
% 39.57/26.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.57/26.55
% 39.57/26.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------