%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : BOO006-1 : TPTP v9.0.0. Released v1.0.0.
% 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 : n003.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 05:45:01 PM UTC 2025
% Result : Unsatisfiable 4.70s 2.17s
% Output : CNFRefutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 8 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 64 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > multiply > add > #nlpp > inverse > x > multiplicative_identity > additive_identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(x,type,
x: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(f_52,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file(unknown,unknown) ).
tff(f_190,axiom,
! [X] : product(X,inverse(X),additive_identity),
file(unknown,unknown) ).
tff(f_207,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) ),
file(unknown,unknown) ).
tff(f_188,axiom,
! [X] : product(inverse(X),X,additive_identity),
file(unknown,unknown) ).
tff(f_64,axiom,
! [X] : sum(additive_identity,X,X),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X] : sum(X,additive_identity,X),
file(unknown,unknown) ).
tff(f_126,axiom,
! [V3,Z,V1,X,Y,V2,V4] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) ),
file(unknown,unknown) ).
tff(f_211,axiom,
~ product(x,additive_identity,additive_identity),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4] : product(X_3,Y_4,multiply(X_3,Y_4)),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_82,plain,
! [Y_100,X_101,Z_102] :
( product(Y_100,X_101,Z_102)
| ~ product(X_101,Y_100,Z_102) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_93,plain,
! [Y_4,X_3] : product(Y_4,X_3,multiply(X_3,Y_4)),
inference(resolution,[status(thm)],[c_4,c_82]) ).
tff(c_40,plain,
! [X_74] : product(X_74,inverse(X_74),additive_identity),
inference(cnfTransformation,[status(thm)],[f_190]) ).
tff(c_107,plain,
! [V_105,U_106,X_107,Y_108] :
( ( V_105 = U_106 )
| ~ product(X_107,Y_108,V_105)
| ~ product(X_107,Y_108,U_106) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_549,plain,
! [U_145,X_146] :
( ( additive_identity = U_145 )
| ~ product(X_146,inverse(X_146),U_145) ),
inference(resolution,[status(thm)],[c_40,c_107]) ).
tff(c_572,plain,
! [X_3] : ( multiply(X_3,inverse(X_3)) = additive_identity ),
inference(resolution,[status(thm)],[c_4,c_549]) ).
tff(c_38,plain,
! [X_73] : product(inverse(X_73),X_73,additive_identity),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_10,plain,
! [X_11] : sum(additive_identity,X_11,X_11),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_12,plain,
! [X_12] : sum(X_12,additive_identity,X_12),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_327,plain,
! [V3_121,Y_123,V4_122,V2_126,V1_125,X_127,Z_124] :
( product(V3_121,X_127,V4_122)
| ~ sum(V1_125,V2_126,V4_122)
| ~ sum(Y_123,Z_124,V3_121)
| ~ product(Z_124,X_127,V2_126)
| ~ product(Y_123,X_127,V1_125) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_1566,plain,
! [X_248,Y_247,V3_251,X_250,Z_249] :
( product(V3_251,X_250,X_248)
| ~ sum(Y_247,Z_249,V3_251)
| ~ product(Z_249,X_250,additive_identity)
| ~ product(Y_247,X_250,X_248) ),
inference(resolution,[status(thm)],[c_12,c_327]) ).
tff(c_1856,plain,
! [X_270,X_271,X_272] :
( product(X_270,X_271,X_272)
| ~ product(X_270,X_271,additive_identity)
| ~ product(additive_identity,X_271,X_272) ),
inference(resolution,[status(thm)],[c_10,c_1566]) ).
tff(c_2060,plain,
! [X_281,X_282] :
( product(inverse(X_281),X_281,X_282)
| ~ product(additive_identity,X_281,X_282) ),
inference(resolution,[status(thm)],[c_38,c_1856]) ).
tff(c_120,plain,
! [X_3,Y_4,U_106] :
( ( multiply(X_3,Y_4) = U_106 )
| ~ product(Y_4,X_3,U_106) ),
inference(resolution,[status(thm)],[c_93,c_107]) ).
tff(c_2089,plain,
! [X_281,X_282] :
( ( multiply(X_281,inverse(X_281)) = X_282 )
| ~ product(additive_identity,X_281,X_282) ),
inference(resolution,[status(thm)],[c_2060,c_120]) ).
tff(c_2138,plain,
! [X_283,X_284] :
( ( additive_identity = X_283 )
| ~ product(additive_identity,X_284,X_283) ),
inference(demodulation,[status(thm),theory(equality)],[c_572,c_2089]) ).
tff(c_2178,plain,
! [X_285] : ( multiply(X_285,additive_identity) = additive_identity ),
inference(resolution,[status(thm)],[c_93,c_2138]) ).
tff(c_2203,plain,
! [X_285] : product(X_285,additive_identity,additive_identity),
inference(superposition,[status(thm),theory(equality)],[c_2178,c_4]) ).
tff(c_46,plain,
~ product(x,additive_identity,additive_identity),
inference(cnfTransformation,[status(thm)],[f_211]) ).
tff(c_2347,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2203,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO006-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 15:21:03 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.70/2.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.94/2.17
% 4.94/2.17 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------