%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG001-5 : 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 : n005.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 08:31:12 PM UTC 2025
% Result : Unsatisfiable 146.41s 131.36s
% Output : CNFRefutation 146.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 38 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 83 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > equalish > multiply > add > #nlpp > additive_inverse > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(additive_inverse,type,
additive_inverse: $i > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(f_123,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file(unknown,unknown) ).
tff(f_119,axiom,
! [X] : sum(additive_identity,X,X),
file(unknown,unknown) ).
tff(f_192,axiom,
! [V3,Z,V1,X,Y,V2,V4] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ),
file(unknown,unknown) ).
tff(f_129,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity),
file(unknown,unknown) ).
tff(f_121,axiom,
! [X] : sum(X,additive_identity,X),
file(unknown,unknown) ).
tff(f_151,axiom,
! [W,U,Z,X,Y,V] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W)
| sum(U,Z,W) ),
file(unknown,unknown) ).
tff(f_243,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| equalish(U,V) ),
file(unknown,unknown) ).
tff(f_117,axiom,
! [X,Y,W,Z] :
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) ),
file(unknown,unknown) ).
tff(f_253,axiom,
~ product(a,additive_identity,additive_identity),
file(unknown,unknown) ).
tff(c_30,plain,
! [X_41,Y_42] : product(X_41,Y_42,multiply(X_41,Y_42)),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_26,plain,
! [X_39] : sum(additive_identity,X_39,X_39),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_1484,plain,
! [Y_290,V4_287,X_289,Z_288,V2_286,V1_285,V3_291] :
( sum(V1_285,V2_286,V4_287)
| ~ product(X_289,V3_291,V4_287)
| ~ sum(Y_290,Z_288,V3_291)
| ~ product(X_289,Z_288,V2_286)
| ~ product(X_289,Y_290,V1_285) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_18238,plain,
! [V2_641,X_636,Y_638,V1_637,Z_639,Y_640] :
( sum(V1_637,V2_641,multiply(X_636,Y_640))
| ~ sum(Y_638,Z_639,Y_640)
| ~ product(X_636,Z_639,V2_641)
| ~ product(X_636,Y_638,V1_637) ),
inference(resolution,[status(thm)],[c_30,c_1484]) ).
tff(c_386078,plain,
! [V1_2626,V2_2627,X_2628,X_2629] :
( sum(V1_2626,V2_2627,multiply(X_2628,X_2629))
| ~ product(X_2628,X_2629,V2_2627)
| ~ product(X_2628,additive_identity,V1_2626) ),
inference(resolution,[status(thm)],[c_26,c_18238]) ).
tff(c_36,plain,
! [X_46] : sum(X_46,additive_inverse(X_46),additive_identity),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_28,plain,
! [X_40] : sum(X_40,additive_identity,X_40),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_917,plain,
! [U_243,Y_247,X_244,Z_245,W_246,V_248] :
( sum(U_243,Z_245,W_246)
| ~ sum(X_244,V_248,W_246)
| ~ sum(Y_247,Z_245,V_248)
| ~ sum(X_244,Y_247,U_243) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_4551,plain,
! [U_404,Z_405,X_406,Y_407] :
( sum(U_404,Z_405,X_406)
| ~ sum(Y_407,Z_405,additive_identity)
| ~ sum(X_406,Y_407,U_404) ),
inference(resolution,[status(thm)],[c_28,c_917]) ).
tff(c_20904,plain,
! [U_669,X_670,X_671] :
( sum(U_669,additive_inverse(X_670),X_671)
| ~ sum(X_671,X_670,U_669) ),
inference(resolution,[status(thm)],[c_36,c_4551]) ).
tff(c_341,plain,
! [U_194,V_195,X_196,Y_197] :
( equalish(U_194,V_195)
| ~ sum(X_196,Y_197,V_195)
| ~ sum(X_196,Y_197,U_194) ),
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_384,plain,
! [U_194,X_46] :
( equalish(U_194,additive_identity)
| ~ sum(X_46,additive_inverse(X_46),U_194) ),
inference(resolution,[status(thm)],[c_36,c_341]) ).
tff(c_21025,plain,
! [X_671,X_670] :
( equalish(X_671,additive_identity)
| ~ sum(X_671,X_670,X_670) ),
inference(resolution,[status(thm)],[c_20904,c_384]) ).
tff(c_386361,plain,
! [V1_2626,X_2628,X_2629] :
( equalish(V1_2626,additive_identity)
| ~ product(X_2628,X_2629,multiply(X_2628,X_2629))
| ~ product(X_2628,additive_identity,V1_2626) ),
inference(resolution,[status(thm)],[c_386078,c_21025]) ).
tff(c_386614,plain,
! [V1_2630,X_2631] :
( equalish(V1_2630,additive_identity)
| ~ product(X_2631,additive_identity,V1_2630) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_386361]) ).
tff(c_386732,plain,
! [X_2632] : equalish(multiply(X_2632,additive_identity),additive_identity),
inference(resolution,[status(thm)],[c_30,c_386614]) ).
tff(c_487,plain,
! [W_202,Z_203,Y_204,X_205] :
( product(W_202,Z_203,Y_204)
| ~ product(W_202,Z_203,X_205)
| ~ equalish(X_205,Y_204) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_493,plain,
! [X_41,Y_42,Y_204] :
( product(X_41,Y_42,Y_204)
| ~ equalish(multiply(X_41,Y_42),Y_204) ),
inference(resolution,[status(thm)],[c_30,c_487]) ).
tff(c_386830,plain,
! [X_2632] : product(X_2632,additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_386732,c_493]) ).
tff(c_60,plain,
~ product(a,additive_identity,additive_identity),
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_386837,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_386830,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG001-5 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % 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
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 18:14:27 EDT 2025
% 0.12/0.34 % CPUTime :
% 146.41/131.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 146.41/131.36
% 146.41/131.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------