%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG041-1 : 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 : n013.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 08:31:21 PM UTC 2025
% Result : Unsatisfiable 5.57s 2.32s
% Output : CNFRefutation 5.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > multiply > add > #nlpp > h > additive_inverse > multiplicative_identity > b > 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(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(add,type,
add: ( $i * $i ) > $i ).
tff(h,type,
h: $i > $i ).
tff(f_203,axiom,
b != additive_identity,
file(unknown,unknown) ).
tff(f_201,axiom,
a != additive_identity,
file(unknown,unknown) ).
tff(f_198,axiom,
! [A] :
( product(h(A),A,multiplicative_identity)
| ( A = additive_identity ) ),
file(unknown,unknown) ).
tff(f_199,axiom,
product(a,b,additive_identity),
file(unknown,unknown) ).
tff(f_186,axiom,
! [A] : product(A,additive_identity,additive_identity),
file(unknown,unknown) ).
tff(f_107,axiom,
! [W,U,Z,X,Y,V] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file(unknown,unknown) ).
tff(f_190,axiom,
! [A] : product(multiplicative_identity,A,A),
file(unknown,unknown) ).
tff(f_180,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| ( U = V ) ),
file(unknown,unknown) ).
tff(c_52,plain,
b != additive_identity,
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_50,plain,
additive_identity != a,
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_46,plain,
! [A_77] :
( ( additive_identity = A_77 )
| product(h(A_77),A_77,multiplicative_identity) ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_48,plain,
product(a,b,additive_identity),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_38,plain,
! [A_73] : product(A_73,additive_identity,additive_identity),
inference(cnfTransformation,[status(thm)],[f_186]) ).
tff(c_508,plain,
! [Y_320,W_319,X_318,U_315,Z_317,V_316] :
( product(U_315,Z_317,W_319)
| ~ product(X_318,V_316,W_319)
| ~ product(Y_320,Z_317,V_316)
| ~ product(X_318,Y_320,U_315) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_1620,plain,
! [U_412,Z_413,Y_414,A_415] :
( product(U_412,Z_413,additive_identity)
| ~ product(Y_414,Z_413,additive_identity)
| ~ product(A_415,Y_414,U_412) ),
inference(resolution,[status(thm)],[c_38,c_508]) ).
tff(c_3254,plain,
! [U_465,A_466] :
( product(U_465,b,additive_identity)
| ~ product(A_466,a,U_465) ),
inference(resolution,[status(thm)],[c_48,c_1620]) ).
tff(c_3257,plain,
( product(multiplicative_identity,b,additive_identity)
| ( additive_identity = a ) ),
inference(resolution,[status(thm)],[c_46,c_3254]) ).
tff(c_3269,plain,
product(multiplicative_identity,b,additive_identity),
inference(negUnitSimplification,[status(thm)],[c_50,c_3257]) ).
tff(c_42,plain,
! [A_75] : product(multiplicative_identity,A_75,A_75),
inference(cnfTransformation,[status(thm)],[f_190]) ).
tff(c_136,plain,
! [V_103,U_104,X_105,Y_106] :
( ( V_103 = U_104 )
| ~ product(X_105,Y_106,V_103)
| ~ product(X_105,Y_106,U_104) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_157,plain,
! [U_104,A_75] :
( ( U_104 = A_75 )
| ~ product(multiplicative_identity,A_75,U_104) ),
inference(resolution,[status(thm)],[c_42,c_136]) ).
tff(c_3292,plain,
b = additive_identity,
inference(resolution,[status(thm)],[c_3269,c_157]) ).
tff(c_3309,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_3292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG041-1 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.13 % 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 : n013.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 18:30:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.57/2.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.57/2.33
% 5.57/2.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------