%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD071-3 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n027.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 06:10:55 PM UTC 2025
% Result : Unsatisfiable 7.01s 2.66s
% Output : CNFRefutation 7.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > 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(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(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_250,axiom,
defined(b),
file(unknown,unknown) ).
tff(f_251,axiom,
less_or_equal(additive_identity,a),
file(unknown,unknown) ).
tff(f_252,axiom,
less_or_equal(additive_identity,b),
file(unknown,unknown) ).
tff(f_196,axiom,
! [X,Y] :
( product(X,Y,multiply(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_244,axiom,
! [Z,X,Y] :
( less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,X)
| ~ less_or_equal(additive_identity,Y)
| ~ product(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_254,axiom,
~ less_or_equal(additive_identity,multiply(a,b)),
file(unknown,unknown) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_56,plain,
defined(b),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_58,plain,
less_or_equal(additive_identity,a),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_60,plain,
less_or_equal(additive_identity,b),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_40,plain,
! [Y_58,X_57] :
( ~ defined(Y_58)
| ~ defined(X_57)
| product(X_57,Y_58,multiply(X_57,Y_58)) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_240,plain,
! [X_117,Y_118,Z_119] :
( ~ product(X_117,Y_118,Z_119)
| ~ less_or_equal(additive_identity,Y_118)
| ~ less_or_equal(additive_identity,X_117)
| less_or_equal(additive_identity,Z_119) ),
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_3578,plain,
! [Y_250,X_251] :
( ~ less_or_equal(additive_identity,Y_250)
| ~ less_or_equal(additive_identity,X_251)
| less_or_equal(additive_identity,multiply(X_251,Y_250))
| ~ defined(Y_250)
| ~ defined(X_251) ),
inference(resolution,[status(thm)],[c_40,c_240]) ).
tff(c_62,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_3595,plain,
( ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| ~ defined(b)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_3578,c_62]) ).
tff(c_3611,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_56,c_58,c_60,c_3595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD071-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n027.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 : Mon Apr 7 18:57:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.01/2.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.01/2.66
% 7.01/2.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------