%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI621_3 : TPTP v9.0.0. Released v5.1.0.
% 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 : 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 05:40:43 PM UTC 2025
% Result : Theorem 3.39s 1.95s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 40 ( 12 ~; 24 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 80 ( 4 atm; 6 fun; 63 num; 7 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 1 usr; 6 con; 0-2 aty)
% Number of variables : 7 ( 6 !; 1 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
%$ pow2 > #nlpp > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(pow2,type,
pow2: $real > $o ).
tff('#skF_1',type,
'#skF_1': $real > $real ).
tff(f_42,negated_conjecture,
~ ( ! [Xa: $real] :
( pow2(Xa)
<=> ( ( Xa = 1 )
| ( $lesseq(2,Xa)
& ? [Ya: $real] :
( ( $product(2,Ya) = Xa )
& pow2(Ya) ) ) ) )
=> ~ pow2(12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_pow_of_2_10) ).
tff(c_2,plain,
pow2(12),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_29,plain,
! [X_9a: $real] :
( ( $product(2,'#skF_1'(X_9a)) = X_9a )
| ~ pow2(X_9a)
| ( X_9a = 1 ) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_36,plain,
( ( $product(2,'#skF_1'(12)) = 12 )
| ( 12 = 1 ) ),
inference(resolution,[status(thm)],[c_2,c_29]) ).
tff(c_37,plain,
'#skF_1'(12) = 6,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_36]) ).
tff(c_3,plain,
! [X_1a: $real] :
( pow2('#skF_1'(X_1a))
| ~ pow2(X_1a)
| ( X_1a = 1 ) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_166,plain,
( pow2(6)
| ~ pow2(12)
| ( 12 = 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_37,c_3]) ).
tff(c_170,plain,
( pow2(6)
| ( 12 = 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_166]) ).
tff(c_171,plain,
pow2(6),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_170]) ).
tff(c_4,plain,
! [X_1a: $real] :
( ( $product(2,'#skF_1'(X_1a)) = X_1a )
| ~ pow2(X_1a)
| ( X_1a = 1 ) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_183,plain,
( ( $product(2,'#skF_1'(6)) = 6 )
| ( 6 = 1 ) ),
inference(resolution,[status(thm)],[c_171,c_4]) ).
tff(c_184,plain,
'#skF_1'(6) = 3,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_183]) ).
tff(c_191,plain,
( pow2(3)
| ~ pow2(6)
| ( 6 = 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_3]) ).
tff(c_195,plain,
( pow2(3)
| ( 6 = 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_171,c_191]) ).
tff(c_196,plain,
pow2(3),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_195]) ).
tff(c_218,plain,
( ( $product(2,'#skF_1'(3)) = 3 )
| ( 3 = 1 ) ),
inference(resolution,[status(thm)],[c_196,c_4]) ).
tff(c_219,plain,
'#skF_1'(3) = 3/2,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_218]) ).
tff(c_388,plain,
( pow2(3/2)
| ~ pow2(3)
| ( 3 = 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_219,c_3]) ).
tff(c_392,plain,
( pow2(3/2)
| ( 3 = 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_196,c_388]) ).
tff(c_393,plain,
pow2(3/2),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_392]) ).
tff(c_5,plain,
! [X_1a: $real] :
( ~ pow2(X_1a)
| ( X_1a = 1 )
| $lesseq(2,X_1a) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_6,plain,
! [X_1a: $real] :
( ~ pow2(X_1a)
| ( X_1a = 1 )
| ~ $less(X_1a,2) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_407,plain,
( ( 3/2 = 1 )
| ~ $less(3/2,2) ),
inference(resolution,[status(thm)],[c_393,c_6]) ).
tff(c_409,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_407]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ARI621_3 : TPTP v9.0.0. Released v5.1.0.
% 0.11/0.13 % 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
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 15:15:03 EDT 2025
% 0.14/0.34 % CPUTime :
% 3.39/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/1.96
% 3.39/1.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------