%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI695_1 : TPTP v9.0.0. Released v6.3.0.
% 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 : n006.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 05:40:51 PM UTC 2025
% Result : Theorem 4.36s 2.24s
% Output : CNFRefutation 4.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 8 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 125 ( 0 atm; 90 fun; 23 num; 12 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 4 usr; 7 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff(c,type,
c: $int ).
tff(d,type,
d: $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
%Foreground operators:
tff(f_60,axiom,
! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).
tff(f_31,negated_conjecture,
$sum($product($product($uminus(1),d),$sum(2,c)),$product($uminus(1),$product(d,$difference($product($uminus(1),2),c)))) != 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f_68,axiom,
! [A: $int,B: $int] : ( $uminus($product(A,B)) = $product($uminus(A),B) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',minus_mult_left) ).
tff(c_40,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2,plain,
$sum($product($uminus(d),$sum(2,c)),$uminus($product(d,$sum($uminus(2),$uminus(c))))) != 0,
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_30,plain,
$product($uminus(d),$sum(2,c)) != $product(d,$sum($uminus(2),$uminus(c))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_52,plain,
$product($sum($uminus(2),$uminus(c)),d) != $product($sum(2,c),$uminus(d)),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_40,c_30]) ).
tff(c_55,plain,
$product($sum(2,c),$uminus(d)) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_52]) ).
tff(c_54,plain,
$product($sum($uminus(2),$uminus(c)),d) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_52]) ).
tff(c_53,plain,
$product($sum($uminus(2),$uminus(c)),d) != $product($sum(2,c),$uminus(d)),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_40,c_30]) ).
tff(c_66,plain,
'#skE_2' != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_55,c_54,c_53]) ).
tff(c_68,plain,
$product($sum(2,c),$uminus(d)) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_52]) ).
tff(c_223,plain,
$product($sum($uminus(2),$uminus(c)),d) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_52]) ).
tff(c_35,plain,
! [A_17: $int,B_18: $int,X_37: $int] :
( ( $uminus($product(A_17,B_18)) = $product(X_37,B_18) )
| ( X_37 != $uminus(A_17) ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_37,plain,
! [X_37: $int,B_18: $int,A_17: $int] :
( ( $uminus($product(X_37,B_18)) = $product(A_17,B_18) )
| ( X_37 != $uminus(A_17) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_35]) ).
tff(c_343,plain,
$uminus($product($uminus($sum($uminus(2),$uminus(c))),d)) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_223,c_37]) ).
tff(c_623,plain,
$product($sum(2,c),d) = $uminus('#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_343]) ).
tff(c_1047,plain,
$product(d,$sum(2,c)) = $uminus('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_623,c_40]) ).
tff(c_1094,plain,
$uminus($product($uminus(d),$sum(2,c))) = $uminus('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_1047,c_37]) ).
tff(c_1203,plain,
$uminus('#skE_2') = $uminus('#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_40,c_1094]) ).
tff(c_1205,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1203]) ).
tff(c_1259,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66,c_1205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ARI695_1 : TPTP v9.0.0. Released v6.3.0.
% 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
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 7 15:17:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 4.36/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.36/2.24
% 4.36/2.24 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------