%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI741_1 : TPTP v9.0.0. Released v7.0.0.
% 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 : n026.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 05:40:55 PM UTC 2025
% Result : Theorem 5.96s 2.63s
% Output : CNFRefutation 5.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 8 ~; 8 |; 0 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 91 ( 3 atm; 32 fun; 37 num; 19 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
%$ pow > #nlpp > sqrt > sqr > log2 > log10 > log > exp
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $real ).
tff('#skE_2',type,
'#skE_2': $real ).
tff('#skE_3',type,
'#skE_3': $real ).
%Foreground operators:
tff(log,type,
log: $real > $real ).
tff(sqrt,type,
sqrt: $real > $real ).
tff(log2,type,
log2: $real > $real ).
tff(exp,type,
exp: $real > $real ).
tff(pow,type,
pow: ( $real * $real ) > $real ).
tff(log10,type,
log10: $real > $real ).
tff(sqr,type,
sqr: $real > $real ).
tff(f_109,negated_conjecture,
pow(2,2) != 4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pow_2_21) ).
tff(f_103,axiom,
! [Xa: $real] :
( $less(0,Xa)
=> ( pow(Xa,2) = sqr(Xa) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pow_x_two) ).
tff(f_75,axiom,
! [Xa: $real] : ( sqr(Xa) = $product(Xa,Xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sqr_def) ).
tff(f_923,axiom,
! [X: $real,Y: $real,Z: $real] :
( ( Y != 0 )
=> ( ( Z = $quotient(X,Y) )
<=> ( X = $product(Y,Z) ) ) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas_real.p',nonzero_eq_divide_eq) ).
tff(f_968,axiom,
! [A: $real,B: $real] : ( $quotient($uminus(A),B) = $uminus($quotient(A,B)) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas_real.p',divide_minus_left) ).
tff(f_911,axiom,
! [X: $real,Y: $real] :
( ( Y != 0 )
=> ( X = $product(Y,$quotient(X,Y)) ) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas_real.p',quo_1) ).
tff(c_36,plain,
pow(2,2) != 4,
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_142,plain,
pow(2,2) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_36]) ).
tff(c_594,plain,
! [X_189a: $real] :
( ( pow(X_189a,2) = sqr(X_189a) )
| ~ $less(0,X_189a) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_610,plain,
( ( sqr(2) = '#skE_1' )
| ~ $less(0,2) ),
inference(superposition,[status(thm),theory(equality)],[c_142,c_594]) ).
tff(c_619,plain,
sqr(2) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_610]) ).
tff(c_177,plain,
! [X_140a: $real] : ( $product(X_140a,X_140a) = sqr(X_140a) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_44,plain,
! [Y_41: $real,Z_42: $real] :
( ( $quotient($product(Y_41,Z_42),Y_41) = Z_42 )
| ( Y_41 = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_923]) ).
tff(c_185,plain,
! [X_140a: $real] :
( ( $quotient(sqr(X_140a),X_140a) = X_140a )
| ( X_140a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_177,c_44]) ).
tff(c_657,plain,
( ( $quotient('#skE_1',2) = 2 )
| ( 2 = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_619,c_185]) ).
tff(c_856,plain,
$quotient('#skE_1',2) = 2,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_657]) ).
tff(c_118,plain,
! [A_83: $real,B_84: $real,X_134: $real] :
( ( $uminus($quotient(A_83,B_84)) = $quotient(X_134,B_84) )
| ( X_134 != $uminus(A_83) ) ),
inference(cnfTransformation,[status(thm)],[f_968]) ).
tff(c_921,plain,
$quotient($uminus('#skE_1'),2) = $uminus(2),
inference(superposition,[status(thm),theory(equality)],[c_856,c_118]) ).
tff(c_1060,plain,
$quotient($uminus('#skE_1'),2) = $uminus(2),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_921]) ).
tff(c_41,plain,
! [Y_36: $real,X_37: $real] :
( ( $product(Y_36,$quotient(X_37,Y_36)) = X_37 )
| ( Y_36 = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_911]) ).
tff(c_1133,plain,
( ( $product(2,$uminus(2)) = $uminus('#skE_1') )
| ( 2 = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1060,c_41]) ).
tff(c_1134,plain,
$uminus('#skE_1') = $uminus(4),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_1133]) ).
tff(c_144,plain,
'#skE_1' != 4,
inference(demodulation,[status(thm),theory(equality)],[c_142,c_36]) ).
tff(c_1264,plain,
$false,
inference(close,[status(thm),theory('LFA')],[c_1134,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ARI741_1 : TPTP v9.0.0. Released v7.0.0.
% 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
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 15:19:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.96/2.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.96/2.63
% 5.96/2.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------