TSTP Solution File: ARI742_1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI742_1 : TPTP v8.1.2. Released v7.0.0.
% 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 : n032.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 : Tue Aug 22 10:34:19 EDT 2023
% Result : Theorem 3.43s 1.89s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 8 unt; 3 typ; 0 def)
% Number of atoms : 25 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 6 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 40 ( 3 atm; 8 fun; 19 num; 10 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 10 (; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > sqrt > sqr
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $real ).
%Foreground operators:
tff(sqrt,type,
sqrt: $real > $real ).
tff(sqr,type,
sqr: $real > $real ).
tff(f_55,negated_conjecture,
sqrt(0) != 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sqrt_zero) ).
tff(f_37,axiom,
! [Xa: $real] :
( $lesseq(0,Xa)
=> ( sqr(sqrt(Xa)) = Xa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sqrt_square) ).
tff(f_29,axiom,
! [Xa: $real] : ( sqr(Xa) = $product(Xa,Xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sqr_def) ).
tff(f_374,axiom,
! [X: $real,Y: $real,Z: $real] :
( ( Y != 0 )
=> ( ( Z = $quotient(X,Y) )
<=> ( X = $product(Y,Z) ) ) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas_real.p',nonzero_eq_divide_eq) ).
tff(c_11,plain,
sqrt(0) != 0,
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_99,plain,
sqrt(0) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_11]) ).
tff(c_101,plain,
'#skE_1' != 0,
inference(demodulation,[status(thm),theory(equality)],[c_99,c_11]) ).
tff(c_184,plain,
! [X_115a: $real] :
( ( sqr(sqrt(X_115a)) = X_115a )
| ~ $lesseq(0,X_115a) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_197,plain,
( ( sqr('#skE_1') = 0 )
| ~ $lesseq(0,0) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_184]) ).
tff(c_199,plain,
sqr('#skE_1') = 0,
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_197]) ).
tff(c_114,plain,
! [X_111a: $real] : ( $product(X_111a,X_111a) = sqr(X_111a) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_19,plain,
! [Y_18: $real,Z_19: $real] :
( ( $quotient($product(Y_18,Z_19),Y_18) = Z_19 )
| ( Y_18 = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_236,plain,
! [X_121a: $real] :
( ( $quotient(sqr(X_121a),X_121a) = X_121a )
| ( X_121a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_114,c_19]) ).
tff(c_302,plain,
( ( $quotient(0,'#skE_1') = '#skE_1' )
| ( '#skE_1' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_199,c_236]) ).
tff(c_303,plain,
( ( '#skE_1' = 0 )
| ( '#skE_1' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LFA')],[c_302]) ).
tff(c_304,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_101,c_101,c_303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ARI742_1 : TPTP v8.1.2. Released v7.0.0.
% 0.00/0.11 % 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
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Aug 4 00:12:36 EDT 2023
% 0.10/0.30 % CPUTime :
% 3.43/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.45/1.89
% 3.45/1.89 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.47/1.91
% 3.47/1.91 Inference rules
% 3.47/1.91 ----------------------
% 3.47/1.91 #Ref : 0
% 3.47/1.91 #Sup : 53
% 3.47/1.91 #Fact : 0
% 3.47/1.91 #Define : 1
% 3.47/1.91 #Split : 0
% 3.47/1.91 #Chain : 0
% 3.47/1.91 #Close : 0
% 3.47/1.91
% 3.47/1.91 Ordering : LPO
% 3.47/1.91
% 3.47/1.91 Simplification rules
% 3.47/1.91 ----------------------
% 3.47/1.91 #Subsume : 0
% 3.47/1.91 #Demod : 7
% 3.47/1.91 #Tautology : 21
% 3.47/1.91 #SimpNegUnit : 1
% 3.47/1.91 #BackRed : 0
% 3.47/1.91
% 3.47/1.91 #Partial instantiations: 0
% 3.47/1.91 #Strategies tried : 1
% 3.47/1.91
% 3.47/1.91 Timing (in seconds)
% 3.47/1.91 ----------------------
% 3.47/1.91 Preprocessing : 0.65
% 3.47/1.91 Parsing : 0.31
% 3.47/1.91 CNF conversion : 0.03
% 3.47/1.92 Main loop : 0.24
% 3.47/1.92 Inferencing : 0.08
% 3.47/1.92 Reduction : 0.07
% 3.47/1.92 Demodulation : 0.05
% 3.47/1.92 BG Simplification : 0.04
% 3.47/1.92 Subsumption : 0.03
% 3.47/1.92 Abstraction : 0.01
% 3.47/1.92 MUC search : 0.00
% 3.47/1.92 Cooper : 0.00
% 3.47/1.92 Total : 0.93
% 3.47/1.92 Index Insertion : 0.00
% 3.47/1.92 Index Deletion : 0.00
% 3.47/1.92 Index Matching : 0.00
% 3.47/1.92 BG Taut test : 0.00
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