%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI673_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 : n015.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 05:40:49 PM UTC 2025
% Result : Theorem 4.09s 2.12s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 62 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 19 ~; 18 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 150 ( 0 atm; 73 fun; 55 num; 22 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 : 7 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_228,axiom,
! [C: $int,B: $int] :
( ( $product(C,B) = C )
<=> ( ( C = 0 )
| ( B = 1 ) ) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_cancel_right1) ).
tff(f_212,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_220,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(f_35,negated_conjecture,
~ ( ( $product(a,a) = 1 )
<=> ( ( a = $uminus(1) )
| ( a = 1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f_209,axiom,
! [M: $int,N: $int] : ( $product($sum(1,M),N) = $sum(N,$product(M,N)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_def_2) ).
tff(c_50,plain,
! [C_23: $int] : ( $product(C_23,1) = C_23 ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_57,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_52,plain,
! [A_17: $int,B_18: $int,X_45: $int] :
( ( $uminus($product(A_17,B_18)) = $product(X_45,B_18) )
| ( X_45 != $uminus(A_17) ) ),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_54,plain,
! [X_45: $int,B_18: $int,A_17: $int] :
( ( $uminus($product(X_45,B_18)) = $product(A_17,B_18) )
| ( X_45 != $uminus(A_17) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_52]) ).
tff(c_47,plain,
( ( $product(a,a) != 1 )
| ( a != 1 ) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_69,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_47]) ).
tff(c_62,plain,
( ( $product(a,a) != 1 )
| ( a != 1 ) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_76,plain,
( ( '#skE_1' != 1 )
| ( a != 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_69,c_62]) ).
tff(c_78,plain,
a != 1,
inference(splitLeft,[status(thm)],[c_76]) ).
tff(c_80,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_47]) ).
tff(c_43,plain,
( ( $product(a,a) != 1 )
| ( a != $uminus(1) ) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_226,plain,
( ( '#skE_1' != 1 )
| ( a != $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_43]) ).
tff(c_228,plain,
a != $uminus(1),
inference(splitLeft,[status(thm)],[c_226]) ).
tff(c_34,plain,
( ( $product(a,a) = 1 )
| ( a = $uminus(1) )
| ( a = 1 ) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_229,plain,
( ( '#skE_1' = 1 )
| ( a = $uminus(1) )
| ( a = 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_34]) ).
tff(c_231,plain,
'#skE_1' = 1,
inference(negUnitSimplification,[status(thm)],[c_78,c_228,c_229]) ).
tff(c_81,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_47]) ).
tff(c_59,plain,
! [X_47: $int,N_4: $int,M_3: $int] :
( ( $product(X_47,N_4) = $sum(N_4,$product(M_3,N_4)) )
| ( X_47 != $sum(1,M_3) ) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_161,plain,
$product($sum(1,a),a) = $sum(a,'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_81,c_59]) ).
tff(c_164,plain,
$product($sum(1,a),a) = $sum('#skE_1',a),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_161]) ).
tff(c_737,plain,
$product($sum(1,a),a) = $sum(1,a),
inference(demodulation,[status(thm),theory(equality)],[c_231,c_164]) ).
tff(c_51,plain,
! [C_21: $int,B_22: $int] :
( ( $product(C_21,B_22) != C_21 )
| ( C_21 = 0 )
| ( B_22 = 1 ) ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_889,plain,
( ( $sum(1,a) = 0 )
| ( a = 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_737,c_51]) ).
tff(c_891,plain,
( ( a = $uminus(1) )
| ( a = 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_889]) ).
tff(c_940,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_78,c_228,c_891]) ).
tff(c_944,plain,
a = $uminus(1),
inference(splitRight,[status(thm)],[c_226]) ).
tff(c_75,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_47]) ).
tff(c_949,plain,
$product($uminus(1),$uminus(1)) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_944,c_944,c_75]) ).
tff(c_991,plain,
$uminus($product($uminus($uminus(1)),$uminus(1))) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_54,c_949]) ).
tff(c_1034,plain,
$uminus($product($uminus(1),$uminus($uminus(1)))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_991]) ).
tff(c_1036,plain,
$product($uminus(1),1) = $uminus('#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1034]) ).
tff(c_1045,plain,
$uminus('#skE_1') = $uminus(1),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_1036]) ).
tff(c_1047,plain,
'#skE_1' = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1045]) ).
tff(c_943,plain,
'#skE_1' != 1,
inference(splitRight,[status(thm)],[c_226]) ).
tff(c_1054,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1047,c_943]) ).
tff(c_1057,plain,
'#skE_1' != 1,
inference(splitRight,[status(thm)],[c_76]) ).
tff(c_1058,plain,
a = 1,
inference(splitRight,[status(thm)],[c_76]) ).
tff(c_1060,plain,
$product(1,1) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_1058,c_1058,c_75]) ).
tff(c_1090,plain,
'#skE_1' = 1,
inference(superposition,[status(thm),theory(equality)],[c_1060,c_50]) ).
tff(c_1139,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1057,c_1090]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ARI673_1 : TPTP v9.0.0. Released v6.3.0.
% 0.06/0.13 % 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
% 0.14/0.34 % Computer : n015.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 15:16:20 EDT 2025
% 0.14/0.34 % CPUTime :
% 4.09/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.09/2.13
% 4.09/2.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------