%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI120_1 : TPTP v9.0.0. Released v5.0.0.
% 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 : n009.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 05:39:43 PM UTC 2025
% Result : Theorem 7.39s 2.88s
% Output : CNFRefutation 7.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 46 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 24 ~; 23 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 168 ( 0 atm; 86 fun; 35 num; 47 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 0 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 45 !; 2 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
%$ p > #nlpp
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(p,type,
p: $int > $o ).
tff(f_160,axiom,
! [C: $int,B: $int] :
( ( $product(C,B) = C )
<=> ( ( C = 0 )
| ( B = 1 ) ) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_cancel_right1) ).
tff(f_146,axiom,
! [A: $int,B: $int,C: $int] : ( $product(A,$sum(B,C)) = $sum($product(A,B),$product(A,C)) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_dist) ).
tff(f_144,axiom,
! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).
tff(f_152,axiom,
! [A: $int,B: $int] : ( $uminus($product(A,B)) = $product($uminus(A),B) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',minus_mult_left) ).
tff(f_37,negated_conjecture,
~ ( p(2)
=> ? [Xa: $int,Ya: $int] :
( p(Xa)
& ( Xa != Ya )
& ( $product(Ya,Ya) = 4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_X_X_4_predicate) ).
tff(c_31,plain,
! [C_25: $int] : ( $product(C_25,1) = C_25 ),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_11,plain,
! [A_11: $int,C_13: $int,B_12: $int] : ( $product(A_11,$sum(C_13,B_12)) = $sum($product(A_11,B_12),$product(A_11,C_13)) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_37,plain,
! [A_14: $int,X_32: $int,B_15: $int,C_16: $int] :
( ( $product(A_14,X_32) = $sum($product(A_14,B_15),$product(A_14,C_16)) )
| ( X_32 != $sum(B_15,C_16) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_11]) ).
tff(c_38,plain,
! [B_9: $int,A_10: $int] : ( $product(B_9,A_10) = $product(A_10,B_9) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_33,plain,
! [A_19: $int,B_20: $int,X_31: $int] :
( ( $uminus($product(A_19,B_20)) = $product(X_31,B_20) )
| ( X_31 != $uminus(A_19) ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_35,plain,
! [X_31: $int,B_20: $int,A_19: $int] :
( ( $uminus($product(X_31,B_20)) = $product(A_19,B_20) )
| ( X_31 != $uminus(A_19) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_33]) ).
tff(c_27,plain,
p(2),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_44,plain,
! [Y_34a: $int,X_35a: $int] :
( ( $product(Y_34a,Y_34a) != 4 )
| ~ p(X_35a)
| ( Y_34a = X_35a ) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_50,plain,
! [Y_36a: $int] :
( ( $product(Y_36a,Y_36a) != 4 )
| ( Y_36a = 2 ) ),
inference(resolution,[status(thm)],[c_27,c_44]) ).
tff(c_59,plain,
! [Y_36a: $int] :
( ( $uminus($product($uminus(Y_36a),Y_36a)) != 4 )
| ( Y_36a = 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_35,c_50]) ).
tff(c_75,plain,
! [Y_36a: $int] :
( ( $uminus($product(Y_36a,$uminus(Y_36a))) != 4 )
| ( Y_36a = 2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_59]) ).
tff(c_85,plain,
! [Y_39a: $int] :
( ( $product(Y_39a,$uminus(Y_39a)) != $uminus(4) )
| ( Y_39a = 2 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_75]) ).
tff(c_119,plain,
! [Y_39a: $int,B_15: $int,C_16: $int] :
( ( $sum($product(Y_39a,B_15),$product(Y_39a,C_16)) != $uminus(4) )
| ( Y_39a = 2 )
| ( $uminus(Y_39a) != $sum(B_15,C_16) ) ),
inference(superposition,[status(thm),theory(equality)],[c_37,c_85]) ).
tff(c_1274,plain,
! [X_152: $int,B_150: $int,C_148: $int,Y_149a: $int,X_151: $int] :
( ( $product(Y_149a,B_150) != $sum($uminus(4),$uminus($product(Y_149a,C_148))) )
| ( Y_149a = 2 )
| ( Y_149a != $sum(X_152,X_151) )
| ( X_151 != $uminus(B_150) )
| ( X_152 != $uminus(C_148) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_119]) ).
tff(c_1345,plain,
! [Y_149a: $int,B_150: $int,X_151: $int] :
( ( $product(Y_149a,B_150) != $sum($uminus(4),$uminus(Y_149a)) )
| ( Y_149a = 2 )
| ( Y_149a != $sum($uminus(1),X_151) )
| ( X_151 != $uminus(B_150) ) ),
inference(superposition,[status(thm),theory(equality)],[c_31,c_1274]) ).
tff(c_4491,plain,
! [Y_478a: $int,B_479: $int,X_480: $int] :
( ( $product(Y_478a,B_479) != $sum($uminus(4),$uminus(Y_478a)) )
| ( Y_478a = 2 )
| ( Y_478a != $sum($uminus(1),X_480) )
| ( X_480 != $uminus(B_479) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1345]) ).
tff(c_4522,plain,
( ( $sum($uminus(4),$uminus($sum($uminus(1),$uminus(1)))) != $sum($uminus(1),$uminus(1)) )
| ( $sum($uminus(1),$uminus(1)) = 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_31,c_4491]) ).
tff(c_4524,plain,
$uminus(2) = 2,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4522]) ).
tff(c_4527,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ARI120_1 : TPTP v9.0.0. Released v5.0.0.
% 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
% 0.14/0.34 % Computer : n009.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 15:04:11 EDT 2025
% 0.14/0.34 % CPUTime :
% 7.39/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.39/2.88
% 7.39/2.88 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------