%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV488+2 : TPTP v9.0.0. Released v4.0.0.
% 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 : n004.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 09:30:41 PM UTC 2025
% Result : Theorem 4.78s 2.19s
% Output : CNFRefutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 18 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 56 ( 20 ~; 15 |; 12 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ int_less > int_leq > plus > lu > a > #nlpp > real_zero > real_one > n > int_zero > int_one > #skF_2 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(int_one,type,
int_one: $i ).
tff(plus,type,
plus: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(int_zero,type,
int_zero: $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(a,type,
a: ( $i * $i ) > $i ).
tff(real_one,type,
real_one: $i ).
tff(n,type,
n: $i ).
tff(int_leq,type,
int_leq: ( $i * $i ) > $o ).
tff(int_less,type,
int_less: ( $i * $i ) > $o ).
tff(lu,type,
lu: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(real_zero,type,
real_zero: $i ).
tff(f_69,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
tff(f_120,negated_conjecture,
~ ! [I,J] :
( ( int_leq(int_one,I)
& int_leq(I,J)
& int_leq(J,n) )
=> ( ( I = J )
=> ( a(I,J) != real_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lti) ).
tff(f_30,axiom,
! [I,J] :
( int_leq(I,J)
<=> ( int_less(I,J)
| ( I = J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
tff(f_108,hypothesis,
! [I,J] :
( ( int_leq(int_one,I)
& int_leq(I,n)
& int_leq(int_one,J)
& int_leq(J,n) )
=> ( ! [C] :
( ( int_less(int_zero,C)
& ( I = plus(J,C) ) )
=> ! [K] :
( ( int_leq(int_one,K)
& int_leq(K,J) )
=> ( a(plus(K,C),K) = lu(plus(K,C),K) ) ) )
& ! [K] :
( ( int_leq(int_one,K)
& int_leq(K,J) )
=> ( a(K,K) = real_one ) )
& ! [C] :
( ( int_less(int_zero,C)
& ( J = plus(I,C) ) )
=> ! [K] :
( ( int_leq(int_one,K)
& int_leq(K,I) )
=> ( a(K,plus(K,C)) = real_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qil) ).
tff(c_32,plain,
real_zero != real_one,
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_42,plain,
'#skF_2' = '#skF_3',
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_48,plain,
int_leq(int_one,'#skF_2'),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_49,plain,
int_leq(int_one,'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_48]) ).
tff(c_40,plain,
a('#skF_2','#skF_3') = real_zero,
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_51,plain,
a('#skF_3','#skF_3') = real_zero,
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40]) ).
tff(c_44,plain,
int_leq('#skF_3',n),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_4,plain,
! [J_2] : int_leq(J_2,J_2),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_36,plain,
! [K_35,J_24,I_23] :
( ( a(K_35,K_35) = real_one )
| ~ int_leq(K_35,J_24)
| ~ int_leq(int_one,K_35)
| ~ int_leq(J_24,n)
| ~ int_leq(int_one,J_24)
| ~ int_leq(I_23,n)
| ~ int_leq(int_one,I_23) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_633,plain,
! [I_84] :
( ~ int_leq(I_84,n)
| ~ int_leq(int_one,I_84) ),
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_649,plain,
~ int_leq(int_one,'#skF_3'),
inference(resolution,[status(thm)],[c_44,c_633]) ).
tff(c_657,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_49,c_649]) ).
tff(c_844,plain,
! [K_94,J_95] :
( ( a(K_94,K_94) = real_one )
| ~ int_leq(K_94,J_95)
| ~ int_leq(int_one,K_94)
| ~ int_leq(J_95,n)
| ~ int_leq(int_one,J_95) ),
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_1610,plain,
! [J_121] :
( ( a(J_121,J_121) = real_one )
| ~ int_leq(J_121,n)
| ~ int_leq(int_one,J_121) ),
inference(resolution,[status(thm)],[c_4,c_844]) ).
tff(c_1632,plain,
( ( a('#skF_3','#skF_3') = real_one )
| ~ int_leq(int_one,'#skF_3') ),
inference(resolution,[status(thm)],[c_44,c_1610]) ).
tff(c_1640,plain,
real_zero = real_one,
inference(demodulation,[status(thm),theory(equality)],[c_49,c_51,c_1632]) ).
tff(c_1642,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_1640]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV488+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % 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
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Apr 9 03:32:52 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.78/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.78/2.19
% 4.78/2.19 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------