%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ITP010+2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 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 : n027.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 06:51:59 PM UTC 2025
% Result : Theorem 3.91s 1.81s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 9 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 9 ( 4 ~; 0 |; 0 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-4 aty)
% Number of variables : 4 ( 4 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ mem > p > ne > k > c_2Ecardinal_2Ecardleq > arr > ap > #nlpp > i > c_2Emin_2E_3D > c_2Ebool_2E_21 > ind > c_2Emin_2E_3D_3D_3E > c_2Ebool_2E_7E > c_2Ebool_2E_5C_2F > c_2Ebool_2E_2F_5C > c_2Ebool_2ET > c_2Ebool_2EF > bool > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_2Ecardinal_2Ecardleq,type,
c_2Ecardinal_2Ecardleq: ( $i * $i ) > $i ).
tff(arr,type,
arr: ( $i * $i ) > $i ).
tff(ne,type,
ne: $i > $o ).
tff(c_2Ebool_2EF,type,
c_2Ebool_2EF: $i ).
tff(i,type,
i: $i > $i ).
tff(c_2Ebool_2E_21,type,
c_2Ebool_2E_21: $i > $i ).
tff(bool,type,
bool: $i ).
tff(mem,type,
mem: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(ap,type,
ap: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(p,type,
p: $i > $o ).
tff(ind,type,
ind: $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $i ).
tff(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
tff(c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
tff(k,type,
k: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i * $i ) > $i ).
tff(c_2Emin_2E_3D,type,
c_2Emin_2E_3D: $i > $i ).
tff(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $i ).
tff(f_438,negated_conjecture,
~ ! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
tff(c_1247,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq('#skF_4','#skF_5'),'#skF_6'),'#skF_7')),
inference(cnfTransformation,[status(thm)],[f_438]) ).
tff(c_1245,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq('#skF_4','#skF_5'),'#skF_6'),'#skF_7')),
inference(cnfTransformation,[status(thm)],[f_438]) ).
tff(c_1256,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1247,c_1245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP010+2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.07/0.13 % 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
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Tue Apr 8 00:37:21 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.91/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.91/1.82
% 3.91/1.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------