%------------------------------------------------------------------------------
% 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 : n002.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 4.13s 1.98s
% Output : CNFRefutation 4.13s
% 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 : 7 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 14 con; 0-4 aty)
% Number of variables : 4 ( 4 !; 0 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
%$ mem > p > k > fo__c_2Emin_2E_3D_3D_3E > fo__c_2Ebool_2E_5C_2F > fo__c_2Ebool_2E_2F_5C > c_2Ecardinal_2Ecardleq > arr > ap > #nlpp > surj__o > inj__o > i > fo__c_2Ebool_2E_7E > c_2Emin_2E_3D > c_2Ebool_2E_21 > ind > fo__c_2Ebool_2ET > fo__c_2Ebool_2EF > 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_6 > #skF_5 > #skF_4 > #skF_1 > #skF_3 > #skF_2
%Foreground sorts:
tff(tp__o,type,
tp__o: $tType ).
tff(del,type,
del: $tType ).
%Background operators:
%Foreground operators:
tff(fo__c_2Ebool_2ET,type,
fo__c_2Ebool_2ET: tp__o ).
tff(c_2Ebool_2EF,type,
c_2Ebool_2EF: $i ).
tff(surj__o,type,
surj__o: $i > tp__o ).
tff(i,type,
i: del > $i ).
tff(fo__c_2Ebool_2E_2F_5C,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(fo__c_2Emin_2E_3D_3D_3E,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(fo__c_2Ebool_2E_7E,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(ap,type,
ap: ( $i * $i ) > $i ).
tff(fo__c_2Ebool_2EF,type,
fo__c_2Ebool_2EF: tp__o ).
tff(p,type,
p: $i > $o ).
tff(k,type,
k: ( del * $i ) > $i ).
tff(c_2Ecardinal_2Ecardleq,type,
c_2Ecardinal_2Ecardleq: ( del * del ) > $i ).
tff(c_2Ebool_2E_21,type,
c_2Ebool_2E_21: del > $i ).
tff(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_5',type,
'#skF_5': del ).
tff(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $i ).
tff('#skF_4',type,
'#skF_4': del ).
tff(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
tff(fo__c_2Ebool_2E_5C_2F,type,
fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).
tff(arr,type,
arr: ( del * del ) > del ).
tff(c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
tff(c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
tff(ind,type,
ind: del ).
tff(mem,type,
mem: ( $i * del ) > $o ).
tff(bool,type,
bool: del ).
tff(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $i ).
tff('#skF_1',type,
'#skF_1': ( del * del * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( del * tp__o ) > $i ).
tff(inj__o,type,
inj__o: tp__o > $i ).
tff('#skF_2',type,
'#skF_2': ( del * $i ) > $i ).
tff(f_380,negated_conjecture,
~ ! [A_27a: del,A_27b: del,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_1257,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq('#skF_4','#skF_5'),'#skF_6'),'#skF_7')),
inference(cnfTransformation,[status(thm)],[f_380]) ).
tff(c_1255,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq('#skF_4','#skF_5'),'#skF_6'),'#skF_7')),
inference(cnfTransformation,[status(thm)],[f_380]) ).
tff(c_1262,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1257,c_1255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ITP010_2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.10/0.12 % 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 : n002.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Apr 8 00:37:32 EDT 2025
% 0.13/0.33 % CPUTime :
% 4.13/1.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.13/1.98
% 4.13/1.98 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------