%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ITP019_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 : n025.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 06:52:11 PM UTC 2025
% Result : Theorem 5.78s 2.24s
% Output : CNFRefutation 5.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 7 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 37 ( 37 usr; 16 con; 0-4 aty)
% Number of variables : 5 ( 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
%$ mem > p > ty_2Epair_2Eprod > k > fo__c_2Emin_2E_3D_3D_3E > fo__c_2Ebool_2E_2F_5C > arr > ap > #nlpp > surj__ty_2Erealax_2Ereal > surj__ty_2Enum_2Enum > surj__o > surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal > inj__ty_2Erealax_2Ereal > inj__ty_2Enum_2Enum > inj__o > inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal > i > fo__c_2Ebool_2E_7E > c_2Emin_2E_3D > c_2Ebool_2E_21 > ty_2Erealax_2Ereal > ty_2Enum_2Enum > ind > fo__c_2Enum_2E0 > fo__c_2Ebool_2ET > fo__c_2Ebool_2EF > c_2Enum_2E0 > c_2Emin_2E_3D_3D_3E > c_2Ecomplex_2Ecomplex__of__num > c_2Ecomplex_2Ecomplex__inv > c_2Ebool_2E_7E > c_2Ebool_2E_2F_5C > c_2Ebool_2ET > c_2Ebool_2EF > bool > #skF_4 > #skF_1 > #skF_3 > #skF_2
%Foreground sorts:
tff(tp__o,type,
tp__o: $tType ).
tff(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,type,
tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $tType ).
tff(del,type,
del: $tType ).
tff(tp__ty_2Enum_2Enum,type,
tp__ty_2Enum_2Enum: $tType ).
tff(tp__ty_2Erealax_2Ereal,type,
tp__ty_2Erealax_2Ereal: $tType ).
%Background operators:
%Foreground operators:
tff(fo__c_2Ebool_2ET,type,
fo__c_2Ebool_2ET: tp__o ).
tff(c_2Enum_2E0,type,
c_2Enum_2E0: $i ).
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(ty_2Erealax_2Ereal,type,
ty_2Erealax_2Ereal: del ).
tff(ty_2Enum_2Enum,type,
ty_2Enum_2Enum: del ).
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(ap,type,
ap: ( $i * $i ) > $i ).
tff(fo__c_2Ebool_2EF,type,
fo__c_2Ebool_2EF: tp__o ).
tff(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,type,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $i > tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).
tff(p,type,
p: $i > $o ).
tff(k,type,
k: ( del * $i ) > $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(fo__c_2Enum_2E0,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
tff(c_2Ecomplex_2Ecomplex__of__num,type,
c_2Ecomplex_2Ecomplex__of__num: $i ).
tff(inj__ty_2Enum_2Enum,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
tff(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
tff(arr,type,
arr: ( del * del ) > del ).
tff(surj__ty_2Enum_2Enum,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
tff(c_2Ecomplex_2Ecomplex__inv,type,
c_2Ecomplex_2Ecomplex__inv: $i ).
tff(c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
tff(c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
tff(surj__ty_2Erealax_2Ereal,type,
surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).
tff(ind,type,
ind: del ).
tff(mem,type,
mem: ( $i * del ) > $o ).
tff('#skF_4',type,
'#skF_4': tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).
tff(bool,type,
bool: del ).
tff(ty_2Epair_2Eprod,type,
ty_2Epair_2Eprod: ( del * del ) > del ).
tff(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,type,
inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal > $i ).
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__ty_2Erealax_2Ereal,type,
inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
tff(inj__o,type,
inj__o: tp__o > $i ).
tff('#skF_2',type,
'#skF_2': ( del * $i ) > $i ).
tff(f_159,axiom,
inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = c_2Enum_2E0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Enum_2E0) ).
tff(f_243,negated_conjecture,
~ ! [V0z: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( V0z != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
tff(f_236,axiom,
! [V0z: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
tff(c_74,plain,
inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = c_2Enum_2E0,
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_122,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal('#skF_4'))),
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_128,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal('#skF_4'))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),
inference(demodulation,[status(thm),theory(equality)],[c_74,c_122]) ).
tff(c_124,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_125,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal('#skF_4'))) != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_122,c_124]) ).
tff(c_129,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_128,c_125]) ).
tff(c_118,plain,
! [V0z_63: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = V0z_63 )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z_63))) ) ),
inference(cnfTransformation,[status(thm)],[f_236]) ).
tff(c_127,plain,
! [V0z_63: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal('#skF_4'))) = V0z_63 )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z_63))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal('#skF_4'))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_118]) ).
tff(c_1693,plain,
! [V0z_628: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = V0z_628 )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z_628))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_128,c_127]) ).
tff(c_1699,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_128,c_1693]) ).
tff(c_1705,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_129,c_1699]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP019_2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.10/0.13 % 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 : n025.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 : Tue Apr 8 00:55:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.78/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.78/2.25
% 5.78/2.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------