%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ITP023+1 : 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 : n016.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 06:52:15 PM UTC 2025
% Result : Theorem 36.15s 18.23s
% Output : CNFRefutation 36.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 6 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 4 |; 4 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 42 ( 42 usr; 21 con; 0-4 aty)
% Number of variables : 20 ( 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ p > tyop_2Epair_2Eprod > tyop_2Emin_2Efun > s > c_2Epred__set_2ESUBSET_2E2 > c_2Epair_2E_2C_2E2 > c_2Emin_2E_3D_3D_3E_2E2 > c_2Emin_2E_3D_2E2 > c_2Ebool_2E_5C_2F_2E2 > c_2Ebool_2E_2F_5C_2E2 > app_2E2 > #nlpp > c_2Ereal__topology_2Ecball_2E1 > c_2Ereal__topology_2Ebounded__def_2E1 > c_2Ereal__topology_2Eball_2E1 > c_2Ebool_2E_7E_2E1 > c_2Ebool_2E_3F_2E1 > c_2Ebool_2E_21_2E1 > tyop_2Erealax_2Ereal > tyop_2Emin_2Ebool > combin_s_2E0 > combin_k_2E0 > combin_i_2E0 > c_2Ereal__topology_2Ecball_2E0 > c_2Ereal__topology_2Ebounded__def_2E0 > c_2Ereal__topology_2Eball_2E0 > c_2Epred__set_2ESUBSET_2E0 > c_2Epair_2E_2C_2E0 > c_2Emin_2E_3D_3D_3E_2E0 > c_2Emin_2E_3D_2E0 > c_2Ebool_2E_7E_2E0 > c_2Ebool_2E_5C_2F_2E0 > c_2Ebool_2E_3F_2E0 > c_2Ebool_2E_2F_5C_2E0 > c_2Ebool_2E_21_2E0 > c_2Ebool_2ET_2E0 > c_2Ebool_2EF_2E0 > #skF_7 > #skF_3 > #skF_6 > #skF_2 > #skF_1 > #skF_5 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: $i ).
tff(app_2E2,type,
app_2E2: ( $i * $i ) > $i ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( $i * $i ) > $i ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $i ).
tff(c_2Ereal__topology_2Eball_2E1,type,
c_2Ereal__topology_2Eball_2E1: $i > $i ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: $i ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: $i ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( $i * $i ) > $i ).
tff(c_2Ereal__topology_2Ecball_2E1,type,
c_2Ereal__topology_2Ecball_2E1: $i > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $i * $i ) > $i ).
tff(p,type,
p: $i > $o ).
tff(c_2Ereal__topology_2Ebounded__def_2E1,type,
c_2Ereal__topology_2Ebounded__def_2E1: $i > $i ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: ( $i * $i ) > $i ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( $i * $i ) > $i ).
tff(combin_s_2E0,type,
combin_s_2E0: $i ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0: $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: $i ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $i * $i ) > $i ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2: ( $i * $i ) > $i ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: $i ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: $i ).
tff(c_2Ereal__topology_2Ebounded__def_2E0,type,
c_2Ereal__topology_2Ebounded__def_2E0: $i ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: $i > $i ).
tff(c_2Epred__set_2ESUBSET_2E2,type,
c_2Epred__set_2ESUBSET_2E2: ( $i * $i ) > $i ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: $i > $i ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: $i ).
tff(s,type,
s: ( $i * $i ) > $i ).
tff(c_2Epred__set_2ESUBSET_2E0,type,
c_2Epred__set_2ESUBSET_2E0: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: $i > $i ).
tff(c_2Ereal__topology_2Ecball_2E0,type,
c_2Ereal__topology_2Ecball_2E0: $i ).
tff(combin_i_2E0,type,
combin_i_2E0: $i ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: $i ).
tff(c_2Ereal__topology_2Eball_2E0,type,
c_2Ereal__topology_2Eball_2E0: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i * $i ) > $i ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff(combin_k_2E0,type,
combin_k_2E0: $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $i ).
tff(f_41,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
tff(f_223,axiom,
! [V0t_2E0] :
( ( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) )
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) )
<=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
<=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(f_460,negated_conjecture,
~ ! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
tff(f_283,axiom,
! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
tff(f_275,axiom,
! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
tff(f_281,axiom,
! [V0s_2E0,V1t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
tff(c_14,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_172,plain,
! [V0t_2E0_71] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0_71) )
| p(s(tyop_2Emin_2Ebool,V0t_2E0_71)) ),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_964,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,'#skF_6'),s(tyop_2Erealax_2Ereal,'#skF_7')))))))),
inference(cnfTransformation,[status(thm)],[f_460]) ).
tff(c_1034,plain,
s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,'#skF_6'),s(tyop_2Erealax_2Ereal,'#skF_7'))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(resolution,[status(thm)],[c_172,c_964]) ).
tff(c_208,plain,
! [V0x_2E0_91,V1e_2E0_92] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0_91),s(tyop_2Erealax_2Ereal,V1e_2E0_92)))))))),
inference(cnfTransformation,[status(thm)],[f_283]) ).
tff(c_55076,plain,
! [V0x_2E0_320,V1e_2E0_321] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0_320),s(tyop_2Erealax_2Ereal,V1e_2E0_321))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0_320),s(tyop_2Erealax_2Ereal,V1e_2E0_321)))))))),
inference(cnfTransformation,[status(thm)],[f_275]) ).
tff(c_206,plain,
! [V0s_2E0_89,V1t_2E0_90] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0_89))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0_89),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0_90))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0_90)))) ),
inference(cnfTransformation,[status(thm)],[f_281]) ).
tff(c_55079,plain,
! [V0x_2E0_320,V1e_2E0_321] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0_320),s(tyop_2Erealax_2Ereal,V1e_2E0_321))))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0_320),s(tyop_2Erealax_2Ereal,V1e_2E0_321)))))))) ),
inference(resolution,[status(thm)],[c_55076,c_206]) ).
tff(c_156336,plain,
! [V0x_2E0_460,V1e_2E0_461] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0_460),s(tyop_2Erealax_2Ereal,V1e_2E0_461)))))))),
inference(demodulation,[status(thm),theory(equality)],[c_208,c_55079]) ).
tff(c_156458,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(superposition,[status(thm),theory(equality)],[c_1034,c_156336]) ).
tff(c_156507,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_156458]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP023+1 : 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 : n016.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 01:02:23 EDT 2025
% 0.13/0.33 % CPUTime :
% 36.15/18.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.15/18.23
% 36.15/18.23 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------