%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU361+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n006.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 08:53:46 PM UTC 2025
% Result : Theorem 3.91s 1.94s
% Output : CNFRefutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 108 ( 9 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 113 ( 44 ~; 39 |; 14 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 32 ( 31 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relstr_set_smaller > relstr_element_smaller > related > in > ex_sup_of_relstr_set > ex_inf_of_relstr_set > element > rel_str > one_sorted_str > lower_bounded_relstr > finite > empty_carrier > empty > antisymmetric_relstr > join_on_relstr > #nlpp > the_carrier > bottom_of_relstr > empty_set > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_2 > #skF_1 > #skF_9 > #skF_4 > #skF_3 > #skF_8
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(bottom_of_relstr,type,
bottom_of_relstr: $i > $i ).
tff(empty_carrier,type,
empty_carrier: $i > $o ).
tff(related,type,
related: ( $i * $i * $i ) > $o ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(relstr_set_smaller,type,
relstr_set_smaller: ( $i * $i * $i ) > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff(lower_bounded_relstr,type,
lower_bounded_relstr: $i > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(ex_sup_of_relstr_set,type,
ex_sup_of_relstr_set: ( $i * $i ) > $o ).
tff(join_on_relstr,type,
join_on_relstr: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(rel_str,type,
rel_str: $i > $o ).
tff(relstr_element_smaller,type,
relstr_element_smaller: ( $i * $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff(ex_inf_of_relstr_set,type,
ex_inf_of_relstr_set: ( $i * $i ) > $o ).
tff(f_155,negated_conjecture,
~ ! [A] :
( ( ~ empty_carrier(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> related(A,bottom_of_relstr(A),B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_yellow_0) ).
tff(f_75,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_159,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_168,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_set_smaller(A,empty_set,B)
& relstr_element_smaller(A,empty_set,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
tff(f_140,axiom,
! [A] :
( ( ~ empty_carrier(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) )
=> ( ex_sup_of_relstr_set(A,empty_set)
& ex_inf_of_relstr_set(A,the_carrier(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_0) ).
tff(f_39,axiom,
! [A] :
( rel_str(A)
=> ( bottom_of_relstr(A) = join_on_relstr(A,empty_set) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_yellow_0) ).
tff(f_44,axiom,
! [A,B] :
( rel_str(A)
=> element(join_on_relstr(A,B),the_carrier(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
tff(f_127,axiom,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ( B = join_on_relstr(A,C) )
& ex_sup_of_relstr_set(A,C) )
=> ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) ) )
& ( ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) )
=> ( ( B = join_on_relstr(A,C) )
& ex_sup_of_relstr_set(A,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_yellow_0) ).
tff(c_70,plain,
element('#skF_10',the_carrier('#skF_9')),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_72,plain,
rel_str('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_36,plain,
empty('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_98,plain,
! [A_49] :
( ( empty_set = A_49 )
| ~ empty(A_49) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_105,plain,
empty_set = '#skF_5',
inference(resolution,[status(thm)],[c_36,c_98]) ).
tff(c_84,plain,
! [A_41,B_43] :
( relstr_set_smaller(A_41,empty_set,B_43)
| ~ element(B_43,the_carrier(A_41))
| ~ rel_str(A_41) ),
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_179,plain,
! [A_70,B_71] :
( relstr_set_smaller(A_70,'#skF_5',B_71)
| ~ element(B_71,the_carrier(A_70))
| ~ rel_str(A_70) ),
inference(demodulation,[status(thm),theory(equality)],[c_105,c_84]) ).
tff(c_198,plain,
( relstr_set_smaller('#skF_9','#skF_5','#skF_10')
| ~ rel_str('#skF_9') ),
inference(resolution,[status(thm)],[c_70,c_179]) ).
tff(c_210,plain,
relstr_set_smaller('#skF_9','#skF_5','#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_72,c_198]) ).
tff(c_78,plain,
~ empty_carrier('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_76,plain,
antisymmetric_relstr('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_74,plain,
lower_bounded_relstr('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_66,plain,
! [A_38] :
( ex_sup_of_relstr_set(A_38,empty_set)
| ~ rel_str(A_38)
| ~ lower_bounded_relstr(A_38)
| ~ antisymmetric_relstr(A_38)
| empty_carrier(A_38) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_257,plain,
! [A_38] :
( ex_sup_of_relstr_set(A_38,'#skF_5')
| ~ rel_str(A_38)
| ~ lower_bounded_relstr(A_38)
| ~ antisymmetric_relstr(A_38)
| empty_carrier(A_38) ),
inference(demodulation,[status(thm),theory(equality)],[c_105,c_66]) ).
tff(c_6,plain,
! [A_4] :
( ( join_on_relstr(A_4,empty_set) = bottom_of_relstr(A_4) )
| ~ rel_str(A_4) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_132,plain,
! [A_62] :
( ( join_on_relstr(A_62,'#skF_5') = bottom_of_relstr(A_62) )
| ~ rel_str(A_62) ),
inference(demodulation,[status(thm),theory(equality)],[c_105,c_6]) ).
tff(c_140,plain,
join_on_relstr('#skF_9','#skF_5') = bottom_of_relstr('#skF_9'),
inference(resolution,[status(thm)],[c_72,c_132]) ).
tff(c_150,plain,
! [A_64,B_65] :
( element(join_on_relstr(A_64,B_65),the_carrier(A_64))
| ~ rel_str(A_64) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_156,plain,
( element(bottom_of_relstr('#skF_9'),the_carrier('#skF_9'))
| ~ rel_str('#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_140,c_150]) ).
tff(c_160,plain,
element(bottom_of_relstr('#skF_9'),the_carrier('#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_72,c_156]) ).
tff(c_363,plain,
! [A_124,C_125,D_126] :
( related(A_124,join_on_relstr(A_124,C_125),D_126)
| ~ relstr_set_smaller(A_124,C_125,D_126)
| ~ element(D_126,the_carrier(A_124))
| ~ ex_sup_of_relstr_set(A_124,C_125)
| ~ element(join_on_relstr(A_124,C_125),the_carrier(A_124))
| ~ rel_str(A_124)
| ~ antisymmetric_relstr(A_124) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_369,plain,
! [D_126] :
( related('#skF_9',join_on_relstr('#skF_9','#skF_5'),D_126)
| ~ relstr_set_smaller('#skF_9','#skF_5',D_126)
| ~ element(D_126,the_carrier('#skF_9'))
| ~ ex_sup_of_relstr_set('#skF_9','#skF_5')
| ~ element(bottom_of_relstr('#skF_9'),the_carrier('#skF_9'))
| ~ rel_str('#skF_9')
| ~ antisymmetric_relstr('#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_140,c_363]) ).
tff(c_374,plain,
! [D_126] :
( related('#skF_9',bottom_of_relstr('#skF_9'),D_126)
| ~ relstr_set_smaller('#skF_9','#skF_5',D_126)
| ~ element(D_126,the_carrier('#skF_9'))
| ~ ex_sup_of_relstr_set('#skF_9','#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_72,c_160,c_140,c_369]) ).
tff(c_375,plain,
~ ex_sup_of_relstr_set('#skF_9','#skF_5'),
inference(splitLeft,[status(thm)],[c_374]) ).
tff(c_378,plain,
( ~ rel_str('#skF_9')
| ~ lower_bounded_relstr('#skF_9')
| ~ antisymmetric_relstr('#skF_9')
| empty_carrier('#skF_9') ),
inference(resolution,[status(thm)],[c_257,c_375]) ).
tff(c_381,plain,
empty_carrier('#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_74,c_72,c_378]) ).
tff(c_383,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_78,c_381]) ).
tff(c_386,plain,
! [D_127] :
( related('#skF_9',bottom_of_relstr('#skF_9'),D_127)
| ~ relstr_set_smaller('#skF_9','#skF_5',D_127)
| ~ element(D_127,the_carrier('#skF_9')) ),
inference(splitRight,[status(thm)],[c_374]) ).
tff(c_68,plain,
~ related('#skF_9',bottom_of_relstr('#skF_9'),'#skF_10'),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_397,plain,
( ~ relstr_set_smaller('#skF_9','#skF_5','#skF_10')
| ~ element('#skF_10',the_carrier('#skF_9')) ),
inference(resolution,[status(thm)],[c_386,c_68]) ).
tff(c_407,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_70,c_210,c_397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU361+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.32 % Computer : n006.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Apr 8 22:57:22 EDT 2025
% 0.13/0.32 % CPUTime :
% 3.91/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.91/1.94
% 3.91/1.94 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------