%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET579+3 : TPTP v9.0.0. Released v2.2.0.
% 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 : n005.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 08:38:45 PM UTC 2025
% Result : Theorem 6.25s 2.93s
% Output : CNFRefutation 6.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 65 ( 26 ~; 30 |; 3 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > difference > #nlpp > #skF_2 > #skF_3 > #skF_4 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_64,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
& ~ member(E,D) ) )
=> ( B = difference(C,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th20) ).
tff(f_52,axiom,
! [B] : subset(B,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(f_49,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_34,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
tff(f_41,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
tff(c_22,plain,
difference('#skF_3','#skF_4') != '#skF_2',
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_20,plain,
! [B_11] : subset(B_11,B_11),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_42,plain,
! [B_22,C_23] :
( member('#skF_1'(B_22,C_23),B_22)
| subset(B_22,C_23) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_28,plain,
! [E_13] :
( member(E_13,'#skF_3')
| ~ member(E_13,'#skF_2') ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_56,plain,
! [C_23] :
( member('#skF_1'('#skF_2',C_23),'#skF_3')
| subset('#skF_2',C_23) ),
inference(resolution,[status(thm)],[c_42,c_28]) ).
tff(c_106,plain,
! [D_35,B_36,C_37] :
( member(D_35,difference(B_36,C_37))
| member(D_35,C_37)
| ~ member(D_35,B_36) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_16,plain,
! [B_6,C_7] :
( ~ member('#skF_1'(B_6,C_7),C_7)
| subset(B_6,C_7) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_1216,plain,
! [B_101,B_102,C_103] :
( subset(B_101,difference(B_102,C_103))
| member('#skF_1'(B_101,difference(B_102,C_103)),C_103)
| ~ member('#skF_1'(B_101,difference(B_102,C_103)),B_102) ),
inference(resolution,[status(thm)],[c_106,c_16]) ).
tff(c_2141,plain,
! [C_127] :
( member('#skF_1'('#skF_2',difference('#skF_3',C_127)),C_127)
| subset('#skF_2',difference('#skF_3',C_127)) ),
inference(resolution,[status(thm)],[c_56,c_1216]) ).
tff(c_18,plain,
! [B_6,C_7] :
( member('#skF_1'(B_6,C_7),B_6)
| subset(B_6,C_7) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_96,plain,
! [D_32,C_33,B_34] :
( member(D_32,C_33)
| ~ member(D_32,B_34)
| ~ subset(B_34,C_33) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_123,plain,
! [B_38,C_39,C_40] :
( member('#skF_1'(B_38,C_39),C_40)
| ~ subset(B_38,C_40)
| subset(B_38,C_39) ),
inference(resolution,[status(thm)],[c_18,c_96]) ).
tff(c_26,plain,
! [E_13] :
( ~ member(E_13,'#skF_4')
| ~ member(E_13,'#skF_2') ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_156,plain,
! [B_38,C_39] :
( ~ member('#skF_1'(B_38,C_39),'#skF_4')
| ~ subset(B_38,'#skF_2')
| subset(B_38,C_39) ),
inference(resolution,[status(thm)],[c_123,c_26]) ).
tff(c_2158,plain,
( ~ subset('#skF_2','#skF_2')
| subset('#skF_2',difference('#skF_3','#skF_4')) ),
inference(resolution,[status(thm)],[c_2141,c_156]) ).
tff(c_2196,plain,
subset('#skF_2',difference('#skF_3','#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_2158]) ).
tff(c_8,plain,
! [C_5,B_4] :
( ( C_5 = B_4 )
| ~ subset(C_5,B_4)
| ~ subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_2206,plain,
( ( difference('#skF_3','#skF_4') = '#skF_2' )
| ~ subset(difference('#skF_3','#skF_4'),'#skF_2') ),
inference(resolution,[status(thm)],[c_2196,c_8]) ).
tff(c_2210,plain,
~ subset(difference('#skF_3','#skF_4'),'#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_22,c_2206]) ).
tff(c_6,plain,
! [D_3,B_1,C_2] :
( member(D_3,B_1)
| ~ member(D_3,difference(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_55,plain,
! [B_1,C_2,C_23] :
( member('#skF_1'(difference(B_1,C_2),C_23),B_1)
| subset(difference(B_1,C_2),C_23) ),
inference(resolution,[status(thm)],[c_42,c_6]) ).
tff(c_71,plain,
! [E_29] :
( member(E_29,'#skF_2')
| member(E_29,'#skF_4')
| ~ member(E_29,'#skF_3') ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_518,plain,
! [B_77] :
( subset(B_77,'#skF_2')
| member('#skF_1'(B_77,'#skF_2'),'#skF_4')
| ~ member('#skF_1'(B_77,'#skF_2'),'#skF_3') ),
inference(resolution,[status(thm)],[c_71,c_16]) ).
tff(c_2712,plain,
! [C_136] :
( member('#skF_1'(difference('#skF_3',C_136),'#skF_2'),'#skF_4')
| subset(difference('#skF_3',C_136),'#skF_2') ),
inference(resolution,[status(thm)],[c_55,c_518]) ).
tff(c_58,plain,
! [D_24,C_25,B_26] :
( ~ member(D_24,C_25)
| ~ member(D_24,difference(B_26,C_25)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_63,plain,
! [B_26,C_25,C_7] :
( ~ member('#skF_1'(difference(B_26,C_25),C_7),C_25)
| subset(difference(B_26,C_25),C_7) ),
inference(resolution,[status(thm)],[c_18,c_58]) ).
tff(c_2720,plain,
subset(difference('#skF_3','#skF_4'),'#skF_2'),
inference(resolution,[status(thm)],[c_2712,c_63]) ).
tff(c_2739,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2210,c_2210,c_2720]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET579+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.11 % 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
% 0.10/0.32 % Computer : n005.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue Apr 8 21:15:12 EDT 2025
% 0.10/0.32 % CPUTime :
% 6.25/2.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.25/2.94
% 6.25/2.94 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------