%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET603+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/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 : n015.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 08:38:50 PM UTC 2025
% Result : Theorem 9.04s 3.28s
% Output : CNFRefutation 9.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 12 ~; 12 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > difference > #nlpp > empty_set > #skF_7 > #skF_3 > #skF_2 > #skF_1 > #skF_5 > #skF_6 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_69,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_42,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
tff(f_46,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_53,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
tff(f_83,negated_conjecture,
~ ! [B] : ( difference(B,empty_set) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th74) ).
tff(c_40,plain,
! [B_15,C_16] :
( member('#skF_5'(B_15,C_16),B_15)
| subset(B_15,C_16) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_190,plain,
! [D_56,B_57,C_58] :
( member(D_56,difference(B_57,C_58))
| member(D_56,C_58)
| ~ member(D_56,B_57) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_38,plain,
! [B_15,C_16] :
( ~ member('#skF_5'(B_15,C_16),C_16)
| subset(B_15,C_16) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_13994,plain,
! [B_559,B_560,C_561] :
( subset(B_559,difference(B_560,C_561))
| member('#skF_5'(B_559,difference(B_560,C_561)),C_561)
| ~ member('#skF_5'(B_559,difference(B_560,C_561)),B_560) ),
inference(resolution,[status(thm)],[c_190,c_38]) ).
tff(c_14040,plain,
! [B_562,C_563] :
( member('#skF_5'(B_562,difference(B_562,C_563)),C_563)
| subset(B_562,difference(B_562,C_563)) ),
inference(resolution,[status(thm)],[c_40,c_13994]) ).
tff(c_16,plain,
! [B_7] : ~ member(B_7,empty_set),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_14148,plain,
! [B_564] : subset(B_564,difference(B_564,empty_set)),
inference(resolution,[status(thm)],[c_14040,c_16]) ).
tff(c_76,plain,
! [D_35,B_36,C_37] :
( member(D_35,B_36)
| ~ member(D_35,difference(B_36,C_37)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_1745,plain,
! [B_179,C_180,C_181] :
( member('#skF_5'(difference(B_179,C_180),C_181),B_179)
| subset(difference(B_179,C_180),C_181) ),
inference(resolution,[status(thm)],[c_40,c_76]) ).
tff(c_1799,plain,
! [B_182,C_183] : subset(difference(B_182,C_183),B_182),
inference(resolution,[status(thm)],[c_1745,c_38]) ).
tff(c_18,plain,
! [C_9,B_8] :
( ( C_9 = B_8 )
| ~ subset(C_9,B_8)
| ~ subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_1873,plain,
! [B_182,C_183] :
( ( difference(B_182,C_183) = B_182 )
| ~ subset(B_182,difference(B_182,C_183)) ),
inference(resolution,[status(thm)],[c_1799,c_18]) ).
tff(c_14331,plain,
! [B_564] : ( difference(B_564,empty_set) = B_564 ),
inference(resolution,[status(thm)],[c_14148,c_1873]) ).
tff(c_48,plain,
difference('#skF_7',empty_set) != '#skF_7',
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_14351,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14331,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET603+3 : TPTP v9.0.0. Released v2.2.0.
% 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
% 0.13/0.31 % Computer : n015.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Apr 8 21:18:05 EDT 2025
% 0.13/0.32 % CPUTime :
% 9.04/3.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.04/3.29
% 9.04/3.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------