%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET009+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 : 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 08:37:26 PM UTC 2025
% Result : Theorem 15.61s 5.05s
% Output : CNFRefutation 15.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 37 ( 15 ~; 17 |; 1 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 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_52,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_difference) ).
tff(f_43,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_35,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(c_18,plain,
subset('#skF_2','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_12,plain,
! [B_4,C_5] :
( member('#skF_1'(B_4,C_5),B_4)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_34,plain,
! [D_18,B_19,C_20] :
( member(D_18,B_19)
| ~ member(D_18,difference(B_19,C_20)) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_39,plain,
! [B_19,C_20,C_5] :
( member('#skF_1'(difference(B_19,C_20),C_5),B_19)
| subset(difference(B_19,C_20),C_5) ),
inference(resolution,[status(thm)],[c_12,c_34]) ).
tff(c_44,plain,
! [D_24,B_25,C_26] :
( member(D_24,difference(B_25,C_26))
| member(D_24,C_26)
| ~ member(D_24,B_25) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_10,plain,
! [B_4,C_5] :
( ~ member('#skF_1'(B_4,C_5),C_5)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_281,plain,
! [B_71,B_72,C_73] :
( subset(B_71,difference(B_72,C_73))
| member('#skF_1'(B_71,difference(B_72,C_73)),C_73)
| ~ member('#skF_1'(B_71,difference(B_72,C_73)),B_72) ),
inference(resolution,[status(thm)],[c_44,c_10]) ).
tff(c_1152,plain,
! [B_145,C_146,C_147] :
( member('#skF_1'(difference(B_145,C_146),difference(B_145,C_147)),C_147)
| subset(difference(B_145,C_146),difference(B_145,C_147)) ),
inference(resolution,[status(thm)],[c_39,c_281]) ).
tff(c_8,plain,
! [D_8,C_5,B_4] :
( member(D_8,C_5)
| ~ member(D_8,B_4)
| ~ subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_20622,plain,
! [B_660,C_661,C_662,C_663] :
( member('#skF_1'(difference(B_660,C_661),difference(B_660,C_662)),C_663)
| ~ subset(C_662,C_663)
| subset(difference(B_660,C_661),difference(B_660,C_662)) ),
inference(resolution,[status(thm)],[c_1152,c_8]) ).
tff(c_21,plain,
! [B_14,C_15] :
( member('#skF_1'(B_14,C_15),B_14)
| subset(B_14,C_15) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_4,plain,
! [D_3,C_2,B_1] :
( ~ member(D_3,C_2)
| ~ member(D_3,difference(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_26,plain,
! [B_1,C_2,C_15] :
( ~ member('#skF_1'(difference(B_1,C_2),C_15),C_2)
| subset(difference(B_1,C_2),C_15) ),
inference(resolution,[status(thm)],[c_21,c_4]) ).
tff(c_20692,plain,
! [C_664,C_665,B_666] :
( ~ subset(C_664,C_665)
| subset(difference(B_666,C_665),difference(B_666,C_664)) ),
inference(resolution,[status(thm)],[c_20622,c_26]) ).
tff(c_16,plain,
~ subset(difference('#skF_4','#skF_3'),difference('#skF_4','#skF_2')),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_20793,plain,
~ subset('#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_20692,c_16]) ).
tff(c_20839,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18,c_20793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET009+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n016.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 19:39:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 15.61/5.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.61/5.06
% 15.61/5.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------