TSTP Solution File: SET974+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n007.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 : Tue Aug 22 10:57:26 EDT 2023
% Result : Theorem 7.05s 2.77s
% Output : CNFRefutation 7.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 22
% Syntax : Number of formulae : 45 ( 11 unt; 17 typ; 0 def)
% Number of atoms : 50 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 23 ~; 14 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 11 >; 15 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-5 aty)
% Number of variables : 63 (; 62 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > disjoint > empty > unordered_pair > set_intersection2 > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_4 > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_1 > #skF_3 > #skF_8 > #skF_9
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i * $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff(f_69,negated_conjecture,
~ ! [A,B,C,D] :
( ( disjoint(A,B)
| disjoint(C,D) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
tff(f_51,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
tff(f_83,axiom,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ~ ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
tff(f_62,axiom,
! [A,B,C,D,E] :
~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
& ! [F,G] :
~ ( ( A = ordered_pair(F,G) )
& in(F,set_intersection2(B,D))
& in(G,set_intersection2(C,E)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
tff(f_35,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(c_28,plain,
( disjoint('#skF_7','#skF_8')
| disjoint('#skF_5','#skF_6') ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_110,plain,
disjoint('#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_18,plain,
! [B_14,A_13] :
( disjoint(B_14,A_13)
| ~ disjoint(A_13,B_14) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_113,plain,
disjoint('#skF_6','#skF_5'),
inference(resolution,[status(thm)],[c_110,c_18]) ).
tff(c_30,plain,
! [A_22,B_23] :
( in('#skF_9'(A_22,B_23),set_intersection2(A_22,B_23))
| disjoint(A_22,B_23) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_296,plain,
! [C_56,A_60,E_59,B_58,D_57] :
( in('#skF_3'(C_56,D_57,B_58,E_59,A_60),set_intersection2(B_58,D_57))
| ~ in(A_60,set_intersection2(cartesian_product2(B_58,C_56),cartesian_product2(D_57,E_59))) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_2411,plain,
! [C_237,D_238,B_239,E_240] :
( in('#skF_3'(C_237,D_238,B_239,E_240,'#skF_9'(cartesian_product2(B_239,C_237),cartesian_product2(D_238,E_240))),set_intersection2(B_239,D_238))
| disjoint(cartesian_product2(B_239,C_237),cartesian_product2(D_238,E_240)) ),
inference(resolution,[status(thm)],[c_30,c_296]) ).
tff(c_6,plain,
! [B_6,A_5] : ( set_intersection2(B_6,A_5) = set_intersection2(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_119,plain,
! [A_38,B_39,C_40] :
( ~ disjoint(A_38,B_39)
| ~ in(C_40,set_intersection2(A_38,B_39)) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_122,plain,
! [A_5,B_6,C_40] :
( ~ disjoint(A_5,B_6)
| ~ in(C_40,set_intersection2(B_6,A_5)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_119]) ).
tff(c_2452,plain,
! [D_241,B_242,C_243,E_244] :
( ~ disjoint(D_241,B_242)
| disjoint(cartesian_product2(B_242,C_243),cartesian_product2(D_241,E_244)) ),
inference(resolution,[status(thm)],[c_2411,c_122]) ).
tff(c_26,plain,
~ disjoint(cartesian_product2('#skF_5','#skF_7'),cartesian_product2('#skF_6','#skF_8')),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_2476,plain,
~ disjoint('#skF_6','#skF_5'),
inference(resolution,[status(thm)],[c_2452,c_26]) ).
tff(c_2489,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_113,c_2476]) ).
tff(c_2490,plain,
disjoint('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_2494,plain,
disjoint('#skF_8','#skF_7'),
inference(resolution,[status(thm)],[c_2490,c_18]) ).
tff(c_2749,plain,
! [B_274,D_273,E_275,A_276,C_272] :
( in('#skF_4'(C_272,D_273,B_274,E_275,A_276),set_intersection2(C_272,E_275))
| ~ in(A_276,set_intersection2(cartesian_product2(B_274,C_272),cartesian_product2(D_273,E_275))) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_5146,plain,
! [C_468,D_469,B_470,E_471] :
( in('#skF_4'(C_468,D_469,B_470,E_471,'#skF_9'(cartesian_product2(B_470,C_468),cartesian_product2(D_469,E_471))),set_intersection2(C_468,E_471))
| disjoint(cartesian_product2(B_470,C_468),cartesian_product2(D_469,E_471)) ),
inference(resolution,[status(thm)],[c_30,c_2749]) ).
tff(c_2500,plain,
! [A_247,B_248,C_249] :
( ~ disjoint(A_247,B_248)
| ~ in(C_249,set_intersection2(A_247,B_248)) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_2503,plain,
! [A_5,B_6,C_249] :
( ~ disjoint(A_5,B_6)
| ~ in(C_249,set_intersection2(B_6,A_5)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_2500]) ).
tff(c_5187,plain,
! [E_472,C_473,B_474,D_475] :
( ~ disjoint(E_472,C_473)
| disjoint(cartesian_product2(B_474,C_473),cartesian_product2(D_475,E_472)) ),
inference(resolution,[status(thm)],[c_5146,c_2503]) ).
tff(c_5211,plain,
~ disjoint('#skF_8','#skF_7'),
inference(resolution,[status(thm)],[c_5187,c_26]) ).
tff(c_5224,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2494,c_5211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % 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
% 0.15/0.37 % Computer : n007.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 16:25:24 EDT 2023
% 0.15/0.37 % CPUTime :
% 7.05/2.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.05/2.78
% 7.05/2.78 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.37/2.81
% 7.37/2.81 Inference rules
% 7.37/2.81 ----------------------
% 7.37/2.81 #Ref : 0
% 7.37/2.81 #Sup : 1339
% 7.37/2.81 #Fact : 0
% 7.37/2.81 #Define : 0
% 7.37/2.81 #Split : 1
% 7.37/2.81 #Chain : 0
% 7.37/2.81 #Close : 0
% 7.37/2.81
% 7.37/2.81 Ordering : KBO
% 7.37/2.81
% 7.37/2.81 Simplification rules
% 7.37/2.81 ----------------------
% 7.37/2.81 #Subsume : 302
% 7.37/2.81 #Demod : 810
% 7.37/2.81 #Tautology : 288
% 7.37/2.81 #SimpNegUnit : 0
% 7.37/2.81 #BackRed : 0
% 7.37/2.81
% 7.37/2.81 #Partial instantiations: 0
% 7.37/2.81 #Strategies tried : 1
% 7.37/2.81
% 7.37/2.81 Timing (in seconds)
% 7.37/2.81 ----------------------
% 7.37/2.81 Preprocessing : 0.47
% 7.37/2.81 Parsing : 0.25
% 7.37/2.81 CNF conversion : 0.03
% 7.37/2.81 Main loop : 1.25
% 7.37/2.81 Inferencing : 0.41
% 7.37/2.81 Reduction : 0.48
% 7.37/2.81 Demodulation : 0.40
% 7.37/2.81 BG Simplification : 0.04
% 7.37/2.81 Subsumption : 0.23
% 7.37/2.81 Abstraction : 0.07
% 7.37/2.81 MUC search : 0.00
% 7.37/2.81 Cooper : 0.00
% 7.37/2.81 Total : 1.76
% 7.37/2.81 Index Insertion : 0.00
% 7.37/2.81 Index Deletion : 0.00
% 7.37/2.81 Index Matching : 0.00
% 7.37/2.81 BG Taut test : 0.00
%------------------------------------------------------------------------------