TSTP Solution File: ALG210+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG210+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n004.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 10:32:21 EDT 2023
% Result : Theorem 10.50s 3.60s
% Output : CNFRefutation 10.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 41 unt; 5 typ; 0 def)
% Number of atoms : 73 ( 51 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 13 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 67 (; 66 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ element > times > #nlpp > #skF_1 > #skF_2 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(times,type,
times: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(element,type,
element: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(f_40,negated_conjecture,
~ ! [A,B] :
( ( element(A)
& element(B) )
=> element(times(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
tff(f_33,axiom,
! [B] :
( element(B)
<=> ? [C] :
( ( times(B,C) = B )
& ( times(B,B) = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(f_26,axiom,
! [A,B,C] : ( times(times(A,B),C) = times(B,times(C,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
tff(c_14,plain,
element('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_8,plain,
! [B_4] :
( ( times(B_4,'#skF_1'(B_4)) = B_4 )
| ~ element(B_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_15,plain,
! [B_8] :
( ( times(B_8,B_8) = '#skF_1'(B_8) )
| ~ element(B_8) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_21,plain,
times('#skF_2','#skF_2') = '#skF_1'('#skF_2'),
inference(resolution,[status(thm)],[c_14,c_15]) ).
tff(c_48,plain,
! [A_11,B_12,C_13] : ( times(times(A_11,B_12),C_13) = times(B_12,times(C_13,A_11)) ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_75,plain,
! [C_13] : ( times('#skF_1'('#skF_2'),C_13) = times('#skF_2',times(C_13,'#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_48]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( times(times(A_1,B_2),C_3) = times(B_2,times(C_3,A_1)) ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_150,plain,
! [B_16,C_17] :
( ( times('#skF_1'(B_16),times(C_17,B_16)) = times(B_16,C_17) )
| ~ element(B_16) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_48]) ).
tff(c_164,plain,
! [C_17] :
( ( times('#skF_2',times(times(C_17,'#skF_2'),'#skF_2')) = times('#skF_2',C_17) )
| ~ element('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_150,c_75]) ).
tff(c_205,plain,
! [C_17] : ( times('#skF_2',times('#skF_2',times('#skF_2',C_17))) = times('#skF_2',C_17) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_2,c_164]) ).
tff(c_302,plain,
! [B_19,C_20,A_21,C_22] : ( times(times(B_19,times(C_20,A_21)),C_22) = times(C_20,times(C_22,times(A_21,B_19))) ),
inference(superposition,[status(thm),theory(equality)],[c_48,c_2]) ).
tff(c_395,plain,
! [B_19,C_22] : ( times(times(B_19,'#skF_1'('#skF_2')),C_22) = times('#skF_2',times(C_22,times('#skF_2',B_19))) ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_302]) ).
tff(c_490,plain,
! [B_24,C_25] : ( times(times(B_24,'#skF_1'('#skF_2')),C_25) = times('#skF_2',times(C_25,times('#skF_2',B_24))) ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_302]) ).
tff(c_556,plain,
! [C_25] :
( ( times('#skF_2',times(C_25,times('#skF_2','#skF_2'))) = times('#skF_2',C_25) )
| ~ element('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_490]) ).
tff(c_574,plain,
! [C_25] : ( times('#skF_2',times(C_25,'#skF_1'('#skF_2'))) = times('#skF_2',C_25) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_21,c_556]) ).
tff(c_5677,plain,
! [C_70,A_71,C_72,A_73] : ( times(times(C_70,A_71),times(C_72,A_73)) = times(C_70,times(C_72,times(A_71,A_73))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_302]) ).
tff(c_6361,plain,
! [C_75,A_76] : ( times(times(C_75,A_76),'#skF_1'('#skF_2')) = times(C_75,times('#skF_2',times(A_76,'#skF_2'))) ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_5677]) ).
tff(c_6534,plain,
! [C_25] : ( times('#skF_2',times('#skF_2',times(times(C_25,'#skF_1'('#skF_2')),'#skF_2'))) = times(times('#skF_2',C_25),'#skF_1'('#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_574,c_6361]) ).
tff(c_6904,plain,
! [C_78] : ( times(C_78,times('#skF_2','#skF_1'('#skF_2'))) = times('#skF_2',C_78) ),
inference(demodulation,[status(thm),theory(equality)],[c_21,c_75,c_2,c_205,c_205,c_395,c_6534]) ).
tff(c_7092,plain,
! [C_78] :
( ( times(C_78,'#skF_2') = times('#skF_2',C_78) )
| ~ element('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_6904]) ).
tff(c_7149,plain,
! [C_78] : ( times(C_78,'#skF_2') = times('#skF_2',C_78) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_7092]) ).
tff(c_12,plain,
element('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_20,plain,
times('#skF_3','#skF_3') = '#skF_1'('#skF_3'),
inference(resolution,[status(thm)],[c_12,c_15]) ).
tff(c_85,plain,
! [C_13] : ( times('#skF_1'('#skF_3'),C_13) = times('#skF_3',times(C_13,'#skF_3')) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_48]) ).
tff(c_180,plain,
! [C_17] :
( ( times('#skF_3',times(times(C_17,'#skF_3'),'#skF_3')) = times('#skF_3',C_17) )
| ~ element('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_85,c_150]) ).
tff(c_210,plain,
! [C_17] : ( times('#skF_3',times('#skF_3',times('#skF_3',C_17))) = times('#skF_3',C_17) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_2,c_180]) ).
tff(c_1459,plain,
! [B_36,C_37] : ( times(times(B_36,'#skF_1'('#skF_3')),C_37) = times('#skF_3',times(C_37,times('#skF_3',B_36))) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_302]) ).
tff(c_1537,plain,
! [C_37] :
( ( times('#skF_3',times(C_37,times('#skF_3','#skF_3'))) = times('#skF_3',C_37) )
| ~ element('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1459]) ).
tff(c_1558,plain,
! [C_37] : ( times('#skF_3',times(C_37,'#skF_1'('#skF_3'))) = times('#skF_3',C_37) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_20,c_1537]) ).
tff(c_405,plain,
! [B_19,C_22] : ( times(times(B_19,'#skF_1'('#skF_3')),C_22) = times('#skF_3',times(C_22,times('#skF_3',B_19))) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_302]) ).
tff(c_7419,plain,
! [C_80,A_81] : ( times(times(C_80,A_81),'#skF_1'('#skF_3')) = times(C_80,times('#skF_3',times(A_81,'#skF_3'))) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_5677]) ).
tff(c_7600,plain,
! [C_37] : ( times('#skF_3',times('#skF_3',times(times(C_37,'#skF_1'('#skF_3')),'#skF_3'))) = times(times('#skF_3',C_37),'#skF_1'('#skF_3')) ),
inference(superposition,[status(thm),theory(equality)],[c_1558,c_7419]) ).
tff(c_8310,plain,
! [C_84] : ( times(C_84,times('#skF_3','#skF_1'('#skF_3'))) = times('#skF_3',C_84) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_85,c_2,c_210,c_210,c_405,c_7600]) ).
tff(c_8502,plain,
times('#skF_2',times(times('#skF_3','#skF_1'('#skF_3')),'#skF_2')) = times('#skF_3','#skF_1'('#skF_2')),
inference(superposition,[status(thm),theory(equality)],[c_75,c_8310]) ).
tff(c_8566,plain,
times('#skF_2',times('#skF_3','#skF_2')) = times('#skF_3','#skF_1'('#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_1558,c_20,c_405,c_8502]) ).
tff(c_10,plain,
~ element(times('#skF_2','#skF_3')),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_7151,plain,
~ element(times('#skF_3','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_7149,c_10]) ).
tff(c_51,plain,
! [B_12,C_13,A_11,C_3] : ( times(times(B_12,times(C_13,A_11)),C_3) = times(C_13,times(C_3,times(A_11,B_12))) ),
inference(superposition,[status(thm),theory(equality)],[c_48,c_2]) ).
tff(c_120,plain,
! [C_15] : ( times('#skF_1'('#skF_3'),C_15) = times('#skF_3',times(C_15,'#skF_3')) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_48]) ).
tff(c_4859,plain,
! [C_65,C_66] : ( times(times('#skF_3',times(C_65,'#skF_3')),C_66) = times(C_65,times(C_66,'#skF_1'('#skF_3'))) ),
inference(superposition,[status(thm),theory(equality)],[c_120,c_2]) ).
tff(c_5030,plain,
! [C_66] : ( times(times('#skF_3','#skF_1'('#skF_3')),C_66) = times('#skF_3',times(C_66,'#skF_1'('#skF_3'))) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_4859]) ).
tff(c_5070,plain,
! [C_67] : ( times(times('#skF_3','#skF_1'('#skF_3')),C_67) = times('#skF_3',C_67) ),
inference(demodulation,[status(thm),theory(equality)],[c_1558,c_5030]) ).
tff(c_5152,plain,
times('#skF_2',times('#skF_3','#skF_1'('#skF_2'))) = times('#skF_2',times('#skF_3','#skF_1'('#skF_3'))),
inference(superposition,[status(thm),theory(equality)],[c_5070,c_574]) ).
tff(c_5226,plain,
times('#skF_2',times('#skF_3','#skF_1'('#skF_3'))) = times('#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_574,c_5152]) ).
tff(c_7150,plain,
times('#skF_2',times('#skF_3','#skF_1'('#skF_3'))) = times('#skF_3','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_7149,c_5226]) ).
tff(c_4,plain,
! [B_4] :
( element(B_4)
| ( times(B_4,times(B_4,B_4)) != B_4 ) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_58,plain,
! [A_11,B_12] :
( element(times(A_11,B_12))
| ( times(times(A_11,B_12),times(B_12,times(times(A_11,B_12),A_11))) != times(A_11,B_12) ) ),
inference(superposition,[status(thm),theory(equality)],[c_48,c_4]) ).
tff(c_87,plain,
! [A_11,B_12] :
( element(times(A_11,B_12))
| ( times(B_12,times(A_11,times(A_11,times(B_12,times(B_12,A_11))))) != times(A_11,B_12) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_2,c_2,c_2,c_2,c_2,c_2,c_2,c_58]) ).
tff(c_7368,plain,
( element(times(times('#skF_3','#skF_1'('#skF_3')),'#skF_2'))
| ( times('#skF_2',times(times('#skF_3','#skF_1'('#skF_3')),times(times('#skF_3','#skF_1'('#skF_3')),times('#skF_2',times('#skF_3','#skF_2'))))) != times(times('#skF_3','#skF_1'('#skF_3')),'#skF_2') ) ),
inference(superposition,[status(thm),theory(equality)],[c_7150,c_87]) ).
tff(c_7404,plain,
( element(times('#skF_3','#skF_2'))
| ( times('#skF_2',times('#skF_3',times('#skF_3',times('#skF_2',times('#skF_3','#skF_2'))))) != times('#skF_3','#skF_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1558,c_20,c_51,c_210,c_51,c_210,c_2,c_51,c_51,c_51,c_405,c_405,c_405,c_1558,c_20,c_405,c_7368]) ).
tff(c_7405,plain,
times('#skF_2',times('#skF_3',times('#skF_3',times('#skF_2',times('#skF_3','#skF_2'))))) != times('#skF_3','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_7151,c_7404]) ).
tff(c_9036,plain,
times('#skF_2',times('#skF_3',times('#skF_3',times('#skF_3','#skF_1'('#skF_2'))))) != times('#skF_3','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_8566,c_7405]) ).
tff(c_9041,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7149,c_574,c_210,c_9036]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG210+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % 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
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 20:17:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 10.50/3.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.50/3.61
% 10.50/3.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.50/3.65
% 10.50/3.65 Inference rules
% 10.50/3.65 ----------------------
% 10.50/3.65 #Ref : 0
% 10.50/3.65 #Sup : 2077
% 10.50/3.65 #Fact : 0
% 10.50/3.65 #Define : 0
% 10.50/3.65 #Split : 3
% 10.50/3.65 #Chain : 0
% 10.50/3.65 #Close : 0
% 10.50/3.65
% 10.50/3.65 Ordering : KBO
% 10.50/3.65
% 10.50/3.65 Simplification rules
% 10.50/3.65 ----------------------
% 10.50/3.65 #Subsume : 61
% 10.50/3.65 #Demod : 7870
% 10.50/3.65 #Tautology : 743
% 10.50/3.65 #SimpNegUnit : 3
% 10.50/3.65 #BackRed : 10
% 10.50/3.65
% 10.50/3.65 #Partial instantiations: 0
% 10.50/3.65 #Strategies tried : 1
% 10.50/3.65
% 10.50/3.65 Timing (in seconds)
% 10.50/3.65 ----------------------
% 10.50/3.66 Preprocessing : 0.55
% 10.50/3.66 Parsing : 0.33
% 10.50/3.66 CNF conversion : 0.03
% 10.50/3.66 Main loop : 2.01
% 10.50/3.66 Inferencing : 0.47
% 10.50/3.66 Reduction : 1.15
% 10.50/3.66 Demodulation : 1.02
% 10.50/3.66 BG Simplification : 0.08
% 10.50/3.66 Subsumption : 0.22
% 10.50/3.66 Abstraction : 0.09
% 10.50/3.66 MUC search : 0.00
% 10.50/3.66 Cooper : 0.00
% 10.50/3.66 Total : 2.62
% 10.50/3.66 Index Insertion : 0.00
% 10.50/3.66 Index Deletion : 0.00
% 10.50/3.66 Index Matching : 0.00
% 10.50/3.66 BG Taut test : 0.00
%------------------------------------------------------------------------------