TSTP Solution File: SET886+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET886+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 : n024.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 10:57:17 EDT 2023
% Result : Theorem 2.88s 1.68s
% Output : CNFRefutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 14 unt; 9 typ; 0 def)
% Number of atoms : 22 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 18 (; 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > empty > unordered_pair > #nlpp > singleton > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_46,axiom,
! [A] : ( unordered_pair(A,A) = singleton(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
tff(f_28,axiom,
! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(f_44,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> ( unordered_pair(A,B) = singleton(C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
tff(f_39,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
tff(c_16,plain,
! [A_8] : ( unordered_pair(A_8,A_8) = singleton(A_8) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_2,plain,
! [B_2,A_1] : ( unordered_pair(B_2,A_1) = unordered_pair(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_14,plain,
subset(unordered_pair('#skF_3','#skF_4'),singleton('#skF_5')),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_17,plain,
subset(unordered_pair('#skF_4','#skF_3'),singleton('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14]) ).
tff(c_62,plain,
! [C_13,A_14,B_15] :
( ( C_13 = A_14 )
| ~ subset(unordered_pair(A_14,B_15),singleton(C_13)) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_75,plain,
'#skF_5' = '#skF_4',
inference(resolution,[status(thm)],[c_17,c_62]) ).
tff(c_76,plain,
subset(unordered_pair('#skF_4','#skF_3'),singleton('#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_75,c_17]) ).
tff(c_94,plain,
! [C_18,A_19,B_20] :
( ( C_18 = A_19 )
| ~ subset(unordered_pair(B_20,A_19),singleton(C_18)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_62]) ).
tff(c_107,plain,
'#skF_3' = '#skF_4',
inference(resolution,[status(thm)],[c_76,c_94]) ).
tff(c_12,plain,
unordered_pair('#skF_3','#skF_4') != singleton('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_18,plain,
unordered_pair('#skF_4','#skF_3') != singleton('#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12]) ).
tff(c_77,plain,
unordered_pair('#skF_4','#skF_3') != singleton('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_75,c_18]) ).
tff(c_109,plain,
unordered_pair('#skF_4','#skF_4') != singleton('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_107,c_77]) ).
tff(c_113,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % 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
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 17:02:00 EDT 2023
% 0.14/0.36 % CPUTime :
% 2.88/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.88/1.69
% 2.88/1.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.93/1.71
% 2.93/1.71 Inference rules
% 2.93/1.71 ----------------------
% 2.93/1.71 #Ref : 0
% 2.93/1.71 #Sup : 22
% 2.93/1.71 #Fact : 0
% 2.93/1.71 #Define : 0
% 2.93/1.71 #Split : 0
% 2.93/1.71 #Chain : 0
% 2.93/1.71 #Close : 0
% 2.93/1.71
% 2.93/1.71 Ordering : KBO
% 2.93/1.71
% 2.93/1.71 Simplification rules
% 2.93/1.71 ----------------------
% 2.93/1.71 #Subsume : 3
% 2.93/1.71 #Demod : 9
% 2.93/1.71 #Tautology : 15
% 2.93/1.71 #SimpNegUnit : 0
% 2.93/1.71 #BackRed : 4
% 2.93/1.71
% 2.93/1.71 #Partial instantiations: 0
% 2.93/1.71 #Strategies tried : 1
% 2.93/1.71
% 2.93/1.71 Timing (in seconds)
% 2.93/1.71 ----------------------
% 2.93/1.72 Preprocessing : 0.43
% 2.93/1.72 Parsing : 0.23
% 2.93/1.72 CNF conversion : 0.02
% 2.93/1.72 Main loop : 0.23
% 2.93/1.72 Inferencing : 0.08
% 2.93/1.72 Reduction : 0.07
% 2.93/1.72 Demodulation : 0.05
% 2.93/1.72 BG Simplification : 0.01
% 2.93/1.72 Subsumption : 0.05
% 2.93/1.72 Abstraction : 0.01
% 2.93/1.72 MUC search : 0.00
% 2.93/1.72 Cooper : 0.00
% 2.93/1.72 Total : 0.70
% 2.93/1.72 Index Insertion : 0.00
% 2.93/1.72 Index Deletion : 0.00
% 2.93/1.72 Index Matching : 0.00
% 2.93/1.72 BG Taut test : 0.00
%------------------------------------------------------------------------------