TSTP Solution File: SET975+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET975+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/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 : n001.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 3.91s 2.09s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 66 ( 26 unt; 18 typ; 0 def)
% Number of atoms : 78 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 32 ~; 24 |; 2 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 30 (; 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_11 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_2 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_40,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_63,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( ( A = C )
& in(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
tff(f_51,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
tff(c_8,plain,
! [C_9] : in(C_9,singleton(C_9)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_36,plain,
( ( '#skF_7' = '#skF_5' )
| ~ in('#skF_10','#skF_12')
| ( '#skF_11' != '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_89,plain,
'#skF_11' != '#skF_9',
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_42,plain,
( ( '#skF_7' = '#skF_5' )
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_212,plain,
in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')),
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_26,plain,
! [A_14,C_16,B_15,D_17] :
( in(A_14,C_16)
| ~ in(ordered_pair(A_14,B_15),cartesian_product2(C_16,D_17)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_218,plain,
in('#skF_9',singleton('#skF_11')),
inference(resolution,[status(thm)],[c_212,c_26]) ).
tff(c_6,plain,
! [C_9,A_5] :
( ( C_9 = A_5 )
| ~ in(C_9,singleton(A_5)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_224,plain,
'#skF_11' = '#skF_9',
inference(resolution,[status(thm)],[c_218,c_6]) ).
tff(c_229,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_89,c_224]) ).
tff(c_231,plain,
~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')),
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_40,plain,
( in('#skF_6','#skF_8')
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_291,plain,
in('#skF_6','#skF_8'),
inference(negUnitSimplification,[status(thm)],[c_231,c_40]) ).
tff(c_22,plain,
! [A_14,B_15,C_16,D_17] :
( in(ordered_pair(A_14,B_15),cartesian_product2(C_16,D_17))
| ~ in(B_15,D_17)
| ~ in(A_14,C_16) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_230,plain,
'#skF_7' = '#skF_5',
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_38,plain,
( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_7'),'#skF_8'))
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_339,plain,
( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8'))
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')) ),
inference(demodulation,[status(thm),theory(equality)],[c_230,c_38]) ).
tff(c_340,plain,
~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8')),
inference(negUnitSimplification,[status(thm)],[c_231,c_339]) ).
tff(c_343,plain,
( ~ in('#skF_6','#skF_8')
| ~ in('#skF_5',singleton('#skF_5')) ),
inference(resolution,[status(thm)],[c_22,c_340]) ).
tff(c_347,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_291,c_343]) ).
tff(c_349,plain,
'#skF_11' = '#skF_9',
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_348,plain,
( ~ in('#skF_10','#skF_12')
| ( '#skF_7' = '#skF_5' ) ),
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_354,plain,
~ in('#skF_10','#skF_12'),
inference(splitLeft,[status(thm)],[c_348]) ).
tff(c_530,plain,
( ( '#skF_7' = '#skF_5' )
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')) ),
inference(demodulation,[status(thm),theory(equality)],[c_349,c_42]) ).
tff(c_531,plain,
in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')),
inference(splitLeft,[status(thm)],[c_530]) ).
tff(c_543,plain,
! [B_76,D_77,A_78,C_79] :
( in(B_76,D_77)
| ~ in(ordered_pair(A_78,B_76),cartesian_product2(C_79,D_77)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_546,plain,
in('#skF_10','#skF_12'),
inference(resolution,[status(thm)],[c_531,c_543]) ).
tff(c_550,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_354,c_546]) ).
tff(c_552,plain,
~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')),
inference(splitRight,[status(thm)],[c_530]) ).
tff(c_558,plain,
( in('#skF_6','#skF_8')
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')) ),
inference(demodulation,[status(thm),theory(equality)],[c_349,c_40]) ).
tff(c_559,plain,
in('#skF_6','#skF_8'),
inference(negUnitSimplification,[status(thm)],[c_552,c_558]) ).
tff(c_551,plain,
'#skF_7' = '#skF_5',
inference(splitRight,[status(thm)],[c_530]) ).
tff(c_611,plain,
( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8'))
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')) ),
inference(demodulation,[status(thm),theory(equality)],[c_349,c_551,c_38]) ).
tff(c_612,plain,
~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8')),
inference(negUnitSimplification,[status(thm)],[c_552,c_611]) ).
tff(c_615,plain,
( ~ in('#skF_6','#skF_8')
| ~ in('#skF_5',singleton('#skF_5')) ),
inference(resolution,[status(thm)],[c_22,c_612]) ).
tff(c_619,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_559,c_615]) ).
tff(c_621,plain,
in('#skF_10','#skF_12'),
inference(splitRight,[status(thm)],[c_348]) ).
tff(c_34,plain,
( in('#skF_6','#skF_8')
| ~ in('#skF_10','#skF_12')
| ( '#skF_11' != '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_630,plain,
in('#skF_6','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_349,c_621,c_34]) ).
tff(c_829,plain,
! [A_128,B_129,C_130,D_131] :
( in(ordered_pair(A_128,B_129),cartesian_product2(C_130,D_131))
| ~ in(B_129,D_131)
| ~ in(A_128,C_130) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_620,plain,
'#skF_7' = '#skF_5',
inference(splitRight,[status(thm)],[c_348]) ).
tff(c_32,plain,
( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_7'),'#skF_8'))
| ~ in('#skF_10','#skF_12')
| ( '#skF_11' != '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_817,plain,
~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8')),
inference(demodulation,[status(thm),theory(equality)],[c_349,c_621,c_620,c_32]) ).
tff(c_832,plain,
( ~ in('#skF_6','#skF_8')
| ~ in('#skF_5',singleton('#skF_5')) ),
inference(resolution,[status(thm)],[c_829,c_817]) ).
tff(c_844,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_630,c_832]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET975+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/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
% 0.15/0.36 % Computer : n001.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 17:06:10 EDT 2023
% 0.15/0.37 % CPUTime :
% 3.91/2.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.91/2.10
% 3.91/2.10 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.91/2.13
% 3.91/2.13 Inference rules
% 3.91/2.13 ----------------------
% 3.91/2.13 #Ref : 0
% 3.91/2.13 #Sup : 197
% 3.91/2.13 #Fact : 0
% 3.91/2.13 #Define : 0
% 3.91/2.13 #Split : 6
% 3.91/2.13 #Chain : 0
% 3.91/2.13 #Close : 0
% 3.91/2.13
% 3.91/2.13 Ordering : KBO
% 3.91/2.13
% 3.91/2.13 Simplification rules
% 3.91/2.13 ----------------------
% 3.91/2.13 #Subsume : 5
% 3.91/2.13 #Demod : 68
% 3.91/2.13 #Tautology : 102
% 3.91/2.13 #SimpNegUnit : 6
% 3.91/2.13 #BackRed : 0
% 3.91/2.13
% 3.91/2.13 #Partial instantiations: 0
% 3.91/2.13 #Strategies tried : 1
% 3.91/2.13
% 3.91/2.13 Timing (in seconds)
% 3.91/2.13 ----------------------
% 3.91/2.14 Preprocessing : 0.50
% 3.91/2.14 Parsing : 0.25
% 3.91/2.14 CNF conversion : 0.04
% 3.91/2.14 Main loop : 0.48
% 3.91/2.14 Inferencing : 0.18
% 3.91/2.14 Reduction : 0.14
% 3.91/2.14 Demodulation : 0.11
% 3.91/2.14 BG Simplification : 0.03
% 3.91/2.14 Subsumption : 0.10
% 3.91/2.14 Abstraction : 0.02
% 3.91/2.14 MUC search : 0.00
% 3.91/2.14 Cooper : 0.00
% 3.91/2.14 Total : 1.03
% 3.91/2.14 Index Insertion : 0.00
% 3.91/2.14 Index Deletion : 0.00
% 3.91/2.14 Index Matching : 0.00
% 3.91/2.14 BG Taut test : 0.00
%------------------------------------------------------------------------------