TSTP Solution File: SEU107+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU107+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 : n031.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 10:57:37 EDT 2023
% Result : Theorem 7.47s 2.75s
% Output : CNFRefutation 7.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 40
% Syntax : Number of formulae : 65 ( 15 unt; 31 typ; 0 def)
% Number of atoms : 81 ( 10 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 79 ( 32 ~; 34 |; 7 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 25 >; 6 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 41 (; 39 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation > preboolean > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > diff_closed > cup_closed > cap_closed > prebool_difference > set_difference > #nlpp > powerset > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_11 > #skF_1 > #skF_5 > #skF_10 > #skF_2 > #skF_3 > #skF_8 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(prebool_difference,type,
prebool_difference: ( $i * $i * $i ) > $i ).
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(cup_closed,type,
cup_closed: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $i > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(preboolean,type,
preboolean: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(diff_closed,type,
diff_closed: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(cap_closed,type,
cap_closed: $i > $o ).
tff(natural,type,
natural: $i > $o ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_175,negated_conjecture,
~ ! [A] :
( ( ~ empty(A)
& preboolean(A) )
=> in(empty_set,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finsub_1) ).
tff(f_68,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
tff(f_167,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_103,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_214,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_189,axiom,
! [A,B] :
( ( set_difference(A,B) = empty_set )
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
tff(f_165,axiom,
! [A,B,C] :
( ( ~ empty(A)
& preboolean(A)
& element(B,A)
& element(C,A) )
=> ( prebool_difference(A,B,C) = set_difference(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
tff(f_65,axiom,
! [A,B,C] :
( ( ~ empty(A)
& preboolean(A)
& element(B,A)
& element(C,A) )
=> element(prebool_difference(A,B,C),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
tff(f_185,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
tff(c_90,plain,
~ empty('#skF_11'),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_88,plain,
preboolean('#skF_11'),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_16,plain,
! [A_12] : element('#skF_1'(A_12),A_12),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_84,plain,
! [A_30] : subset(A_30,A_30),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_42,plain,
empty('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_150,plain,
! [A_69] :
( ( empty_set = A_69 )
| ~ empty(A_69) ),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_167,plain,
empty_set = '#skF_5',
inference(resolution,[status(thm)],[c_42,c_150]) ).
tff(c_98,plain,
! [A_36,B_37] :
( ( set_difference(A_36,B_37) = empty_set )
| ~ subset(A_36,B_37) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_312,plain,
! [A_104,B_105] :
( ( set_difference(A_104,B_105) = '#skF_5' )
| ~ subset(A_104,B_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_167,c_98]) ).
tff(c_333,plain,
! [A_30] : ( set_difference(A_30,A_30) = '#skF_5' ),
inference(resolution,[status(thm)],[c_84,c_312]) ).
tff(c_729,plain,
! [A_147,B_148,C_149] :
( ( prebool_difference(A_147,B_148,C_149) = set_difference(B_148,C_149) )
| ~ element(C_149,A_147)
| ~ element(B_148,A_147)
| ~ preboolean(A_147)
| empty(A_147) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_934,plain,
! [A_175,B_176] :
( ( prebool_difference(A_175,B_176,'#skF_1'(A_175)) = set_difference(B_176,'#skF_1'(A_175)) )
| ~ element(B_176,A_175)
| ~ preboolean(A_175)
| empty(A_175) ),
inference(resolution,[status(thm)],[c_16,c_729]) ).
tff(c_14,plain,
! [A_9,B_10,C_11] :
( element(prebool_difference(A_9,B_10,C_11),A_9)
| ~ element(C_11,A_9)
| ~ element(B_10,A_9)
| ~ preboolean(A_9)
| empty(A_9) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_940,plain,
! [B_176,A_175] :
( element(set_difference(B_176,'#skF_1'(A_175)),A_175)
| ~ element('#skF_1'(A_175),A_175)
| ~ element(B_176,A_175)
| ~ preboolean(A_175)
| empty(A_175)
| ~ element(B_176,A_175)
| ~ preboolean(A_175)
| empty(A_175) ),
inference(superposition,[status(thm),theory(equality)],[c_934,c_14]) ).
tff(c_3153,plain,
! [B_350,A_351] :
( element(set_difference(B_350,'#skF_1'(A_351)),A_351)
| ~ element(B_350,A_351)
| ~ preboolean(A_351)
| empty(A_351) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_940]) ).
tff(c_3237,plain,
! [A_351] :
( element('#skF_5',A_351)
| ~ element('#skF_1'(A_351),A_351)
| ~ preboolean(A_351)
| empty(A_351) ),
inference(superposition,[status(thm),theory(equality)],[c_333,c_3153]) ).
tff(c_3292,plain,
! [A_352] :
( element('#skF_5',A_352)
| ~ preboolean(A_352)
| empty(A_352) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_3237]) ).
tff(c_547,plain,
! [A_120,B_121] :
( in(A_120,B_121)
| empty(B_121)
| ~ element(A_120,B_121) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_86,plain,
~ in(empty_set,'#skF_11'),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_170,plain,
~ in('#skF_5','#skF_11'),
inference(demodulation,[status(thm),theory(equality)],[c_167,c_86]) ).
tff(c_558,plain,
( empty('#skF_11')
| ~ element('#skF_5','#skF_11') ),
inference(resolution,[status(thm)],[c_547,c_170]) ).
tff(c_564,plain,
~ element('#skF_5','#skF_11'),
inference(negUnitSimplification,[status(thm)],[c_90,c_558]) ).
tff(c_3329,plain,
( ~ preboolean('#skF_11')
| empty('#skF_11') ),
inference(resolution,[status(thm)],[c_3292,c_564]) ).
tff(c_3360,plain,
empty('#skF_11'),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_3329]) ).
tff(c_3362,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_90,c_3360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU107+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % 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
% 0.16/0.37 % Computer : n031.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 3 12:18:14 EDT 2023
% 0.16/0.37 % CPUTime :
% 7.47/2.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.47/2.76
% 7.47/2.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.47/2.79
% 7.47/2.79 Inference rules
% 7.47/2.79 ----------------------
% 7.47/2.79 #Ref : 5
% 7.47/2.79 #Sup : 737
% 7.47/2.79 #Fact : 0
% 7.47/2.79 #Define : 0
% 7.47/2.79 #Split : 3
% 7.47/2.79 #Chain : 0
% 7.47/2.79 #Close : 0
% 7.47/2.79
% 7.47/2.79 Ordering : KBO
% 7.47/2.79
% 7.47/2.79 Simplification rules
% 7.47/2.79 ----------------------
% 7.47/2.79 #Subsume : 201
% 7.47/2.79 #Demod : 212
% 7.47/2.79 #Tautology : 179
% 7.47/2.79 #SimpNegUnit : 91
% 7.47/2.79 #BackRed : 14
% 7.47/2.79
% 7.47/2.79 #Partial instantiations: 0
% 7.47/2.79 #Strategies tried : 1
% 7.47/2.79
% 7.47/2.79 Timing (in seconds)
% 7.47/2.79 ----------------------
% 7.47/2.79 Preprocessing : 0.56
% 7.47/2.79 Parsing : 0.30
% 7.47/2.79 CNF conversion : 0.04
% 7.47/2.79 Main loop : 1.08
% 7.47/2.79 Inferencing : 0.38
% 7.47/2.79 Reduction : 0.31
% 7.47/2.79 Demodulation : 0.20
% 7.47/2.79 BG Simplification : 0.04
% 7.47/2.79 Subsumption : 0.28
% 7.47/2.79 Abstraction : 0.04
% 7.47/2.79 MUC search : 0.00
% 7.47/2.79 Cooper : 0.00
% 7.47/2.79 Total : 1.69
% 7.47/2.79 Index Insertion : 0.00
% 7.47/2.79 Index Deletion : 0.00
% 7.47/2.79 Index Matching : 0.00
% 7.47/2.79 BG Taut test : 0.00
%------------------------------------------------------------------------------