TSTP Solution File: HAL003+3 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 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 : n028.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 10:42:10 EDT 2023
% Result : Theorem 5.31s 2.24s
% Output : CNFRefutation 5.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 44
% Syntax : Number of formulae : 61 ( 6 unt; 39 typ; 0 def)
% Number of atoms : 57 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 67 ( 32 ~; 26 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 68 ( 25 >; 43 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 33 ( 33 usr; 14 con; 0-8 aty)
% Number of variables : 35 (; 32 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ commute > morphism > exact > element > surjection > injection > subtract > apply > #nlpp > zero > r > h > gammma > gamma > g > f > e > delta > d > c > beta > b > alpha > a > #skF_16 > #skF_1 > #skF_6 > #skF_4 > #skF_15 > #skF_8 > #skF_7 > #skF_10 > #skF_2 > #skF_13 > #skF_5 > #skF_9 > #skF_11 > #skF_14 > #skF_3 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(gamma,type,
gamma: $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff(h,type,
h: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff(a,type,
a: $i ).
tff(r,type,
r: $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(f,type,
f: $i ).
tff(injection,type,
injection: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(commute,type,
commute: ( $i * $i * $i * $i ) > $o ).
tff(surjection,type,
surjection: $i > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i * $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(morphism,type,
morphism: ( $i * $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(alpha,type,
alpha: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(subtract,type,
subtract: ( $i * $i * $i ) > $i ).
tff(exact,type,
exact: ( $i * $i ) > $o ).
tff(g,type,
g: $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff(zero,type,
zero: $i > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(d,type,
d: $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff(e,type,
e: $i ).
tff(gammma,type,
gammma: $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff(delta,type,
delta: $i ).
tff(beta,type,
beta: $i ).
tff(c,type,
c: $i ).
tff(f_270,negated_conjecture,
~ surjection(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_surjection) ).
tff(f_220,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_morphism) ).
tff(f_125,axiom,
! [Morphism,Dom,Cod] :
( ( morphism(Morphism,Dom,Cod)
& ! [ElCod] :
( element(ElCod,Cod)
=> ? [ElDom] :
( element(ElDom,Dom)
& ( apply(Morphism,ElDom) = ElCod ) ) ) )
=> surjection(Morphism) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',properties_for_surjection) ).
tff(f_268,axiom,
! [E] :
( element(E,e)
=> ? [B1,B2] :
( element(B1,b)
& element(B2,b)
& ( apply(g,subtract(b,B1,B2)) = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma12) ).
tff(f_193,axiom,
! [Dom,El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> element(subtract(Dom,El1,El2),Dom) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).
tff(c_126,plain,
~ surjection(g),
inference(cnfTransformation,[status(thm)],[f_270]) ).
tff(c_74,plain,
morphism(g,b,e),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_22,plain,
! [Morphism_26,Dom_27,Cod_28] :
( element('#skF_4'(Morphism_26,Dom_27,Cod_28),Cod_28)
| surjection(Morphism_26)
| ~ morphism(Morphism_26,Dom_27,Cod_28) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_124,plain,
! [E_102] :
( element('#skF_15'(E_102),b)
| ~ element(E_102,e) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_122,plain,
! [E_102] :
( element('#skF_16'(E_102),b)
| ~ element(E_102,e) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_56,plain,
! [Dom_80,El1_81,El2_82] :
( element(subtract(Dom_80,El1_81,El2_82),Dom_80)
| ~ element(El2_82,Dom_80)
| ~ element(El1_81,Dom_80) ),
inference(cnfTransformation,[status(thm)],[f_193]) ).
tff(c_120,plain,
! [E_102] :
( ( apply(g,subtract(b,'#skF_15'(E_102),'#skF_16'(E_102))) = E_102 )
| ~ element(E_102,e) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_547,plain,
! [Morphism_164,ElDom_165,Dom_166,Cod_167] :
( ( apply(Morphism_164,ElDom_165) != '#skF_4'(Morphism_164,Dom_166,Cod_167) )
| ~ element(ElDom_165,Dom_166)
| surjection(Morphism_164)
| ~ morphism(Morphism_164,Dom_166,Cod_167) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_549,plain,
! [E_102,Dom_166,Cod_167] :
( ( E_102 != '#skF_4'(g,Dom_166,Cod_167) )
| ~ element(subtract(b,'#skF_15'(E_102),'#skF_16'(E_102)),Dom_166)
| surjection(g)
| ~ morphism(g,Dom_166,Cod_167)
| ~ element(E_102,e) ),
inference(superposition,[status(thm),theory(equality)],[c_120,c_547]) ).
tff(c_574,plain,
! [E_102,Dom_166,Cod_167] :
( ( E_102 != '#skF_4'(g,Dom_166,Cod_167) )
| ~ element(subtract(b,'#skF_15'(E_102),'#skF_16'(E_102)),Dom_166)
| ~ morphism(g,Dom_166,Cod_167)
| ~ element(E_102,e) ),
inference(negUnitSimplification,[status(thm)],[c_126,c_549]) ).
tff(c_939,plain,
! [Dom_224,Cod_225] :
( ~ element(subtract(b,'#skF_15'('#skF_4'(g,Dom_224,Cod_225)),'#skF_16'('#skF_4'(g,Dom_224,Cod_225))),Dom_224)
| ~ morphism(g,Dom_224,Cod_225)
| ~ element('#skF_4'(g,Dom_224,Cod_225),e) ),
inference(reflexivity,[status(thm),theory(equality)],[c_574]) ).
tff(c_1096,plain,
! [Cod_234] :
( ~ morphism(g,b,Cod_234)
| ~ element('#skF_4'(g,b,Cod_234),e)
| ~ element('#skF_16'('#skF_4'(g,b,Cod_234)),b)
| ~ element('#skF_15'('#skF_4'(g,b,Cod_234)),b) ),
inference(resolution,[status(thm)],[c_56,c_939]) ).
tff(c_1213,plain,
! [Cod_244] :
( ~ morphism(g,b,Cod_244)
| ~ element('#skF_15'('#skF_4'(g,b,Cod_244)),b)
| ~ element('#skF_4'(g,b,Cod_244),e) ),
inference(resolution,[status(thm)],[c_122,c_1096]) ).
tff(c_1218,plain,
! [Cod_245] :
( ~ morphism(g,b,Cod_245)
| ~ element('#skF_4'(g,b,Cod_245),e) ),
inference(resolution,[status(thm)],[c_124,c_1213]) ).
tff(c_1222,plain,
( surjection(g)
| ~ morphism(g,b,e) ),
inference(resolution,[status(thm)],[c_22,c_1218]) ).
tff(c_1225,plain,
surjection(g),
inference(demodulation,[status(thm),theory(equality)],[c_74,c_1222]) ).
tff(c_1227,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_126,c_1225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % 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
% 0.16/0.35 % Computer : n028.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu Aug 3 20:26:24 EDT 2023
% 0.16/0.35 % CPUTime :
% 5.31/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.55/2.25
% 5.55/2.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.55/2.27
% 5.55/2.27 Inference rules
% 5.55/2.27 ----------------------
% 5.55/2.27 #Ref : 2
% 5.55/2.27 #Sup : 298
% 5.55/2.27 #Fact : 0
% 5.55/2.27 #Define : 0
% 5.55/2.27 #Split : 12
% 5.55/2.27 #Chain : 0
% 5.55/2.27 #Close : 0
% 5.55/2.27
% 5.55/2.27 Ordering : KBO
% 5.55/2.27
% 5.55/2.27 Simplification rules
% 5.55/2.27 ----------------------
% 5.55/2.27 #Subsume : 40
% 5.55/2.27 #Demod : 52
% 5.55/2.27 #Tautology : 96
% 5.55/2.27 #SimpNegUnit : 6
% 5.55/2.27 #BackRed : 0
% 5.55/2.27
% 5.55/2.27 #Partial instantiations: 0
% 5.55/2.27 #Strategies tried : 1
% 5.55/2.27
% 5.55/2.27 Timing (in seconds)
% 5.55/2.27 ----------------------
% 5.55/2.28 Preprocessing : 0.63
% 5.55/2.28 Parsing : 0.29
% 5.55/2.28 CNF conversion : 0.05
% 5.55/2.28 Main loop : 0.59
% 5.55/2.28 Inferencing : 0.22
% 5.55/2.28 Reduction : 0.18
% 5.55/2.28 Demodulation : 0.11
% 5.55/2.28 BG Simplification : 0.04
% 5.55/2.28 Subsumption : 0.11
% 5.55/2.28 Abstraction : 0.03
% 5.55/2.28 MUC search : 0.00
% 5.55/2.28 Cooper : 0.00
% 5.55/2.28 Total : 1.27
% 5.55/2.28 Index Insertion : 0.00
% 5.55/2.28 Index Deletion : 0.00
% 5.55/2.28 Index Matching : 0.00
% 5.55/2.28 BG Taut test : 0.00
%------------------------------------------------------------------------------