TSTP Solution File: HAL006+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : HAL006+1 : 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/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 : n013.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 48.07s 34.21s
% Output : CNFRefutation 48.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 51
% Syntax : Number of formulae : 146 ( 36 unt; 38 typ; 0 def)
% Number of atoms : 269 ( 52 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 309 ( 148 ~; 132 |; 17 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 66 ( 23 >; 43 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 32 ( 32 usr; 15 con; 0-8 aty)
% Number of variables : 132 (; 124 !; 8 ?; 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_1 > #skF_15 > #skF_6 > #skF_4 > #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(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('#skF_15',type,
'#skF_15': $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_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_269,negated_conjecture,
~ ! [E] :
( element(E,e)
=> ? [B1,B2] :
( element(B1,b)
& element(B2,b)
& ( apply(g,subtract(b,B1,B2)) = E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma12) ).
tff(f_215,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alpha_morphism) ).
tff(f_259,axiom,
! [E] :
( element(E,e)
=> ? [B1,E1,A] :
( element(B1,b)
& element(E1,e)
& ( subtract(e,apply(g,B1),E) = E1 )
& element(A,a)
& ( apply(gamma,apply(f,A)) = E1 )
& ( apply(g,apply(alpha,A)) = E1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma8) ).
tff(f_57,axiom,
! [Morphism,Dom,Cod] :
( morphism(Morphism,Dom,Cod)
=> ( ! [El] :
( element(El,Dom)
=> element(apply(Morphism,El),Cod) )
& ( apply(Morphism,zero(Dom)) = zero(Cod) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',morphism) ).
tff(f_220,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
tff(f_193,axiom,
! [Dom,El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> element(subtract(Dom,El1,El2),Dom) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).
tff(f_244,axiom,
! [E] :
( element(E,e)
=> ? [R,B1] :
( element(R,r)
& ( apply(delta,E) = R )
& element(B1,b)
& ( apply(h,apply(beta,B1)) = R )
& ( apply(delta,apply(g,B1)) = R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma3) ).
tff(f_218,axiom,
morphism(delta,e,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_morphism) ).
tff(f_197,axiom,
! [Dom,El] :
( element(El,Dom)
=> ( subtract(Dom,El,El) = zero(Dom) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_to_0) ).
tff(f_212,axiom,
! [Morphism,Dom,Cod] :
( morphism(Morphism,Dom,Cod)
=> ! [El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> ( apply(Morphism,subtract(Dom,El1,El2)) = subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).
tff(f_225,axiom,
surjection(delta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_surjection) ).
tff(f_113,axiom,
! [Morphism,Dom,Cod] :
( ( surjection(Morphism)
& morphism(Morphism,Dom,Cod) )
=> ! [ElCod] :
( element(ElCod,Cod)
=> ? [ElDom] :
( element(ElDom,Dom)
& ( apply(Morphism,ElDom) = ElCod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',surjection_properties) ).
tff(f_203,axiom,
! [Dom,El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> ( subtract(Dom,El1,subtract(Dom,El1,El2)) = El2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_cancellation) ).
tff(c_122,plain,
element('#skF_15',e),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_64,plain,
morphism(alpha,a,b),
inference(cnfTransformation,[status(thm)],[f_215]) ).
tff(c_112,plain,
! [E_98] :
( element('#skF_14'(E_98),a)
| ~ element(E_98,e) ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_402,plain,
! [Morphism_135,El_136,Cod_137,Dom_138] :
( element(apply(Morphism_135,El_136),Cod_137)
| ~ element(El_136,Dom_138)
| ~ morphism(Morphism_135,Dom_138,Cod_137) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_427,plain,
! [Morphism_135,E_98,Cod_137] :
( element(apply(Morphism_135,'#skF_14'(E_98)),Cod_137)
| ~ morphism(Morphism_135,a,Cod_137)
| ~ element(E_98,e) ),
inference(resolution,[status(thm)],[c_112,c_402]) ).
tff(c_118,plain,
! [E_98] :
( element('#skF_12'(E_98),b)
| ~ element(E_98,e) ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_74,plain,
morphism(g,b,e),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_431,plain,
! [Morphism_135,E_98,Cod_137] :
( element(apply(Morphism_135,'#skF_12'(E_98)),Cod_137)
| ~ morphism(Morphism_135,b,Cod_137)
| ~ element(E_98,e) ),
inference(resolution,[status(thm)],[c_118,c_402]) ).
tff(c_114,plain,
! [E_98] :
( ( subtract(e,apply(g,'#skF_12'(E_98)),E_98) = '#skF_13'(E_98) )
| ~ element(E_98,e) ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_300,plain,
! [Dom_128,El1_129,El2_130] :
( element(subtract(Dom_128,El1_129,El2_130),Dom_128)
| ~ element(El2_130,Dom_128)
| ~ element(El1_129,Dom_128) ),
inference(cnfTransformation,[status(thm)],[f_193]) ).
tff(c_104,plain,
! [E_95] :
( ( apply(delta,E_95) = '#skF_10'(E_95) )
| ~ element(E_95,e) ),
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_323,plain,
! [El1_129,El2_130] :
( ( apply(delta,subtract(e,El1_129,El2_130)) = '#skF_10'(subtract(e,El1_129,El2_130)) )
| ~ element(El2_130,e)
| ~ element(El1_129,e) ),
inference(resolution,[status(thm)],[c_300,c_104]) ).
tff(c_70,plain,
morphism(delta,e,r),
inference(cnfTransformation,[status(thm)],[f_218]) ).
tff(c_129,plain,
! [E_113] :
( ( apply(delta,E_113) = '#skF_10'(E_113) )
| ~ element(E_113,e) ),
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_137,plain,
apply(delta,'#skF_15') = '#skF_10'('#skF_15'),
inference(resolution,[status(thm)],[c_122,c_129]) ).
tff(c_433,plain,
! [Morphism_139,Cod_140] :
( element(apply(Morphism_139,'#skF_15'),Cod_140)
| ~ morphism(Morphism_139,e,Cod_140) ),
inference(resolution,[status(thm)],[c_122,c_402]) ).
tff(c_444,plain,
! [Cod_140] :
( element('#skF_10'('#skF_15'),Cod_140)
| ~ morphism(delta,e,Cod_140) ),
inference(superposition,[status(thm),theory(equality)],[c_137,c_433]) ).
tff(c_138,plain,
! [Dom_114,El_115] :
( ( subtract(Dom_114,El_115,El_115) = zero(Dom_114) )
| ~ element(El_115,Dom_114) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_156,plain,
subtract(e,'#skF_15','#skF_15') = zero(e),
inference(resolution,[status(thm)],[c_122,c_138]) ).
tff(c_321,plain,
( element(zero(e),e)
| ~ element('#skF_15',e)
| ~ element('#skF_15',e) ),
inference(superposition,[status(thm),theory(equality)],[c_156,c_300]) ).
tff(c_325,plain,
element(zero(e),e),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_321]) ).
tff(c_165,plain,
! [Cod_116,Morphism_117,Dom_118] :
( ( zero(Cod_116) = apply(Morphism_117,zero(Dom_118)) )
| ~ morphism(Morphism_117,Dom_118,Cod_116) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_182,plain,
apply(delta,zero(e)) = zero(r),
inference(resolution,[status(thm)],[c_70,c_165]) ).
tff(c_330,plain,
apply(delta,zero(e)) = '#skF_10'(zero(e)),
inference(resolution,[status(thm)],[c_325,c_104]) ).
tff(c_333,plain,
'#skF_10'(zero(e)) = zero(r),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_330]) ).
tff(c_106,plain,
! [E_95] :
( element('#skF_10'(E_95),r)
| ~ element(E_95,e) ),
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_343,plain,
( element(zero(r),r)
| ~ element(zero(e),e) ),
inference(superposition,[status(thm),theory(equality)],[c_333,c_106]) ).
tff(c_351,plain,
element(zero(r),r),
inference(demodulation,[status(thm),theory(equality)],[c_325,c_343]) ).
tff(c_1611,plain,
! [Cod_272,El2_273,Dom_271,Morphism_275,El1_274] :
( ( subtract(Cod_272,apply(Morphism_275,El1_274),apply(Morphism_275,El2_273)) = apply(Morphism_275,subtract(Dom_271,El1_274,El2_273)) )
| ~ element(El2_273,Dom_271)
| ~ element(El1_274,Dom_271)
| ~ morphism(Morphism_275,Dom_271,Cod_272) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_7675,plain,
! [El1_703,El2_704] :
( ( subtract(r,apply(delta,El1_703),apply(delta,El2_704)) = apply(delta,subtract(e,El1_703,El2_704)) )
| ~ element(El2_704,e)
| ~ element(El1_703,e) ),
inference(resolution,[status(thm)],[c_70,c_1611]) ).
tff(c_7880,plain,
! [El1_703] :
( ( subtract(r,apply(delta,El1_703),'#skF_10'('#skF_15')) = apply(delta,subtract(e,El1_703,'#skF_15')) )
| ~ element('#skF_15',e)
| ~ element(El1_703,e) ),
inference(superposition,[status(thm),theory(equality)],[c_137,c_7675]) ).
tff(c_8364,plain,
! [El1_720] :
( ( subtract(r,apply(delta,El1_720),'#skF_10'('#skF_15')) = apply(delta,subtract(e,El1_720,'#skF_15')) )
| ~ element(El1_720,e) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_7880]) ).
tff(c_8451,plain,
( ( subtract(r,zero(r),'#skF_10'('#skF_15')) = apply(delta,subtract(e,zero(e),'#skF_15')) )
| ~ element(zero(e),e) ),
inference(superposition,[status(thm),theory(equality)],[c_182,c_8364]) ).
tff(c_8464,plain,
subtract(r,zero(r),'#skF_10'('#skF_15')) = apply(delta,subtract(e,zero(e),'#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_325,c_8451]) ).
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_8528,plain,
( element(apply(delta,subtract(e,zero(e),'#skF_15')),r)
| ~ element('#skF_10'('#skF_15'),r)
| ~ element(zero(r),r) ),
inference(superposition,[status(thm),theory(equality)],[c_8464,c_56]) ).
tff(c_8540,plain,
( element(apply(delta,subtract(e,zero(e),'#skF_15')),r)
| ~ element('#skF_10'('#skF_15'),r) ),
inference(demodulation,[status(thm),theory(equality)],[c_351,c_8528]) ).
tff(c_8542,plain,
~ element('#skF_10'('#skF_15'),r),
inference(splitLeft,[status(thm)],[c_8540]) ).
tff(c_8545,plain,
~ morphism(delta,e,r),
inference(resolution,[status(thm)],[c_444,c_8542]) ).
tff(c_8552,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_70,c_8545]) ).
tff(c_8554,plain,
element('#skF_10'('#skF_15'),r),
inference(splitRight,[status(thm)],[c_8540]) ).
tff(c_7904,plain,
! [El1_703] :
( ( subtract(r,apply(delta,El1_703),'#skF_10'('#skF_15')) = apply(delta,subtract(e,El1_703,'#skF_15')) )
| ~ element(El1_703,e) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_7880]) ).
tff(c_84,plain,
surjection(delta),
inference(cnfTransformation,[status(thm)],[f_225]) ).
tff(c_18,plain,
! [Morphism_18,Dom_19,Cod_20,ElCod_24] :
( element('#skF_3'(Morphism_18,Dom_19,Cod_20,ElCod_24),Dom_19)
| ~ element(ElCod_24,Cod_20)
| ~ morphism(Morphism_18,Dom_19,Cod_20)
| ~ surjection(Morphism_18) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_1050,plain,
! [Morphism_193,Dom_194,Cod_195,ElCod_196] :
( element('#skF_3'(Morphism_193,Dom_194,Cod_195,ElCod_196),Dom_194)
| ~ element(ElCod_196,Cod_195)
| ~ morphism(Morphism_193,Dom_194,Cod_195)
| ~ surjection(Morphism_193) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_11579,plain,
! [Morphism_810,Cod_811,ElCod_812] :
( ( apply(delta,'#skF_3'(Morphism_810,e,Cod_811,ElCod_812)) = '#skF_10'('#skF_3'(Morphism_810,e,Cod_811,ElCod_812)) )
| ~ element(ElCod_812,Cod_811)
| ~ morphism(Morphism_810,e,Cod_811)
| ~ surjection(Morphism_810) ),
inference(resolution,[status(thm)],[c_1050,c_104]) ).
tff(c_16,plain,
! [Morphism_18,Dom_19,Cod_20,ElCod_24] :
( ( apply(Morphism_18,'#skF_3'(Morphism_18,Dom_19,Cod_20,ElCod_24)) = ElCod_24 )
| ~ element(ElCod_24,Cod_20)
| ~ morphism(Morphism_18,Dom_19,Cod_20)
| ~ surjection(Morphism_18) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_11612,plain,
! [Cod_811,ElCod_812] :
( ( '#skF_10'('#skF_3'(delta,e,Cod_811,ElCod_812)) = ElCod_812 )
| ~ element(ElCod_812,Cod_811)
| ~ morphism(delta,e,Cod_811)
| ~ surjection(delta)
| ~ element(ElCod_812,Cod_811)
| ~ morphism(delta,e,Cod_811)
| ~ surjection(delta) ),
inference(superposition,[status(thm),theory(equality)],[c_11579,c_16]) ).
tff(c_11629,plain,
! [Cod_813,ElCod_814] :
( ( '#skF_10'('#skF_3'(delta,e,Cod_813,ElCod_814)) = ElCod_814 )
| ~ element(ElCod_814,Cod_813)
| ~ morphism(delta,e,Cod_813) ),
inference(demodulation,[status(thm),theory(equality)],[c_84,c_84,c_11612]) ).
tff(c_12856,plain,
! [ElCod_908,Cod_909] :
( element(ElCod_908,r)
| ~ element('#skF_3'(delta,e,Cod_909,ElCod_908),e)
| ~ element(ElCod_908,Cod_909)
| ~ morphism(delta,e,Cod_909) ),
inference(superposition,[status(thm),theory(equality)],[c_11629,c_106]) ).
tff(c_12860,plain,
! [ElCod_24,Cod_20] :
( element(ElCod_24,r)
| ~ element(ElCod_24,Cod_20)
| ~ morphism(delta,e,Cod_20)
| ~ surjection(delta) ),
inference(resolution,[status(thm)],[c_18,c_12856]) ).
tff(c_12886,plain,
! [ElCod_915,Cod_916] :
( element(ElCod_915,r)
| ~ element(ElCod_915,Cod_916)
| ~ morphism(delta,e,Cod_916) ),
inference(demodulation,[status(thm),theory(equality)],[c_84,c_12860]) ).
tff(c_13843,plain,
! [Dom_985,El1_986,El2_987] :
( element(subtract(Dom_985,El1_986,El2_987),r)
| ~ morphism(delta,e,Dom_985)
| ~ element(El2_987,Dom_985)
| ~ element(El1_986,Dom_985) ),
inference(resolution,[status(thm)],[c_56,c_12886]) ).
tff(c_13958,plain,
! [El1_703] :
( element(apply(delta,subtract(e,El1_703,'#skF_15')),r)
| ~ morphism(delta,e,r)
| ~ element('#skF_10'('#skF_15'),r)
| ~ element(apply(delta,El1_703),r)
| ~ element(El1_703,e) ),
inference(superposition,[status(thm),theory(equality)],[c_7904,c_13843]) ).
tff(c_14219,plain,
! [El1_999] :
( element(apply(delta,subtract(e,El1_999,'#skF_15')),r)
| ~ element(apply(delta,El1_999),r)
| ~ element(El1_999,e) ),
inference(demodulation,[status(thm),theory(equality)],[c_8554,c_70,c_13958]) ).
tff(c_14233,plain,
! [El1_129] :
( element('#skF_10'(subtract(e,El1_129,'#skF_15')),r)
| ~ element(apply(delta,El1_129),r)
| ~ element(El1_129,e)
| ~ element('#skF_15',e)
| ~ element(El1_129,e) ),
inference(superposition,[status(thm),theory(equality)],[c_323,c_14219]) ).
tff(c_14254,plain,
! [El1_1000] :
( element('#skF_10'(subtract(e,El1_1000,'#skF_15')),r)
| ~ element(apply(delta,El1_1000),r)
| ~ element(El1_1000,e) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_14233]) ).
tff(c_14268,plain,
( element('#skF_10'('#skF_13'('#skF_15')),r)
| ~ element(apply(delta,apply(g,'#skF_12'('#skF_15'))),r)
| ~ element(apply(g,'#skF_12'('#skF_15')),e)
| ~ element('#skF_15',e) ),
inference(superposition,[status(thm),theory(equality)],[c_114,c_14254]) ).
tff(c_14280,plain,
( element('#skF_10'('#skF_13'('#skF_15')),r)
| ~ element(apply(delta,apply(g,'#skF_12'('#skF_15'))),r)
| ~ element(apply(g,'#skF_12'('#skF_15')),e) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_14268]) ).
tff(c_45215,plain,
~ element(apply(g,'#skF_12'('#skF_15')),e),
inference(splitLeft,[status(thm)],[c_14280]) ).
tff(c_45218,plain,
( ~ morphism(g,b,e)
| ~ element('#skF_15',e) ),
inference(resolution,[status(thm)],[c_431,c_45215]) ).
tff(c_45222,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_122,c_74,c_45218]) ).
tff(c_45224,plain,
element(apply(g,'#skF_12'('#skF_15')),e),
inference(splitRight,[status(thm)],[c_14280]) ).
tff(c_58,plain,
! [Dom_83,El_84] :
( ( subtract(Dom_83,El_84,El_84) = zero(Dom_83) )
| ~ element(El_84,Dom_83) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_45252,plain,
subtract(e,apply(g,'#skF_12'('#skF_15')),apply(g,'#skF_12'('#skF_15'))) = zero(e),
inference(resolution,[status(thm)],[c_45224,c_58]) ).
tff(c_60,plain,
! [Dom_85,El1_86,El2_87] :
( ( subtract(Dom_85,El1_86,subtract(Dom_85,El1_86,El2_87)) = El2_87 )
| ~ element(El2_87,Dom_85)
| ~ element(El1_86,Dom_85) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_45536,plain,
( ( subtract(e,apply(g,'#skF_12'('#skF_15')),zero(e)) = apply(g,'#skF_12'('#skF_15')) )
| ~ element(apply(g,'#skF_12'('#skF_15')),e)
| ~ element(apply(g,'#skF_12'('#skF_15')),e) ),
inference(superposition,[status(thm),theory(equality)],[c_45252,c_60]) ).
tff(c_45568,plain,
subtract(e,apply(g,'#skF_12'('#skF_15')),zero(e)) = apply(g,'#skF_12'('#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_45224,c_45224,c_45536]) ).
tff(c_386,plain,
! [E_134] :
( ( subtract(b,'#skF_12'(E_134),'#skF_12'(E_134)) = zero(b) )
| ~ element(E_134,e) ),
inference(resolution,[status(thm)],[c_118,c_138]) ).
tff(c_392,plain,
! [E_134] :
( element(zero(b),b)
| ~ element('#skF_12'(E_134),b)
| ~ element('#skF_12'(E_134),b)
| ~ element(E_134,e) ),
inference(superposition,[status(thm),theory(equality)],[c_386,c_56]) ).
tff(c_2731,plain,
! [E_387] :
( ~ element('#skF_12'(E_387),b)
| ~ element('#skF_12'(E_387),b)
| ~ element(E_387,e) ),
inference(splitLeft,[status(thm)],[c_392]) ).
tff(c_2735,plain,
! [E_388] :
( ~ element('#skF_12'(E_388),b)
| ~ element(E_388,e) ),
inference(resolution,[status(thm)],[c_118,c_2731]) ).
tff(c_2739,plain,
! [E_98] : ~ element(E_98,e),
inference(resolution,[status(thm)],[c_118,c_2735]) ).
tff(c_2745,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2739,c_325]) ).
tff(c_2746,plain,
element(zero(b),b),
inference(splitRight,[status(thm)],[c_392]) ).
tff(c_185,plain,
apply(g,zero(b)) = zero(e),
inference(resolution,[status(thm)],[c_74,c_165]) ).
tff(c_6534,plain,
! [El1_674,El2_675] :
( ( subtract(e,apply(g,El1_674),apply(g,El2_675)) = apply(g,subtract(b,El1_674,El2_675)) )
| ~ element(El2_675,b)
| ~ element(El1_674,b) ),
inference(resolution,[status(thm)],[c_74,c_1611]) ).
tff(c_6675,plain,
! [El1_674] :
( ( subtract(e,apply(g,El1_674),zero(e)) = apply(g,subtract(b,El1_674,zero(b))) )
| ~ element(zero(b),b)
| ~ element(El1_674,b) ),
inference(superposition,[status(thm),theory(equality)],[c_185,c_6534]) ).
tff(c_6685,plain,
! [El1_674] :
( ( subtract(e,apply(g,El1_674),zero(e)) = apply(g,subtract(b,El1_674,zero(b))) )
| ~ element(El1_674,b) ),
inference(demodulation,[status(thm),theory(equality)],[c_2746,c_6675]) ).
tff(c_45886,plain,
( ( apply(g,subtract(b,'#skF_12'('#skF_15'),zero(b))) = apply(g,'#skF_12'('#skF_15')) )
| ~ element('#skF_12'('#skF_15'),b) ),
inference(superposition,[status(thm),theory(equality)],[c_45568,c_6685]) ).
tff(c_46673,plain,
~ element('#skF_12'('#skF_15'),b),
inference(splitLeft,[status(thm)],[c_45886]) ).
tff(c_46676,plain,
~ element('#skF_15',e),
inference(resolution,[status(thm)],[c_118,c_46673]) ).
tff(c_46680,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_122,c_46676]) ).
tff(c_46682,plain,
element('#skF_12'('#skF_15'),b),
inference(splitRight,[status(thm)],[c_45886]) ).
tff(c_648,plain,
! [Dom_166,El1_167,El2_168] :
( ( subtract(Dom_166,El1_167,subtract(Dom_166,El1_167,El2_168)) = El2_168 )
| ~ element(El2_168,Dom_166)
| ~ element(El1_167,Dom_166) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_676,plain,
! [E_98] :
( ( subtract(e,apply(g,'#skF_12'(E_98)),'#skF_13'(E_98)) = E_98 )
| ~ element(E_98,e)
| ~ element(apply(g,'#skF_12'(E_98)),e)
| ~ element(E_98,e) ),
inference(superposition,[status(thm),theory(equality)],[c_114,c_648]) ).
tff(c_108,plain,
! [E_98] :
( ( apply(g,apply(alpha,'#skF_14'(E_98))) = '#skF_13'(E_98) )
| ~ element(E_98,e) ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_111171,plain,
! [El1_3925,E_3926] :
( ( apply(g,subtract(b,El1_3925,apply(alpha,'#skF_14'(E_3926)))) = subtract(e,apply(g,El1_3925),'#skF_13'(E_3926)) )
| ~ element(apply(alpha,'#skF_14'(E_3926)),b)
| ~ element(El1_3925,b)
| ~ element(E_3926,e) ),
inference(superposition,[status(thm),theory(equality)],[c_108,c_6534]) ).
tff(c_120,plain,
! [B1_104,B2_105] :
( ( apply(g,subtract(b,B1_104,B2_105)) != '#skF_15' )
| ~ element(B2_105,b)
| ~ element(B1_104,b) ),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_111338,plain,
! [El1_3927,E_3928] :
( ( subtract(e,apply(g,El1_3927),'#skF_13'(E_3928)) != '#skF_15' )
| ~ element(apply(alpha,'#skF_14'(E_3928)),b)
| ~ element(El1_3927,b)
| ~ element(apply(alpha,'#skF_14'(E_3928)),b)
| ~ element(El1_3927,b)
| ~ element(E_3928,e) ),
inference(superposition,[status(thm),theory(equality)],[c_111171,c_120]) ).
tff(c_111494,plain,
! [E_3954] :
( ( E_3954 != '#skF_15' )
| ~ element(apply(alpha,'#skF_14'(E_3954)),b)
| ~ element('#skF_12'(E_3954),b)
| ~ element(apply(alpha,'#skF_14'(E_3954)),b)
| ~ element('#skF_12'(E_3954),b)
| ~ element(E_3954,e)
| ~ element(E_3954,e)
| ~ element(apply(g,'#skF_12'(E_3954)),e)
| ~ element(E_3954,e) ),
inference(superposition,[status(thm),theory(equality)],[c_676,c_111338]) ).
tff(c_111501,plain,
( ~ element(apply(alpha,'#skF_14'('#skF_15')),b)
| ~ element('#skF_12'('#skF_15'),b)
| ~ element('#skF_15',e) ),
inference(resolution,[status(thm)],[c_45224,c_111494]) ).
tff(c_111518,plain,
~ element(apply(alpha,'#skF_14'('#skF_15')),b),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_46682,c_111501]) ).
tff(c_111529,plain,
( ~ morphism(alpha,a,b)
| ~ element('#skF_15',e) ),
inference(resolution,[status(thm)],[c_427,c_111518]) ).
tff(c_111533,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_122,c_64,c_111529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HAL006+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % 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
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 20:06:18 EDT 2023
% 0.14/0.36 % CPUTime :
% 48.07/34.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.07/34.22
% 48.07/34.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.31/34.26
% 48.31/34.26 Inference rules
% 48.31/34.26 ----------------------
% 48.31/34.26 #Ref : 9
% 48.31/34.26 #Sup : 29910
% 48.31/34.26 #Fact : 0
% 48.31/34.26 #Define : 0
% 48.31/34.26 #Split : 118
% 48.31/34.26 #Chain : 0
% 48.31/34.26 #Close : 0
% 48.31/34.26
% 48.31/34.26 Ordering : KBO
% 48.31/34.26
% 48.31/34.26 Simplification rules
% 48.31/34.26 ----------------------
% 48.31/34.26 #Subsume : 10286
% 48.31/34.26 #Demod : 18084
% 48.31/34.26 #Tautology : 6554
% 48.31/34.26 #SimpNegUnit : 124
% 48.31/34.26 #BackRed : 43
% 48.31/34.26
% 48.31/34.26 #Partial instantiations: 0
% 48.31/34.26 #Strategies tried : 1
% 48.31/34.26
% 48.31/34.26 Timing (in seconds)
% 48.31/34.26 ----------------------
% 48.31/34.26 Preprocessing : 0.63
% 48.31/34.26 Parsing : 0.29
% 48.31/34.26 CNF conversion : 0.05
% 48.31/34.26 Main loop : 32.55
% 48.31/34.26 Inferencing : 7.98
% 48.31/34.26 Reduction : 11.72
% 48.31/34.26 Demodulation : 8.63
% 48.31/34.26 BG Simplification : 0.29
% 48.31/34.26 Subsumption : 10.70
% 48.31/34.26 Abstraction : 0.47
% 48.31/34.26 MUC search : 0.00
% 48.31/34.26 Cooper : 0.00
% 48.31/34.26 Total : 33.24
% 48.31/34.27 Index Insertion : 0.00
% 48.31/34.27 Index Deletion : 0.00
% 48.31/34.27 Index Matching : 0.00
% 48.31/34.27 BG Taut test : 0.00
%------------------------------------------------------------------------------