TSTP Solution File: NUM847+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM847+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n011.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 : Thu Aug 31 10:25:21 EDT 2023
% Result : Theorem 0.21s 0.65s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : NUM847+1 : TPTP v8.1.2. Released v4.1.0.
% 0.09/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n011.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 : Fri Aug 25 08:14:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 % File :CSE---1.6
% 0.21/0.64 % Problem :theBenchmark
% 0.21/0.64 % Transform :cnf
% 0.21/0.64 % Format :tptp:raw
% 0.21/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.64
% 0.21/0.64 % Result :Theorem 0.000000s
% 0.21/0.64 % Output :CNFRefutation 0.000000s
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 %------------------------------------------------------------------------------
% 0.21/0.64 % File : NUM847+1 : TPTP v8.1.2. Released v4.1.0.
% 0.21/0.64 % Domain : Number Theory
% 0.21/0.64 % Problem : holds(286,441,3)
% 0.21/0.64 % Version : Especial.
% 0.21/0.64 % English :
% 0.21/0.64
% 0.21/0.64 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.64 % : [Kue09] Kuehlwein (2009), Email to Geoff Sutcliffe
% 0.21/0.64 % : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% 0.21/0.64 % Source : [Kue09]
% 0.21/0.64 % Names :
% 0.21/0.64
% 0.21/0.64 % Status : Theorem
% 0.21/0.64 % Rating : 0.17 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.27 v7.3.0, 0.21 v7.1.0, 0.30 v7.0.0, 0.27 v6.4.0, 0.35 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.37 v6.0.0, 0.35 v5.5.0, 0.26 v5.4.0, 0.29 v5.3.0, 0.33 v5.2.0, 0.25 v5.1.0, 0.24 v5.0.0, 0.21 v4.1.0
% 0.21/0.64 % Syntax : Number of formulae : 56 ( 20 unt; 0 def)
% 0.21/0.64 % Number of atoms : 106 ( 50 equ)
% 0.21/0.64 % Maximal formula atoms : 5 ( 1 avg)
% 0.21/0.64 % Number of connectives : 70 ( 20 ~; 14 |; 10 &)
% 0.21/0.64 % ( 4 <=>; 22 =>; 0 <=; 0 <~>)
% 0.21/0.64 % Maximal formula depth : 8 ( 4 avg)
% 0.21/0.64 % Maximal term depth : 4 ( 1 avg)
% 0.21/0.64 % Number of predicates : 5 ( 4 usr; 0 prp; 2-2 aty)
% 0.21/0.64 % Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% 0.21/0.64 % Number of variables : 115 ( 107 !; 8 ?)
% 0.21/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.64
% 0.21/0.64 % Comments : From the Landau in Naproche 0.45 collection.
% 0.21/0.64 %------------------------------------------------------------------------------
% 0.21/0.64 fof('holds(286, 441, 3)',conjecture,
% 0.21/0.64 vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) ).
% 0.21/0.64
% 0.21/0.64 fof('holds(286, 441, 2)',axiom,
% 0.21/0.64 vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ).
% 0.21/0.64
% 0.21/0.64 fof('holds(286, 441, 1)',axiom,
% 0.21/0.64 vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436) ).
% 0.21/0.64
% 0.21/0.64 fof('holds(286, 441, 0)',axiom,
% 0.21/0.64 vmul(vd436,vplus(vd437,vsucc(vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))) ).
% 0.21/0.64
% 0.21/0.64 fof('holds(285, 440, 0)',axiom,
% 0.21/0.64 vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)) ).
% 0.21/0.64
% 0.21/0.64 fof('holds(284, 438, 2)',axiom,
% 0.21/0.64 vplus(vmul(vd436,vd437),vd436) = vplus(vmul(vd436,vd437),vmul(vd436,v1)) ).
% 0.21/0.64
% 0.21/0.64 fof('holds(284, 438, 1)',axiom,
% 0.21/0.64 vmul(vd436,vsucc(vd437)) = vplus(vmul(vd436,vd437),vd436) ).
% 0.21/0.64
% 0.21/0.64 fof('holds(284, 438, 0)',axiom,
% 0.21/0.64 vmul(vd436,vplus(vd437,v1)) = vmul(vd436,vsucc(vd437)) ).
% 0.21/0.64
% 0.21/0.64 fof('ass(cond(270, 0), 0)',axiom,
% 0.21/0.64 ! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418) ).
% 0.21/0.64
% 0.21/0.64 fof('ass(cond(261, 0), 0)',axiom,
% 0.21/0.64 ! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409) ).
% 0.21/0.64
% 0.21/0.64 fof('ass(cond(253, 0), 0)',axiom,
% 0.21/0.64 ! [Vd400] : vmul(v1,Vd400) = Vd400 ).
% 0.21/0.64
% 0.21/0.64 fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
% 0.21/0.64 ! [Vd396,Vd397] :
% 0.21/0.64 ( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
% 0.21/0.64 & vmul(Vd396,v1) = Vd396 ) ).
% 0.21/0.64
% 0.21/0.64 fof('ass(cond(241, 0), 0)',axiom,
% 0.21/0.64 ! [Vd386,Vd387] :
% 0.21/0.64 ( less(Vd386,vplus(Vd387,v1))
% 0.21/0.64 => leq(Vd386,Vd387) ) ).
% 0.21/0.64
% 0.21/0.64 fof('ass(cond(234, 0), 0)',axiom,
% 0.21/0.64 ! [Vd375,Vd376] :
% 0.21/0.65 ( greater(Vd375,Vd376)
% 0.21/0.65 => geq(Vd375,vplus(Vd376,v1)) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(228, 0), 0)',axiom,
% 0.21/0.65 ! [Vd369] : geq(Vd369,v1) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(223, 0), 0)',axiom,
% 0.21/0.65 ! [Vd362,Vd363,Vd365,Vd366] :
% 0.21/0.65 ( ( geq(Vd365,Vd366)
% 0.21/0.65 & geq(Vd362,Vd363) )
% 0.21/0.65 => geq(vplus(Vd362,Vd365),vplus(Vd363,Vd366)) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(216), 0), 0)',axiom,
% 0.21/0.65 ! [Vd353,Vd354,Vd355,Vd356] :
% 0.21/0.65 ( ( ( greater(Vd355,Vd356)
% 0.21/0.65 & geq(Vd353,Vd354) )
% 0.21/0.65 | ( geq(Vd355,Vd356)
% 0.21/0.65 & greater(Vd353,Vd354) ) )
% 0.21/0.65 => greater(vplus(Vd353,Vd355),vplus(Vd354,Vd356)) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(209, 0), 0)',axiom,
% 0.21/0.65 ! [Vd337,Vd338,Vd340,Vd341] :
% 0.21/0.65 ( ( greater(Vd340,Vd341)
% 0.21/0.65 & greater(Vd337,Vd338) )
% 0.21/0.65 => greater(vplus(Vd337,Vd340),vplus(Vd338,Vd341)) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(202), 0), 0)',axiom,
% 0.21/0.65 ! [Vd328,Vd329,Vd330] :
% 0.21/0.65 ( less(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
% 0.21/0.65 => less(Vd328,Vd329) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(202), 0), 1)',axiom,
% 0.21/0.65 ! [Vd328,Vd329,Vd330] :
% 0.21/0.65 ( vplus(Vd328,Vd330) = vplus(Vd329,Vd330)
% 0.21/0.65 => Vd328 = Vd329 ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(202), 0), 2)',axiom,
% 0.21/0.65 ! [Vd328,Vd329,Vd330] :
% 0.21/0.65 ( greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
% 0.21/0.65 => greater(Vd328,Vd329) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(193), 0), 0)',axiom,
% 0.21/0.65 ! [Vd301,Vd302,Vd303] :
% 0.21/0.65 ( less(Vd301,Vd302)
% 0.21/0.65 => less(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(193), 0), 1)',axiom,
% 0.21/0.65 ! [Vd301,Vd302,Vd303] :
% 0.21/0.65 ( Vd301 = Vd302
% 0.21/0.65 => vplus(Vd301,Vd303) = vplus(Vd302,Vd303) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(193), 0), 2)',axiom,
% 0.21/0.65 ! [Vd301,Vd302,Vd303] :
% 0.21/0.65 ( greater(Vd301,Vd302)
% 0.21/0.65 => greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(189, 0), 0)',axiom,
% 0.21/0.65 ! [Vd295,Vd296] : greater(vplus(Vd295,Vd296),Vd295) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(184, 0), 0)',axiom,
% 0.21/0.65 ! [Vd289,Vd290,Vd292] :
% 0.21/0.65 ( ( leq(Vd290,Vd292)
% 0.21/0.65 & leq(Vd289,Vd290) )
% 0.21/0.65 => leq(Vd289,Vd292) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(177), 0), 0)',axiom,
% 0.21/0.65 ! [Vd281,Vd282,Vd283] :
% 0.21/0.65 ( ( ( less(Vd282,Vd283)
% 0.21/0.65 & leq(Vd281,Vd282) )
% 0.21/0.65 | ( leq(Vd282,Vd283)
% 0.21/0.65 & less(Vd281,Vd282) ) )
% 0.21/0.65 => less(Vd281,Vd283) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(168, 0), 0)',axiom,
% 0.21/0.65 ! [Vd262,Vd263,Vd265] :
% 0.21/0.65 ( ( less(Vd263,Vd265)
% 0.21/0.65 & less(Vd262,Vd263) )
% 0.21/0.65 => less(Vd262,Vd265) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(163, 0), 0)',axiom,
% 0.21/0.65 ! [Vd258,Vd259] :
% 0.21/0.65 ( leq(Vd258,Vd259)
% 0.21/0.65 => geq(Vd259,Vd258) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(158, 0), 0)',axiom,
% 0.21/0.65 ! [Vd254,Vd255] :
% 0.21/0.65 ( geq(Vd254,Vd255)
% 0.21/0.65 => leq(Vd255,Vd254) ) ).
% 0.21/0.65
% 0.21/0.65 fof('def(cond(conseq(axiom(3)), 17), 1)',axiom,
% 0.21/0.65 ! [Vd249,Vd250] :
% 0.21/0.65 ( leq(Vd250,Vd249)
% 0.21/0.65 <=> ( less(Vd250,Vd249)
% 0.21/0.65 | Vd250 = Vd249 ) ) ).
% 0.21/0.65
% 0.21/0.65 fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
% 0.21/0.65 ! [Vd244,Vd245] :
% 0.21/0.65 ( geq(Vd245,Vd244)
% 0.21/0.65 <=> ( greater(Vd245,Vd244)
% 0.21/0.65 | Vd245 = Vd244 ) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(147, 0), 0)',axiom,
% 0.21/0.65 ! [Vd226,Vd227] :
% 0.21/0.65 ( less(Vd226,Vd227)
% 0.21/0.65 => greater(Vd227,Vd226) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(140, 0), 0)',axiom,
% 0.21/0.65 ! [Vd208,Vd209] :
% 0.21/0.65 ( greater(Vd208,Vd209)
% 0.21/0.65 => less(Vd209,Vd208) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(130), 0), 0)',axiom,
% 0.21/0.65 ! [Vd203,Vd204] :
% 0.21/0.65 ( Vd203 = Vd204
% 0.21/0.65 | greater(Vd203,Vd204)
% 0.21/0.65 | less(Vd203,Vd204) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(130), 0), 1)',axiom,
% 0.21/0.65 ! [Vd203,Vd204] :
% 0.21/0.65 ( Vd203 != Vd204
% 0.21/0.65 | ~ less(Vd203,Vd204) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(130), 0), 2)',axiom,
% 0.21/0.65 ! [Vd203,Vd204] :
% 0.21/0.65 ( ~ greater(Vd203,Vd204)
% 0.21/0.65 | ~ less(Vd203,Vd204) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(130), 0), 3)',axiom,
% 0.21/0.65 ! [Vd203,Vd204] :
% 0.21/0.65 ( Vd203 != Vd204
% 0.21/0.65 | ~ greater(Vd203,Vd204) ) ).
% 0.21/0.65
% 0.21/0.65 fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
% 0.21/0.65 ! [Vd198,Vd199] :
% 0.21/0.65 ( less(Vd199,Vd198)
% 0.21/0.65 <=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ) ).
% 0.21/0.65
% 0.21/0.65 fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
% 0.21/0.65 ! [Vd193,Vd194] :
% 0.21/0.65 ( greater(Vd194,Vd193)
% 0.21/0.65 <=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(88), 0), 0)',axiom,
% 0.21/0.65 ! [Vd120,Vd121] :
% 0.21/0.65 ( Vd120 = Vd121
% 0.21/0.65 | ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 0.21/0.65 | ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(88), 0), 1)',axiom,
% 0.21/0.65 ! [Vd120,Vd121] :
% 0.21/0.65 ( Vd120 != Vd121
% 0.21/0.65 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(88), 0), 2)',axiom,
% 0.21/0.65 ! [Vd120,Vd121] :
% 0.21/0.65 ( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
% 0.21/0.65 | ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(goal(88), 0), 3)',axiom,
% 0.21/0.65 ! [Vd120,Vd121] :
% 0.21/0.65 ( Vd120 != Vd121
% 0.21/0.65 | ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(81, 0), 0)',axiom,
% 0.21/0.65 ! [Vd104,Vd105] :
% 0.21/0.65 ( Vd104 != Vd105
% 0.21/0.65 => ! [Vd107] : vplus(Vd107,Vd104) != vplus(Vd107,Vd105) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(73, 0), 0)',axiom,
% 0.21/0.65 ! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(61, 0), 0)',axiom,
% 0.21/0.65 ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(52, 0), 0)',axiom,
% 0.21/0.65 ! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(43, 0), 0)',axiom,
% 0.21/0.65 ! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(33, 0), 0)',axiom,
% 0.21/0.65 ! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) ).
% 0.21/0.65
% 0.21/0.65 fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
% 0.21/0.65 ! [Vd42,Vd43] :
% 0.21/0.65 ( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
% 0.21/0.65 & vplus(Vd42,v1) = vsucc(Vd42) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(20, 0), 0)',axiom,
% 0.21/0.65 ! [Vd24] :
% 0.21/0.65 ( Vd24 != v1
% 0.21/0.65 => Vd24 = vsucc(vskolem2(Vd24)) ) ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(12, 0), 0)',axiom,
% 0.21/0.65 ! [Vd16] : vsucc(Vd16) != Vd16 ).
% 0.21/0.65
% 0.21/0.65 fof('ass(cond(6, 0), 0)',axiom,
% 0.21/0.65 ! [Vd7,Vd8] :
% 0.21/0.65 ( Vd7 != Vd8
% 0.21/0.65 => vsucc(Vd7) != vsucc(Vd8) ) ).
% 0.21/0.65
% 0.21/0.65 fof('qu(antec(axiom(3)), imp(antec(axiom(3))))',axiom,
% 0.21/0.65 ! [Vd3,Vd4] :
% 0.21/0.65 ( vsucc(Vd3) = vsucc(Vd4)
% 0.21/0.65 => Vd3 = Vd4 ) ).
% 0.21/0.65
% 0.21/0.65 fof('qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))',axiom,
% 0.21/0.65 ! [Vd1] : vsucc(Vd1) != v1 ).
% 0.21/0.65
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 % Proof found
% 0.21/0.65 % SZS status Theorem for theBenchmark
% 0.21/0.65 % SZS output start Proof
% 0.21/0.65 %ClaNum:87(EqnAxiom:24)
% 0.21/0.65 %VarNum:254(SingletonVarNum:122)
% 0.21/0.65 %MaxLitNum:3
% 0.21/0.65 %MaxfuncDepth:3
% 0.21/0.65 %SharedTerms:30
% 0.21/0.65 %goalClause: 46
% 0.21/0.65 %singleGoalClaCount:1
% 0.21/0.65 [38]E(f10(f6(a7,a8),f6(a7,a9)),f6(a7,f10(a8,a9)))
% 0.21/0.65 [39]E(f10(f6(a7,a8),f6(a7,a1)),f10(f6(a7,a8),a7))
% 0.21/0.65 [40]E(f6(a7,f10(f10(a8,a9),a1)),f6(a7,f10(a8,f10(a9,a1))))
% 0.21/0.65 [42]E(f10(f10(f6(a7,a8),f6(a7,a9)),a7),f10(f6(a7,f10(a8,a9)),a7))
% 0.21/0.65 [46]~E(f10(f10(f6(a7,a8),f6(a7,a9)),a7),f10(f6(a7,a8),f10(f6(a7,a9),a7)))
% 0.21/0.65 [25]P1(x251,a1)
% 0.21/0.65 [26]E(f6(x261,a1),x261)
% 0.21/0.65 [27]E(f6(a1,x271),x271)
% 0.21/0.65 [44]~E(f10(x441,a1),x441)
% 0.21/0.65 [29]E(f6(x291,x292),f6(x292,x291))
% 0.21/0.65 [30]E(f10(x301,x302),f10(x302,x301))
% 0.21/0.65 [31]P2(f10(x311,x312),x311)
% 0.21/0.65 [45]~E(f10(x451,x452),x452)
% 0.21/0.65 [34]E(f10(f10(x341,a1),x342),f10(f10(x341,x342),a1))
% 0.21/0.65 [35]E(f10(f6(x351,x352),x351),f6(x351,f10(x352,a1)))
% 0.21/0.65 [36]E(f10(f6(x361,x362),x362),f6(f10(x361,a1),x362))
% 0.21/0.65 [37]E(f10(f10(x371,x372),x373),f10(x371,f10(x372,x373)))
% 0.21/0.65 [49]E(x491,a1)+E(f10(f11(x491),a1),x491)
% 0.21/0.65 [47]~E(x471,x472)+P3(x471,x472)
% 0.21/0.65 [48]~E(x481,x482)+P1(x481,x482)
% 0.21/0.65 [50]~P4(x501,x502)+~E(x501,x502)
% 0.21/0.65 [51]~P2(x511,x512)+~E(x511,x512)
% 0.21/0.65 [55]~P2(x552,x551)+P4(x551,x552)
% 0.21/0.65 [56]~P1(x562,x561)+P3(x561,x562)
% 0.21/0.65 [57]~P4(x571,x572)+P3(x571,x572)
% 0.21/0.65 [58]~P4(x582,x581)+P2(x581,x582)
% 0.21/0.65 [59]~P3(x592,x591)+P1(x591,x592)
% 0.21/0.65 [60]~P2(x601,x602)+P1(x601,x602)
% 0.21/0.65 [67]~P2(x671,x672)+~P4(x671,x672)
% 0.21/0.65 [75]~P2(x751,x752)+P1(x751,f10(x752,a1))
% 0.21/0.65 [78]P3(x781,x782)+~P4(x781,f10(x782,a1))
% 0.21/0.65 [76]~P4(x761,x762)+E(f10(x761,f2(x762,x761)),x762)
% 0.21/0.65 [77]~P2(x772,x771)+E(f10(x771,f3(x771,x772)),x772)
% 0.21/0.65 [52]~E(x521,x522)+~E(x522,f10(x521,x523))
% 0.21/0.65 [53]~E(x531,x532)+~E(x531,f10(x532,x533))
% 0.21/0.65 [61]P4(x611,x612)+~E(x612,f10(x611,x613))
% 0.21/0.65 [62]P2(x621,x622)+~E(x621,f10(x622,x623))
% 0.21/0.65 [68]E(x681,x682)+~E(f10(x681,x683),f10(x682,x683))
% 0.21/0.65 [69]E(x691,x692)+~E(f10(x693,x691),f10(x693,x692))
% 0.21/0.65 [80]~P4(x801,x803)+P4(f10(x801,x802),f10(x803,x802))
% 0.21/0.65 [81]~P2(x811,x813)+P2(f10(x811,x812),f10(x813,x812))
% 0.21/0.65 [86]P4(x861,x862)+~P4(f10(x861,x863),f10(x862,x863))
% 0.21/0.65 [87]P2(x871,x872)+~P2(f10(x871,x873),f10(x872,x873))
% 0.21/0.65 [70]~E(x701,f10(x702,x703))+~E(x702,f10(x701,x704))
% 0.21/0.65 [54]P4(x541,x542)+P2(x541,x542)+E(x541,x542)
% 0.21/0.65 [63]P4(x631,x632)+~P3(x631,x632)+E(x631,x632)
% 0.21/0.65 [64]P2(x641,x642)+~P1(x641,x642)+E(x641,x642)
% 0.21/0.65 [79]E(x791,x792)+E(f10(x791,f4(x791,x792)),x792)+E(f10(x792,f5(x791,x792)),x791)
% 0.21/0.65 [71]~P4(x713,x712)+P4(x711,x712)+~P4(x711,x713)
% 0.21/0.65 [72]~P3(x723,x722)+P4(x721,x722)+~P4(x721,x723)
% 0.21/0.65 [73]~P3(x731,x733)+P4(x731,x732)+~P4(x733,x732)
% 0.21/0.65 [74]~P3(x743,x742)+P3(x741,x742)+~P3(x741,x743)
% 0.21/0.65 [82]~P2(x821,x823)+~P2(x822,x824)+P2(f10(x821,x822),f10(x823,x824))
% 0.21/0.65 [83]~P2(x831,x833)+~P1(x832,x834)+P2(f10(x831,x832),f10(x833,x834))
% 0.21/0.65 [84]~P2(x842,x844)+~P1(x841,x843)+P2(f10(x841,x842),f10(x843,x844))
% 0.21/0.65 [85]~P1(x851,x853)+~P1(x852,x854)+P1(f10(x851,x852),f10(x853,x854))
% 0.21/0.65 %EqnAxiom
% 0.21/0.65 [1]E(x11,x11)
% 0.21/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.65 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.21/0.65 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.21/0.65 [6]~E(x61,x62)+E(f10(x61,x63),f10(x62,x63))
% 0.21/0.65 [7]~E(x71,x72)+E(f10(x73,x71),f10(x73,x72))
% 0.21/0.65 [8]~E(x81,x82)+E(f11(x81),f11(x82))
% 0.21/0.65 [9]~E(x91,x92)+E(f2(x91,x93),f2(x92,x93))
% 0.21/0.65 [10]~E(x101,x102)+E(f2(x103,x101),f2(x103,x102))
% 0.21/0.65 [11]~E(x111,x112)+E(f3(x111,x113),f3(x112,x113))
% 0.21/0.65 [12]~E(x121,x122)+E(f3(x123,x121),f3(x123,x122))
% 0.21/0.65 [13]~E(x131,x132)+E(f4(x131,x133),f4(x132,x133))
% 0.21/0.65 [14]~E(x141,x142)+E(f4(x143,x141),f4(x143,x142))
% 0.21/0.65 [15]~E(x151,x152)+E(f5(x151,x153),f5(x152,x153))
% 0.21/0.65 [16]~E(x161,x162)+E(f5(x163,x161),f5(x163,x162))
% 0.21/0.65 [17]P1(x172,x173)+~E(x171,x172)+~P1(x171,x173)
% 0.21/0.65 [18]P1(x183,x182)+~E(x181,x182)+~P1(x183,x181)
% 0.21/0.65 [19]P2(x192,x193)+~E(x191,x192)+~P2(x191,x193)
% 0.21/0.65 [20]P2(x203,x202)+~E(x201,x202)+~P2(x203,x201)
% 0.21/0.65 [21]P3(x212,x213)+~E(x211,x212)+~P3(x211,x213)
% 0.21/0.65 [22]P3(x223,x222)+~E(x221,x222)+~P3(x223,x221)
% 0.21/0.65 [23]P4(x232,x233)+~E(x231,x232)+~P4(x231,x233)
% 0.21/0.65 [24]P4(x243,x242)+~E(x241,x242)+~P4(x243,x241)
% 0.21/0.65
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 cnf(88,plain,
% 0.21/0.65 ($false),
% 0.21/0.65 inference(scs_inference,[],[46,37]),
% 0.21/0.65 ['proof']).
% 0.21/0.65 % SZS output end Proof
% 0.21/0.65 % Total time :0.000000s
%------------------------------------------------------------------------------