%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV282-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:20:43 PM UTC 2026
% Result : Unsatisfiable 0.56s 0.29s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 21
% Syntax : Number of formulae : 124 ( 28 unt; 12 def)
% Number of atoms : 301 ( 112 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 286 ( 109 ~; 165 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 13 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 104 ( 0 sgn 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] :
( X0 = X1
| X2 = X1
| X0 = X2
| c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,plain,
! [X2,X0,X1] :
( X0 = X1
| X1 = X2
| X0 = X2
| c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg) ),
inference(reorient_equations,[],[f1]) ).
fof(f8,axiom,
! [X0,X1] :
( c_minus(X0,X1,tc_nat) != c_0
| c_lessequals(X0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f9,plain,
! [X0,X1] :
( c_0 != c_minus(X0,X1,tc_nat)
| c_lessequals(X0,X1,tc_nat) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0] : c_minus(X0,X0,tc_nat) = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f11,plain,
! [X0] : c_0 = c_minus(X0,X0,tc_nat),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] : c_lessequals(X0,c_plus(X0,X1,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add1_0) ).
fof(f13,axiom,
! [X0] : c_less(X0,c_Suc(X0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f14,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_less(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc__eq__le_1) ).
fof(f16,axiom,
! [X0,X1] : ~ c_less(c_plus(X0,X1,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f17,axiom,
! [X0,X1] :
( ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(X1),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(X1),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__supply__lemma_0) ).
fof(f18,axiom,
! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_Suc(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f19,plain,
! [X0] : c_Suc(X0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),
inference(reorient_equations,[],[f18]) ).
fof(f23,plain,
! [X0] : c_less(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f13,f19]) ).
fof(f24,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_less(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f14,f19]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg)
| X0 = X2
| X1 = X2
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f26,plain,
! [X0,X1] :
( c_0 != c_minus(X0,X1,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f27,plain,
! [X0,X1] : ~ c_lessequals(X0,c_plus(X0,X1,tc_nat),tc_nat),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f28,plain,
! [X0,X1] :
( c_less(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f30,plain,
! [X0,X1] :
( c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(X1),tc_Message_Omsg)
| c_lessequals(v_sko__urX(X1),X0,tc_nat) ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f33,plain,
! [X0] :
( c_0 != c_0
| ~ c_lessequals(X0,X0,tc_nat) ),
inference(superposition,[],[f26,f11]) ).
fof(f34,plain,
! [X0] : ~ c_lessequals(X0,X0,tc_nat),
inference(trivial_inequality_removal,[],[f33]) ).
fof(f35,plain,
! [X2,X0,X1] :
( c_lessequals(v_sko__urX(v_evs_H),X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs),tc_Message_Omsg)
| X0 = X2
| X0 = X1
| X1 = X2 ),
inference(resolution,[],[f30,f25]) ).
fof(f37,plain,
! [X2,X0,X1] :
( c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| X0 = X1
| X1 = X2
| X0 = X2 ),
inference(resolution,[],[f30,f25]) ).
fof(f39,plain,
! [X0,X1] :
( ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| v_sko__urX(v_evs_H) = X1
| v_sko__urX(v_evs_H) = X0
| X0 = X1 ),
inference(resolution,[],[f35,f34]) ).
fof(f40,plain,
! [X0,X1] :
( c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| v_sko__urX(v_evs_H) = X0
| v_sko__urX(v_evs_H) = X1
| X0 = X1
| ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(resolution,[],[f39,f30]) ).
fof(f42,plain,
! [X0,X1] :
( ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| v_sko__urX(v_evs_H) = X1
| c_plus(v_sko__urX(v_evs),X0,tc_nat) = X1
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X0,tc_nat) ),
inference(resolution,[],[f40,f27]) ).
fof(f48,definition,
( spl0_2
<=> v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f49,plain,
( v_sko__urX(v_evs_H) != v_sko__urX(v_evs)
| spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f50,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f56,definition,
( spl0_3
<=> v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f63,plain,
! [X0,X1] : c_lessequals(c_plus(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat),tc_nat),X1,tc_nat),
inference(resolution,[],[f28,f16]) ).
fof(f73,plain,
! [X0,X1] :
( c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat)
| c_plus(v_sko__urX(v_evs),X1,tc_nat) = X0
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X1,tc_nat)
| v_sko__urX(v_evs_H) = X0 ),
inference(resolution,[],[f42,f30]) ).
fof(f74,plain,
! [X0,X1] :
( c_plus(v_sko__urX(v_evs),X0,tc_nat) = c_plus(v_sko__urX(v_evs_H_H),X1,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X0,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X1,tc_nat) ),
inference(resolution,[],[f73,f27]) ).
fof(f75,plain,
! [X0] :
( v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs),X0,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X0,tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[],[f73,f34]) ).
fof(f92,definition,
( spl0_5
<=> v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f140,plain,
! [X0,X1] :
( ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = X0
| X0 = X1
| v_sko__urX(v_evs) = X1 ),
inference(resolution,[],[f37,f34]) ).
fof(f143,plain,
! [X0,X1] :
( c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs) = X1
| X0 = X1
| v_sko__urX(v_evs) = X0
| ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolution,[],[f140,f30]) ).
fof(f144,plain,
! [X0,X1] :
( c_lessequals(v_sko__urX(v_evs_H),X0,tc_nat)
| v_sko__urX(v_evs) = X0
| X0 = X1
| v_sko__urX(v_evs) = X1
| ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg) ),
inference(resolution,[],[f140,f30]) ).
fof(f145,plain,
! [X0,X1] :
( ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_plus(v_sko__urX(v_evs_H_H),X1,tc_nat) = X0
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),X1,tc_nat)
| v_sko__urX(v_evs) = X0 ),
inference(resolution,[],[f143,f27]) ).
fof(f147,plain,
! [X0,X1] :
( ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| c_plus(v_sko__urX(v_evs_H),X0,tc_nat) = X1
| v_sko__urX(v_evs) = X1
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat) ),
inference(resolution,[],[f144,f27]) ).
fof(f152,plain,
! [X0,X1] :
( c_lessequals(v_sko__urX(v_evs_H),X1,tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs) = X1
| c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) = X1 ),
inference(resolution,[],[f145,f30]) ).
fof(f154,plain,
! [X0] :
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[],[f152,f34]) ).
fof(f165,plain,
! [X0,X1] :
( c_lessequals(v_sko__urX(v_evs_H_H),X1,tc_nat)
| v_sko__urX(v_evs) = X1
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat)
| c_plus(v_sko__urX(v_evs_H),X0,tc_nat) = X1 ),
inference(resolution,[],[f147,f30]) ).
fof(f167,plain,
! [X0] :
( v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat) ),
inference(resolution,[],[f165,f34]) ).
fof(f219,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X1,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(superposition,[],[f27,f74]) ).
fof(f220,plain,
! [X0,X1] :
( ~ c_less(c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),X1,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X1,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(superposition,[],[f16,f74]) ).
fof(f230,definition,
( spl0_7
<=> ! [X1] : v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f231,plain,
( ! [X1] : v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X1,tc_nat)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f237,definition,
( spl0_9
<=> ! [X1] : v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f238,plain,
( ! [X1] : v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X1,tc_nat)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,definition,
( spl0_10
<=> ! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f241,plain,
( ! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f242,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f219,f240,f237]) ).
fof(f250,plain,
( ! [X0] : ~ c_less(v_sko__urX(v_evs_H),X0,tc_nat)
| ~ spl0_7 ),
inference(superposition,[],[f16,f231]) ).
fof(f251,plain,
( $false
| ~ spl0_7 ),
inference(resolution,[],[f250,f23]) ).
fof(f255,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f251]) ).
fof(f261,plain,
( ! [X0] : ~ c_less(v_sko__urX(v_evs_H),X0,tc_nat)
| ~ spl0_9 ),
inference(superposition,[],[f16,f238]) ).
fof(f264,definition,
( spl0_12
<=> ! [X0] :
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f265,plain,
( ! [X0] :
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f271,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f167,f92,f264]) ).
fof(f329,plain,
( ! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs),tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat) )
| ~ spl0_12 ),
inference(superposition,[],[f27,f265]) ).
fof(f333,definition,
( spl0_17
<=> ! [X0] : v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f334,plain,
( ! [X0] : v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f337,definition,
( spl0_18
<=> c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs),tc_nat) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f343,definition,
( spl0_19
<=> ! [X0] :
( v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs),X0,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f344,plain,
( ! [X0] :
( v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),X0,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs),X0,tc_nat) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f345,plain,
( spl0_3
| spl0_19 ),
inference(avatar_split_clause,[],[f75,f343,f56]) ).
fof(f353,definition,
( spl0_21
<=> ! [X0] :
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f354,plain,
( ! [X0] :
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f356,plain,
( spl0_2
| spl0_21 ),
inference(avatar_split_clause,[],[f154,f353,f48]) ).
fof(f385,plain,
( ! [X0] : ~ c_less(v_sko__urX(v_evs_H_H),X0,tc_nat)
| ~ spl0_17 ),
inference(superposition,[],[f16,f334]) ).
fof(f386,plain,
( $false
| ~ spl0_17 ),
inference(resolution,[],[f385,f23]) ).
fof(f389,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f412,plain,
( ! [X0] :
( ~ c_less(v_sko__urX(v_evs),X0,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) )
| ~ spl0_21 ),
inference(superposition,[],[f16,f354]) ).
fof(f415,plain,
( v_sko__urX(v_evs_H) != v_sko__urX(v_evs_H_H)
| spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f49,f94]) ).
fof(f416,plain,
( ~ spl0_3
| spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f415,f92,f48,f56]) ).
fof(f507,plain,
( v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Finite__Set_Ocard(c_SetInterval_OatMost(v_sko__urX(v_evs),tc_nat),tc_nat),tc_nat)
| ~ spl0_21 ),
inference(resolution,[],[f412,f23]) ).
fof(f575,plain,
( ! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) )
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f241,f50]) ).
fof(f713,plain,
! [X0] :
( v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat),tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[],[f220,f23]) ).
fof(f813,plain,
! [X0] :
( c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(superposition,[],[f63,f713]) ).
fof(f816,plain,
! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs_H),tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(superposition,[],[f27,f713]) ).
fof(f837,plain,
( ! [X0] :
( v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) )
| ~ spl0_2
| ~ spl0_10 ),
inference(resolution,[],[f813,f575]) ).
fof(f840,plain,
( ! [X0] : v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| ~ spl0_2
| ~ spl0_10 ),
inference(duplicate_literal_removal,[],[f837]) ).
fof(f841,plain,
( spl0_7
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f840,f240,f48,f230]) ).
fof(f878,definition,
( spl0_42
<=> c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f880,plain,
( ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs_H),tc_nat)
| spl0_42 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f881,plain,
( spl0_7
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f816,f878,f230]) ).
fof(f915,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H),tc_nat)
| ~ spl0_5
| spl0_42 ),
inference(superposition,[],[f880,f94]) ).
fof(f976,plain,
( c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs),tc_nat)
| ~ spl0_21 ),
inference(superposition,[],[f63,f507]) ).
fof(f981,plain,
( spl0_18
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f976,f353,f337]) ).
fof(f1036,plain,
( ! [X0] :
( ~ c_less(v_sko__urX(v_evs_H),X0,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs),X0,tc_nat) )
| ~ spl0_19 ),
inference(superposition,[],[f16,f344]) ).
fof(f1068,plain,
( v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs),c_Finite__Set_Ocard(c_SetInterval_OatMost(v_sko__urX(v_evs_H),tc_nat),tc_nat),tc_nat)
| ~ spl0_19 ),
inference(resolution,[],[f1036,f23]) ).
fof(f1075,plain,
( c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H),tc_nat)
| ~ spl0_19 ),
inference(superposition,[],[f63,f1068]) ).
fof(f1080,plain,
( $false
| ~ spl0_5
| ~ spl0_19
| spl0_42 ),
inference(resolution,[],[f1075,f915]) ).
fof(f1081,plain,
( ~ spl0_5
| ~ spl0_19
| spl0_42 ),
inference(avatar_contradiction_clause,[],[f1080]) ).
fof(f1082,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f329,f264,f337,f333]) ).
fof(f1102,plain,
( $false
| ~ spl0_9 ),
inference(resolution,[],[f261,f23]) ).
fof(f1105,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f1102]) ).
cnf(s5,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f242]) ).
cnf(s7,plain,
~ spl0_7,
inference(sat_conversion,[],[f255]) ).
cnf(s11,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f271]) ).
cnf(s23,plain,
( spl0_3
| spl0_19 ),
inference(sat_conversion,[],[f345]) ).
cnf(s28,plain,
( spl0_2
| spl0_21 ),
inference(sat_conversion,[],[f356]) ).
cnf(s30,plain,
~ spl0_17,
inference(sat_conversion,[],[f389]) ).
cnf(s34,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f416]) ).
cnf(s50,plain,
( ~ spl0_2
| spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f841]) ).
cnf(s63,plain,
( spl0_7
| ~ spl0_42 ),
inference(sat_conversion,[],[f881]) ).
cnf(s72,plain,
( spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f981]) ).
cnf(s78,plain,
( ~ spl0_5
| ~ spl0_19
| spl0_42 ),
inference(sat_conversion,[],[f1081]) ).
cnf(s79,plain,
( ~ spl0_12
| spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1082]) ).
cnf(s86,plain,
~ spl0_9,
inference(sat_conversion,[],[f1105]) ).
cnf(s92,plain,
~ spl0_42,
inference(rat,[],[s63,s7]) ).
cnf(s94,plain,
spl0_10,
inference(rat,[],[s5,s86]) ).
cnf(s95,plain,
~ spl0_2,
inference(rat,[],[s50,s7,s94]) ).
cnf(s96,plain,
spl0_21,
inference(rat,[],[s28,s95]) ).
cnf(s97,plain,
spl0_18,
inference(rat,[],[s72,s96]) ).
cnf(s99,plain,
~ spl0_12,
inference(rat,[],[s79,s30,s97]) ).
cnf(s103,plain,
spl0_5,
inference(rat,[],[s11,s99]) ).
cnf(s104,plain,
~ spl0_19,
inference(rat,[],[s78,s92,s103]) ).
cnf(s110,plain,
~ spl0_3,
inference(rat,[],[s34,s95,s103]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s23,s104,s110]) ).
fof(f1106,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV282-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 10:23:52 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.29 % (1077881)Will run a generic schedule for satisfiability detection.
% 0.56/0.29 % (1077891)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=51933670:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.56/0.29 % (1077886)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1971576193_2999 on theBenchmark for (2999ds/0Mi)
% 0.56/0.29 % (1077892)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2066145662:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.56/0.29 % (1077888)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1352312339:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.56/0.29 % (1077889)dis+10_1_sil=32000:sp=arity:random_seed=439602440:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.56/0.29 % (1077890)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3867243984:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.56/0.29 % TRYING [1]
% 0.56/0.29 % TRYING [2]
% 0.56/0.29 % (1077887)% WARNING: option uhcvi not known.
% 0.56/0.29 % TRYING [3]
% 0.56/0.29 % (1077887)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3080776359:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.56/0.29 % TRYING [4]
% 0.56/0.29 % TRYING [5]
% 0.56/0.29 % (1077891)Instruction limit reached!
% 0.56/0.29 % (1077891)------------------------------
% 0.56/0.29 % (1077891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.29 % (1077891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.29 % (1077891)CaDiCaL version: 2.1.3
% 0.56/0.29 % (1077891)Termination reason: Instruction limit
% 0.56/0.29 % (1077891)Termination phase: Saturation
% 0.56/0.29 % (1077891)Time elapsed: 0.037 s
% 0.56/0.29 % (1077891)Peak memory usage: 12 MB
% 0.56/0.29 % (1077891)Instructions burned: 132 (million)
% 0.56/0.29 % (1077900)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=520214280:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.56/0.29 % TRYING [1]
% 0.56/0.29 % TRYING [2]
% 0.56/0.29 % TRYING [3]
% 0.56/0.29 % (1077892) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1077881-1077892"...
% 0.56/0.29 % (1077892)...printing done.
% 0.56/0.29 % (1077892)Refutation found. Thanks to Tanya!
% 0.56/0.29 % SZS status Unsatisfiable for theBenchmark
% 0.56/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.56/0.29 % (1077892)------------------------------
% 0.56/0.29 % (1077892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.29 % (1077892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.29 % (1077892)CaDiCaL version: 2.1.3
% 0.56/0.29 % (1077892)Termination reason: Refutation
% 0.56/0.29 % (1077892)Time elapsed: 0.051 s
% 0.56/0.29 % (1077892)Peak memory usage: 12 MB
% 0.56/0.29 % (1077892)Instructions burned: 75 (million)
% 0.56/0.29 % (1077881)Success in time 0.084 s
% 0.56/0.29 % Vampire exiting
%------------------------------------------------------------------------------