%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HWV008-1.002 : TPTP v9.3.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 10:58:54 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 50
% Syntax : Number of formulae : 216 ( 38 unt; 21 def)
% Number of atoms : 501 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 583 ( 298 ~; 264 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 27 ( 26 usr; 22 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ connection(X0,X1)
| ~ value(X0,X2)
| value(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax',value_propagation1) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ connection(X0,X1)
| ~ value(X1,X2)
| value(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax',value_propagation2) ).
fof(f3,axiom,
! [X2,X0,X1] :
( equal_value(X1,X2)
| ~ value(X0,X2)
| ~ value(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax',unique_value) ).
fof(f5,axiom,
~ equal_value(n1,n0),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax',equal_value2) ).
fof(f7,axiom,
! [X0,X1] :
( mode(X0,abnormal)
| mode(X0,ok)
| ~ type(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax',ok_or_abnormal) ).
fof(f8,axiom,
! [X0,X1] :
( ~ mode(X0,ok)
| ~ type(X0,and)
| ~ value(in(X1,X0),n0)
| value(out(n1,X0),n0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax',and_0x_0) ).
fof(f15,axiom,
! [X0] :
( ~ mode(X0,ok)
| ~ type(X0,or)
| ~ value(out(n1,X0),n1)
| value(in(n1,X0),n1)
| value(in(n2,X0),n1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax',or_1_11) ).
fof(f23,axiom,
! [X0] :
( type(and2(X0),and)
| ~ type(X0,halfadder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax',halfadder_and2) ).
fof(f28,axiom,
! [X0] :
( connection(in(n1,X0),in(n1,and2(X0)))
| ~ type(X0,halfadder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax',halfadder_connection_in1_in1and2) ).
fof(f31,axiom,
! [X0] :
( connection(out(c,X0),out(n1,and2(X0)))
| ~ type(X0,halfadder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax',halfadder_connection_outc_out1and2) ).
fof(f35,axiom,
! [X0] :
( type(h1(X0),halfadder)
| ~ type(X0,fulladder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax',fulladder_halfadder1) ).
fof(f36,axiom,
! [X0] :
( type(h2(X0),halfadder)
| ~ type(X0,fulladder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax',fulladder_halfadder2) ).
fof(f37,axiom,
! [X0] :
( type(or1(X0),or)
| ~ type(X0,fulladder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax',fulladder_or1) ).
fof(f39,axiom,
! [X0] :
( connection(out(c,h1(X0)),in(n2,or1(X0)))
| ~ type(X0,fulladder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax',fulladder_connection_outch1_in2or1) ).
fof(f40,axiom,
! [X0] :
( connection(out(c,h2(X0)),in(n1,or1(X0)))
| ~ type(X0,fulladder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax',fulladder_connection_outch2_in1or1) ).
fof(f41,axiom,
! [X0] :
( connection(in(n1,X0),in(n1,h2(X0)))
| ~ type(X0,fulladder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax',fulladder_connection_in1_in1h2) ).
fof(f42,axiom,
! [X0] :
( connection(in(n2,X0),in(n1,h1(X0)))
| ~ type(X0,fulladder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax',fulladder_connection_in2_in1h1) ).
fof(f45,axiom,
! [X0] :
( connection(out(c,X0),out(n1,or1(X0)))
| ~ type(X0,fulladder) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax',fulladder_connection_outc_out1or1) ).
fof(f47,axiom,
! [X0] :
( type(f(n2,X0),fulladder)
| ~ type(X0,nbit_adder(n2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nbit_adder_fulladder2) ).
fof(f50,axiom,
! [X0] :
( connection(out(c,X0),out(c,f(n2,X0)))
| ~ type(X0,nbit_adder(n2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nbit_adder_connection_outc_outcf1) ).
fof(f53,axiom,
! [X0] :
( connection(in(a2,X0),in(n1,f(n2,X0)))
| ~ type(X0,nbit_adder(n2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nbit_adder_connection_ina2_in1f2) ).
fof(f54,axiom,
! [X0] :
( connection(in(b2,X0),in(n2,f(n2,X0)))
| ~ type(X0,nbit_adder(n2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nbit_adder_connection_inb2_in2f2) ).
fof(f57,axiom,
type(a,nbit_adder(n2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_isa_2bit_adder) ).
fof(f59,axiom,
value(in(a2,a),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ina2_0) ).
fof(f61,axiom,
value(in(b2,a),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inb2_0) ).
fof(f65,axiom,
value(out(c,a),n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outc_1) ).
fof(f66,negated_conjecture,
~ mode(or1(f(n2,a)),abnormal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_or1f2a) ).
fof(f67,negated_conjecture,
~ mode(and2(h1(f(n2,a))),abnormal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_and2h2f2a) ).
fof(f68,negated_conjecture,
~ mode(and2(h2(f(n2,a))),abnormal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_and2h1f2a) ).
fof(f70,plain,
! [X0] :
( ~ value(X0,n0)
| ~ value(X0,n1) ),
inference(resolution,[],[f3,f5]) ).
fof(f78,plain,
! [X0] :
( mode(or1(f(n2,a)),ok)
| ~ type(or1(f(n2,a)),X0) ),
inference(resolution,[],[f7,f66]) ).
fof(f79,plain,
! [X0] :
( mode(and2(h1(f(n2,a))),ok)
| ~ type(and2(h1(f(n2,a))),X0) ),
inference(resolution,[],[f7,f67]) ).
fof(f80,plain,
! [X0] :
( mode(and2(h2(f(n2,a))),ok)
| ~ type(and2(h2(f(n2,a))),X0) ),
inference(resolution,[],[f7,f68]) ).
fof(f82,definition,
( spl0_1
<=> ! [X0] : ~ type(and2(h2(f(n2,a))),X0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] : ~ type(and2(h2(f(n2,a))),X0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_2
<=> mode(and2(h2(f(n2,a))),ok) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f87,plain,
( mode(and2(h2(f(n2,a))),ok)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f80,f85,f82]) ).
fof(f90,definition,
( spl0_3
<=> ! [X0] : ~ type(and2(h1(f(n2,a))),X0) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f91,plain,
( ! [X0] : ~ type(and2(h1(f(n2,a))),X0)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl0_4
<=> mode(and2(h1(f(n2,a))),ok) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f95,plain,
( mode(and2(h1(f(n2,a))),ok)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f79,f93,f90]) ).
fof(f98,definition,
( spl0_5
<=> ! [X0] : ~ type(or1(f(n2,a)),X0) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f99,plain,
( ! [X0] : ~ type(or1(f(n2,a)),X0)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,definition,
( spl0_6
<=> mode(or1(f(n2,a)),ok) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f103,plain,
( mode(or1(f(n2,a)),ok)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f78,f101,f98]) ).
fof(f105,plain,
( ~ type(f(n2,a),fulladder)
| ~ spl0_5 ),
inference(resolution,[],[f99,f37]) ).
fof(f107,plain,
( ~ type(a,nbit_adder(n2))
| ~ spl0_5 ),
inference(resolution,[],[f47,f105]) ).
fof(f108,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f107,f57]) ).
fof(f109,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f108]) ).
fof(f114,plain,
( ~ type(h1(f(n2,a)),halfadder)
| ~ spl0_3 ),
inference(resolution,[],[f91,f23]) ).
fof(f116,plain,
! [X0,X1] :
( value(in(n1,and2(X0)),X1)
| ~ value(in(n1,X0),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[],[f28,f1]) ).
fof(f117,plain,
( ~ type(f(n2,a),fulladder)
| ~ spl0_3 ),
inference(resolution,[],[f114,f35]) ).
fof(f120,plain,
( ~ type(a,nbit_adder(n2))
| ~ spl0_3 ),
inference(resolution,[],[f117,f47]) ).
fof(f121,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f120,f57]) ).
fof(f122,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f121]) ).
fof(f125,plain,
! [X0,X1] :
( ~ value(out(n1,and2(X0)),X1)
| ~ type(X0,halfadder)
| value(out(c,X0),X1) ),
inference(resolution,[],[f31,f2]) ).
fof(f126,plain,
! [X0,X1] :
( value(out(n1,and2(X0)),X1)
| ~ value(out(c,X0),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[],[f31,f1]) ).
fof(f128,plain,
! [X0,X1] :
( value(in(n1,h2(X0)),X1)
| ~ value(in(n1,X0),X1)
| ~ type(X0,fulladder) ),
inference(resolution,[],[f41,f1]) ).
fof(f130,plain,
! [X0,X1] :
( value(in(n1,h1(X0)),X1)
| ~ value(in(n2,X0),X1)
| ~ type(X0,fulladder) ),
inference(resolution,[],[f42,f1]) ).
fof(f136,plain,
! [X0,X1] :
( value(out(n1,or1(X0)),X1)
| ~ value(out(c,X0),X1)
| ~ type(X0,fulladder) ),
inference(resolution,[],[f45,f1]) ).
fof(f145,plain,
! [X0,X1] :
( value(out(c,h1(X0)),X1)
| ~ value(in(n2,or1(X0)),X1)
| ~ type(X0,fulladder) ),
inference(resolution,[],[f39,f2]) ).
fof(f147,plain,
! [X0,X1] :
( value(out(c,h2(X0)),X1)
| ~ value(in(n1,or1(X0)),X1)
| ~ type(X0,fulladder) ),
inference(resolution,[],[f40,f2]) ).
fof(f154,plain,
! [X0,X1] :
( value(out(c,f(n2,X0)),X1)
| ~ value(out(c,X0),X1)
| ~ type(X0,nbit_adder(n2)) ),
inference(resolution,[],[f50,f1]) ).
fof(f160,plain,
! [X0,X1] :
( value(in(n1,f(n2,X0)),X1)
| ~ value(in(a2,X0),X1)
| ~ type(X0,nbit_adder(n2)) ),
inference(resolution,[],[f53,f1]) ).
fof(f162,plain,
! [X0,X1] :
( value(in(n2,f(n2,X0)),X1)
| ~ value(in(b2,X0),X1)
| ~ type(X0,nbit_adder(n2)) ),
inference(resolution,[],[f54,f1]) ).
fof(f171,plain,
( ! [X0] :
( ~ type(and2(h2(f(n2,a))),and)
| ~ value(in(X0,and2(h2(f(n2,a)))),n0)
| value(out(n1,and2(h2(f(n2,a)))),n0) )
| ~ spl0_2 ),
inference(resolution,[],[f8,f87]) ).
fof(f172,plain,
( ! [X0] :
( ~ type(and2(h1(f(n2,a))),and)
| ~ value(in(X0,and2(h1(f(n2,a)))),n0)
| value(out(n1,and2(h1(f(n2,a)))),n0) )
| ~ spl0_4 ),
inference(resolution,[],[f8,f95]) ).
fof(f174,definition,
( spl0_7
<=> value(out(n1,and2(h1(f(n2,a)))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f176,plain,
( value(out(n1,and2(h1(f(n2,a)))),n0)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f178,definition,
( spl0_8
<=> ! [X0] : ~ value(in(X0,and2(h1(f(n2,a)))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f179,plain,
( ! [X0] : ~ value(in(X0,and2(h1(f(n2,a)))),n0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,definition,
( spl0_9
<=> type(and2(h1(f(n2,a))),and) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f183,plain,
( ~ type(and2(h1(f(n2,a))),and)
| spl0_9 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f172,f93,f181,f178,f174]) ).
fof(f186,definition,
( spl0_10
<=> value(out(n1,and2(h2(f(n2,a)))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f188,plain,
( value(out(n1,and2(h2(f(n2,a)))),n0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f190,definition,
( spl0_11
<=> ! [X0] : ~ value(in(X0,and2(h2(f(n2,a)))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f191,plain,
( ! [X0] : ~ value(in(X0,and2(h2(f(n2,a)))),n0)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,definition,
( spl0_12
<=> type(and2(h2(f(n2,a))),and) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f195,plain,
( ~ type(and2(h2(f(n2,a))),and)
| spl0_12 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f196,plain,
( spl0_10
| spl0_11
| ~ spl0_12
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f171,f85,f193,f190,f186]) ).
fof(f212,plain,
( ~ type(h1(f(n2,a)),halfadder)
| spl0_9 ),
inference(resolution,[],[f183,f23]) ).
fof(f216,plain,
( ~ type(f(n2,a),fulladder)
| spl0_9 ),
inference(resolution,[],[f212,f35]) ).
fof(f221,definition,
( spl0_16
<=> value(out(n1,and2(h1(f(n2,a)))),n1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f222,plain,
( ~ value(out(n1,and2(h1(f(n2,a)))),n1)
| spl0_16 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f223,plain,
( value(out(n1,and2(h1(f(n2,a)))),n1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f245,definition,
( spl0_22
<=> value(out(n1,or1(f(n2,a))),n1) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f246,plain,
( ~ value(out(n1,or1(f(n2,a))),n1)
| spl0_22 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f247,plain,
( value(out(n1,or1(f(n2,a))),n1)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f252,definition,
( spl0_24
<=> type(or1(f(n2,a)),or) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f253,plain,
( type(or1(f(n2,a)),or)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( ~ type(or1(f(n2,a)),or)
| spl0_24 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f256,plain,
( ~ type(a,nbit_adder(n2))
| spl0_9 ),
inference(resolution,[],[f216,f47]) ).
fof(f257,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f256,f57]) ).
fof(f258,plain,
spl0_9,
inference(avatar_contradiction_clause,[],[f257]) ).
fof(f274,plain,
( ~ type(f(n2,a),fulladder)
| spl0_24 ),
inference(resolution,[],[f254,f37]) ).
fof(f279,plain,
( ~ type(a,nbit_adder(n2))
| spl0_24 ),
inference(resolution,[],[f274,f47]) ).
fof(f280,plain,
( $false
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f279,f57]) ).
fof(f281,plain,
spl0_24,
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f326,definition,
( spl0_34
<=> value(in(n1,or1(f(n2,a))),n1) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f327,plain,
( value(in(n1,or1(f(n2,a))),n1)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f340,plain,
( ~ type(h2(f(n2,a)),halfadder)
| spl0_12 ),
inference(resolution,[],[f195,f23]) ).
fof(f347,plain,
( ~ type(f(n2,a),fulladder)
| spl0_12 ),
inference(resolution,[],[f340,f36]) ).
fof(f358,plain,
( ~ type(a,nbit_adder(n2))
| spl0_12 ),
inference(resolution,[],[f347,f47]) ).
fof(f359,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f358,f57]) ).
fof(f360,plain,
spl0_12,
inference(avatar_contradiction_clause,[],[f359]) ).
fof(f380,plain,
( ~ type(or1(f(n2,a)),or)
| ~ value(out(n1,or1(f(n2,a))),n1)
| value(in(n1,or1(f(n2,a))),n1)
| value(in(n2,or1(f(n2,a))),n1)
| ~ spl0_6 ),
inference(resolution,[],[f15,f103]) ).
fof(f383,plain,
( ~ value(out(n1,or1(f(n2,a))),n1)
| value(in(n1,or1(f(n2,a))),n1)
| value(in(n2,or1(f(n2,a))),n1)
| ~ spl0_6
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f380,f253]) ).
fof(f384,plain,
( value(in(n1,or1(f(n2,a))),n1)
| value(in(n2,or1(f(n2,a))),n1)
| ~ spl0_6
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f383,f247]) ).
fof(f386,definition,
( spl0_38
<=> value(in(n2,or1(f(n2,a))),n1) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f389,plain,
( spl0_38
| spl0_34
| ~ spl0_6
| ~ spl0_22
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f384,f252,f245,f101,f326,f386]) ).
fof(f420,plain,
( ~ value(out(n1,and2(h1(f(n2,a)))),n1)
| ~ spl0_7 ),
inference(resolution,[],[f176,f70]) ).
fof(f426,definition,
( spl0_43
<=> type(h1(f(n2,a)),halfadder) ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f427,plain,
( type(h1(f(n2,a)),halfadder)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f428,plain,
( ~ type(h1(f(n2,a)),halfadder)
| spl0_43 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f433,plain,
( ~ type(f(n2,a),fulladder)
| spl0_43 ),
inference(resolution,[],[f428,f35]) ).
fof(f434,plain,
( ~ type(a,nbit_adder(n2))
| spl0_43 ),
inference(resolution,[],[f433,f47]) ).
fof(f435,plain,
( $false
| spl0_43 ),
inference(forward_subsumption_resolution,[],[f434,f57]) ).
fof(f436,plain,
spl0_43,
inference(avatar_contradiction_clause,[],[f435]) ).
fof(f446,plain,
( ~ value(in(n1,h1(f(n2,a))),n0)
| ~ type(h1(f(n2,a)),halfadder)
| ~ spl0_8 ),
inference(resolution,[],[f179,f116]) ).
fof(f449,plain,
( ~ value(in(n1,h1(f(n2,a))),n0)
| ~ spl0_8
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[],[f446,f427]) ).
fof(f455,definition,
( spl0_44
<=> type(f(n2,a),fulladder) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f456,plain,
( type(f(n2,a),fulladder)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f457,plain,
( ~ type(f(n2,a),fulladder)
| spl0_44 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f463,plain,
( ~ type(a,nbit_adder(n2))
| spl0_44 ),
inference(resolution,[],[f457,f47]) ).
fof(f464,plain,
( $false
| spl0_44 ),
inference(forward_subsumption_resolution,[],[f463,f57]) ).
fof(f465,plain,
spl0_44,
inference(avatar_contradiction_clause,[],[f464]) ).
fof(f469,plain,
( ~ value(out(c,f(n2,a)),n1)
| ~ type(f(n2,a),fulladder)
| spl0_22 ),
inference(resolution,[],[f136,f246]) ).
fof(f475,plain,
( ~ value(out(c,f(n2,a)),n1)
| spl0_22
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f469,f456]) ).
fof(f483,plain,
( ~ value(in(n2,f(n2,a)),n0)
| ~ type(f(n2,a),fulladder)
| ~ spl0_8
| ~ spl0_43 ),
inference(resolution,[],[f449,f130]) ).
fof(f484,plain,
( ~ value(in(n2,f(n2,a)),n0)
| ~ spl0_8
| ~ spl0_43
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f483,f456]) ).
fof(f495,plain,
( ~ type(h2(f(n2,a)),halfadder)
| value(out(c,h2(f(n2,a))),n0)
| ~ spl0_10 ),
inference(resolution,[],[f188,f125]) ).
fof(f498,definition,
( spl0_46
<=> value(out(c,h2(f(n2,a))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
fof(f500,plain,
( value(out(c,h2(f(n2,a))),n0)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f502,definition,
( spl0_47
<=> type(h2(f(n2,a)),halfadder) ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
fof(f503,plain,
( type(h2(f(n2,a)),halfadder)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f504,plain,
( ~ type(h2(f(n2,a)),halfadder)
| spl0_47 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f505,plain,
( spl0_46
| ~ spl0_47
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f495,f186,f502,f498]) ).
fof(f512,plain,
( ~ type(f(n2,a),fulladder)
| spl0_47 ),
inference(resolution,[],[f504,f36]) ).
fof(f513,plain,
( $false
| ~ spl0_44
| spl0_47 ),
inference(forward_subsumption_resolution,[],[f512,f456]) ).
fof(f514,plain,
( ~ spl0_44
| spl0_47 ),
inference(avatar_contradiction_clause,[],[f513]) ).
fof(f518,plain,
( ~ value(out(c,h2(f(n2,a))),n1)
| ~ spl0_46 ),
inference(resolution,[],[f500,f70]) ).
fof(f529,plain,
( ~ value(out(c,h1(f(n2,a))),n1)
| ~ type(h1(f(n2,a)),halfadder)
| spl0_16 ),
inference(resolution,[],[f222,f126]) ).
fof(f530,plain,
( ~ value(out(c,h1(f(n2,a))),n1)
| spl0_16
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[],[f529,f427]) ).
fof(f532,plain,
( ~ value(in(n1,or1(f(n2,a))),n1)
| ~ type(f(n2,a),fulladder)
| ~ spl0_46 ),
inference(resolution,[],[f147,f518]) ).
fof(f534,plain,
( ~ value(in(n2,or1(f(n2,a))),n1)
| ~ type(f(n2,a),fulladder)
| spl0_16
| ~ spl0_43 ),
inference(resolution,[],[f530,f145]) ).
fof(f559,plain,
( ~ value(out(c,a),n1)
| ~ type(a,nbit_adder(n2))
| spl0_22
| ~ spl0_44 ),
inference(resolution,[],[f154,f475]) ).
fof(f565,plain,
( ~ type(a,nbit_adder(n2))
| spl0_22
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f559,f65]) ).
fof(f566,plain,
( $false
| spl0_22
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f565,f57]) ).
fof(f567,plain,
( spl0_22
| ~ spl0_44 ),
inference(avatar_contradiction_clause,[],[f566]) ).
fof(f574,plain,
( ~ value(in(n1,or1(f(n2,a))),n1)
| ~ spl0_44
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[],[f532,f456]) ).
fof(f575,plain,
( ~ value(in(n2,or1(f(n2,a))),n1)
| spl0_16
| ~ spl0_43
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f534,f456]) ).
fof(f577,plain,
( $false
| ~ spl0_34
| ~ spl0_44
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[],[f574,f327]) ).
fof(f578,plain,
( ~ spl0_34
| ~ spl0_44
| ~ spl0_46 ),
inference(avatar_contradiction_clause,[],[f577]) ).
fof(f579,plain,
( ~ spl0_38
| spl0_16
| ~ spl0_43
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f575,f455,f426,f221,f386]) ).
fof(f607,plain,
( ~ value(in(b2,a),n0)
| ~ type(a,nbit_adder(n2))
| ~ spl0_8
| ~ spl0_43
| ~ spl0_44 ),
inference(resolution,[],[f162,f484]) ).
fof(f610,plain,
( ~ type(a,nbit_adder(n2))
| ~ spl0_8
| ~ spl0_43
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f607,f61]) ).
fof(f611,plain,
( $false
| ~ spl0_8
| ~ spl0_43
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f610,f57]) ).
fof(f612,plain,
( ~ spl0_8
| ~ spl0_43
| ~ spl0_44 ),
inference(avatar_contradiction_clause,[],[f611]) ).
fof(f613,plain,
( $false
| ~ spl0_7
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f420,f223]) ).
fof(f614,plain,
( ~ spl0_7
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f613]) ).
fof(f617,plain,
( ~ type(h2(f(n2,a)),halfadder)
| ~ spl0_1 ),
inference(resolution,[],[f83,f23]) ).
fof(f619,plain,
( $false
| ~ spl0_1
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f617,f503]) ).
fof(f620,plain,
( ~ spl0_1
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f619]) ).
fof(f662,plain,
( ~ value(in(n1,h2(f(n2,a))),n0)
| ~ type(h2(f(n2,a)),halfadder)
| ~ spl0_11 ),
inference(resolution,[],[f191,f116]) ).
fof(f665,plain,
( ~ value(in(n1,h2(f(n2,a))),n0)
| ~ spl0_11
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f662,f503]) ).
fof(f676,plain,
( ~ value(in(n1,f(n2,a)),n0)
| ~ type(f(n2,a),fulladder)
| ~ spl0_11
| ~ spl0_47 ),
inference(resolution,[],[f665,f128]) ).
fof(f677,plain,
( ~ value(in(n1,f(n2,a)),n0)
| ~ spl0_11
| ~ spl0_44
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f676,f456]) ).
fof(f680,plain,
( ~ value(in(a2,a),n0)
| ~ type(a,nbit_adder(n2))
| ~ spl0_11
| ~ spl0_44
| ~ spl0_47 ),
inference(resolution,[],[f677,f160]) ).
fof(f681,plain,
( ~ type(a,nbit_adder(n2))
| ~ spl0_11
| ~ spl0_44
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f680,f59]) ).
fof(f682,plain,
( $false
| ~ spl0_11
| ~ spl0_44
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f681,f57]) ).
fof(f683,plain,
( ~ spl0_11
| ~ spl0_44
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f682]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f96]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f104]) ).
cnf(s4,plain,
~ spl0_5,
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
~ spl0_3,
inference(sat_conversion,[],[f122]) ).
cnf(s6,plain,
( ~ spl0_4
| spl0_7
| spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f184]) ).
cnf(s7,plain,
( ~ spl0_2
| spl0_10
| spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f196]) ).
cnf(s12,plain,
spl0_9,
inference(sat_conversion,[],[f258]) ).
cnf(s15,plain,
spl0_24,
inference(sat_conversion,[],[f281]) ).
cnf(s24,plain,
spl0_12,
inference(sat_conversion,[],[f360]) ).
cnf(s29,plain,
( ~ spl0_6
| ~ spl0_22
| ~ spl0_24
| spl0_34
| spl0_38 ),
inference(sat_conversion,[],[f389]) ).
cnf(s33,plain,
spl0_43,
inference(sat_conversion,[],[f436]) ).
cnf(s36,plain,
spl0_44,
inference(sat_conversion,[],[f465]) ).
cnf(s37,plain,
( ~ spl0_10
| spl0_46
| ~ spl0_47 ),
inference(sat_conversion,[],[f505]) ).
cnf(s39,plain,
( ~ spl0_44
| spl0_47 ),
inference(sat_conversion,[],[f514]) ).
cnf(s43,plain,
( spl0_22
| ~ spl0_44 ),
inference(sat_conversion,[],[f567]) ).
cnf(s47,plain,
( ~ spl0_34
| ~ spl0_44
| ~ spl0_46 ),
inference(sat_conversion,[],[f578]) ).
cnf(s48,plain,
( spl0_16
| ~ spl0_38
| ~ spl0_43
| ~ spl0_44 ),
inference(sat_conversion,[],[f579]) ).
cnf(s50,plain,
( ~ spl0_8
| ~ spl0_43
| ~ spl0_44 ),
inference(sat_conversion,[],[f612]) ).
cnf(s51,plain,
( ~ spl0_7
| ~ spl0_16 ),
inference(sat_conversion,[],[f614]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_47 ),
inference(sat_conversion,[],[f620]) ).
cnf(s58,plain,
( ~ spl0_11
| ~ spl0_44
| ~ spl0_47 ),
inference(sat_conversion,[],[f683]) ).
cnf(s59,plain,
spl0_22,
inference(rat,[],[s43,s36]) ).
cnf(s60,plain,
spl0_47,
inference(rat,[],[s39,s36]) ).
cnf(s61,plain,
~ spl0_1,
inference(rat,[],[s54,s60]) ).
cnf(s62,plain,
~ spl0_11,
inference(rat,[],[s58,s36,s60]) ).
cnf(s65,plain,
~ spl0_8,
inference(rat,[],[s50,s36,s33]) ).
cnf(s67,plain,
( ~ spl0_6
| ~ spl0_24
| spl0_34
| spl0_38 ),
inference(rat,[],[s29,s59]) ).
cnf(s69,plain,
( ~ spl0_2
| spl0_10 ),
inference(rat,[],[s7,s24,s62]) ).
cnf(s70,plain,
( ~ spl0_4
| spl0_7 ),
inference(rat,[],[s6,s12,s65]) ).
cnf(s71,plain,
spl0_6,
inference(rat,[],[s3,s4]) ).
cnf(s73,plain,
spl0_4,
inference(rat,[],[s2,s5]) ).
cnf(s74,plain,
spl0_7,
inference(rat,[],[s70,s73]) ).
cnf(s75,plain,
~ spl0_16,
inference(rat,[],[s51,s74]) ).
cnf(s77,plain,
~ spl0_38,
inference(rat,[],[s48,s36,s33,s75]) ).
cnf(s79,plain,
spl0_34,
inference(rat,[],[s67,s71,s15,s77]) ).
cnf(s81,plain,
~ spl0_46,
inference(rat,[],[s47,s36,s79]) ).
cnf(s83,plain,
~ spl0_10,
inference(rat,[],[s37,s60,s81]) ).
cnf(s86,plain,
~ spl0_2,
inference(rat,[],[s69,s83]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s1,s86,s61]) ).
fof(f684,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWV008-1.002 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 10:52:52 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.45 Running first-order model finding
% 0.13/0.45 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
% 0.20/0.52 % (3342048)Will run a generic schedule for satisfiability detection.
% 0.20/0.52 % (3342054)% WARNING: option uhcvi not known.
% 0.20/0.52 % (3342054)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3368998450:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.52 % (3342053)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2788399118_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.52 % (3342055)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2515370284:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.52 % (3342058)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=280160381:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.52 % (3342056)dis+10_1_sil=32000:sp=arity:random_seed=2870063558:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.52 % (3342057)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2093513917:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.52 % (3342059)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1972153899:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.53 % TRYING [1]
% 0.20/0.53 % TRYING [2]
% 0.20/0.53 % (3342057) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3342048-3342057"...
% 0.20/0.53 % TRYING [3]
% 0.20/0.53 % (3342058) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3342048-3342058"...
% 0.20/0.53 % (3342056) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3342048-3342056"...
% 0.20/0.53 % (3342057)...printing done.
% 0.20/0.53 % (3342057)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (3342057)------------------------------
% 0.20/0.53 % (3342057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.53 % (3342057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.53 % (3342057)CaDiCaL version: 2.1.3
% 0.20/0.53 % (3342057)Termination reason: Refutation
% 0.20/0.53 % (3342057)Time elapsed: 0.023 s
% 0.20/0.53 % (3342057)Peak memory usage: 12 MB
% 0.20/0.53 % (3342057)Instructions burned: 21 (million)
% 0.20/0.53 % (3342048)Success in time 0.066 s
% 0.20/0.53 % Vampire exiting
%------------------------------------------------------------------------------