%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HWV006-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 10:58:53 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 71
% Syntax : Number of formulae : 251 ( 66 unt; 20 def)
% Number of atoms : 512 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 481 ( 220 ~; 241 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 33 ( 32 usr; 21 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-1 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ connection(X0,X1)
| ~ zero(X0)
| zero(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',value_propagation_zero1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ connection(X0,X1)
| ~ one(X0)
| one(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',value_propagation_one1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ connection(X0,X1)
| ~ zero(X1)
| zero(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',value_propagation_zero2) ).
fof(f4,axiom,
! [X0,X1] :
( ~ connection(X0,X1)
| ~ one(X1)
| one(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',value_propagation_one2) ).
fof(f5,axiom,
! [X0] :
( ~ zero(X0)
| ~ one(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',unique_value) ).
fof(f6,axiom,
! [X0] :
( ~ and_ok(X0)
| ~ zero(in1(X0))
| zero(out1(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',and_0x_0) ).
fof(f8,axiom,
! [X0] :
( ~ and_ok(X0)
| ~ one(in1(X0))
| ~ one(in2(X0))
| one(out1(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',and_11_1) ).
fof(f9,axiom,
! [X0] :
( ~ and_ok(X0)
| ~ zero(out1(X0))
| zero(in1(X0))
| zero(in2(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',and_0_00) ).
fof(f11,axiom,
! [X0] :
( ~ and_ok(X0)
| ~ one(out1(X0))
| one(in2(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',and_1_x1) ).
fof(f13,axiom,
! [X0] :
( ~ logic_and(X0)
| and_ok(X0)
| abnormal(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',and_ok_or_abnormal) ).
fof(f15,axiom,
! [X0] :
( ~ or_ok(X0)
| ~ one(in2(X0))
| one(out1(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',or_x1_1) ).
fof(f18,axiom,
! [X0] :
( ~ or_ok(X0)
| ~ zero(out1(X0))
| zero(in1(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',or_0_0x) ).
fof(f21,axiom,
! [X0] :
( ~ logic_or(X0)
| or_ok(X0)
| abnormal(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',or_ok_or_abnormal) ).
fof(f22,axiom,
! [X0] :
( ~ not_ok(X0)
| ~ zero(in1(X0))
| one(out1(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',not_0_1_fw) ).
fof(f25,axiom,
! [X0] :
( ~ not_ok(X0)
| ~ one(out1(X0))
| zero(in1(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',not_1_0_bw) ).
fof(f27,axiom,
! [X0] :
( ~ logic_not(X0)
| not_ok(X0)
| abnormal(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',not_ok_or_abnormal) ).
fof(f28,axiom,
! [X0] :
( logic_and(and1(X0))
| ~ halfadder(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_and1) ).
fof(f29,axiom,
! [X0] :
( logic_and(and2(X0))
| ~ halfadder(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_and2) ).
fof(f30,axiom,
! [X0] :
( logic_not(not1(X0))
| ~ halfadder(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_not1) ).
fof(f31,axiom,
! [X0] :
( logic_or(or1(X0))
| ~ halfadder(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_or1) ).
fof(f33,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(in2(X0),in2(or1(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_in2_in2or1) ).
fof(f34,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(in1(X0),in1(and2(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_in1_in1and2) ).
fof(f35,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(in2(X0),in2(and2(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_in2_in2and2) ).
fof(f36,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(outs(X0),out1(and1(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_outs_out1and1) ).
fof(f37,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(outc(X0),out1(and2(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_outc_out1and2) ).
fof(f38,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(out1(or1(X0)),in1(and1(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_out1or1_in1_and1) ).
fof(f39,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(out1(and2(X0)),in1(not1(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_out1and2_in1not1) ).
fof(f40,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(out1(not1(X0)),in2(and1(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_out1not1_in2and1) ).
fof(f41,axiom,
! [X0] :
( ~ fulladder(X0)
| halfadder(h1(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_halfadder1) ).
fof(f42,axiom,
! [X0] :
( ~ fulladder(X0)
| halfadder(h2(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_halfadder2) ).
fof(f43,axiom,
! [X0] :
( logic_or(or1(X0))
| ~ fulladder(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_or1) ).
fof(f44,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(outs(h1(X0)),in2(h2(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outsh1_in2h2) ).
fof(f46,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(outc(h2(X0)),in1(or1(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outch2_in1or1) ).
fof(f47,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(in1(X0),in1(h2(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_connection_in1_in1h2) ).
fof(f48,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(in2(X0),in1(h1(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_connection_in2_in1h1) ).
fof(f49,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(inc(X0),in2(h1(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_connection_inc_in2h1) ).
fof(f50,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(outs(X0),outs(h2(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outs_outsh2) ).
fof(f51,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(outc(X0),out1(or1(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outc_out1or1) ).
fof(f52,axiom,
fulladder(f),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_isa_fulladder) ).
fof(f53,axiom,
one(in1(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in1_1) ).
fof(f54,axiom,
zero(in2(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in2_0) ).
fof(f55,axiom,
one(inc(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inc_1) ).
fof(f56,axiom,
one(outs(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outs_1) ).
fof(f57,axiom,
zero(outc(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outc_0) ).
fof(f58,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(not1(h2(f))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_or1_not1h2) ).
fof(f59,negated_conjecture,
~ abnormal(and2(h2(f))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_and2) ).
fof(f60,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_or1_and1h2) ).
fof(f61,negated_conjecture,
~ abnormal(or1(h1(f))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_or1h1) ).
fof(f62,negated_conjecture,
~ abnormal(not1(h1(f))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_not1h1) ).
fof(f63,negated_conjecture,
~ abnormal(and2(h1(f))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_and2h1) ).
fof(f64,negated_conjecture,
~ abnormal(and1(h1(f))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_and1h1) ).
fof(f66,definition,
( spl0_1
<=> abnormal(and1(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f68,plain,
( ~ abnormal(and1(h2(f)))
| spl0_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f70,definition,
( spl0_2
<=> abnormal(or1(f)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ~ abnormal(or1(f))
| spl0_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f60,f70,f66]) ).
fof(f75,definition,
( spl0_3
<=> abnormal(not1(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( ~ abnormal(not1(h2(f)))
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f58,f70,f75]) ).
fof(f81,plain,
halfadder(h1(f)),
inference(resolution,[],[f41,f52]) ).
fof(f82,plain,
halfadder(h2(f)),
inference(resolution,[],[f42,f52]) ).
fof(f83,plain,
! [X0] :
( and_ok(and1(X0))
| abnormal(and1(X0))
| ~ halfadder(X0) ),
inference(resolution,[],[f13,f28]) ).
fof(f84,plain,
! [X0] :
( and_ok(and2(X0))
| abnormal(and2(X0))
| ~ halfadder(X0) ),
inference(resolution,[],[f13,f29]) ).
fof(f85,plain,
! [X0] :
( or_ok(or1(X0))
| abnormal(or1(X0))
| ~ fulladder(X0) ),
inference(resolution,[],[f21,f43]) ).
fof(f86,plain,
! [X0] :
( or_ok(or1(X0))
| abnormal(or1(X0))
| ~ halfadder(X0) ),
inference(resolution,[],[f21,f31]) ).
fof(f87,plain,
! [X0] :
( not_ok(not1(X0))
| abnormal(not1(X0))
| ~ halfadder(X0) ),
inference(resolution,[],[f27,f30]) ).
fof(f90,plain,
connection(in2(h1(f)),in2(or1(h1(f)))),
inference(resolution,[],[f33,f81]) ).
fof(f92,plain,
connection(in1(h1(f)),in1(and2(h1(f)))),
inference(resolution,[],[f34,f81]) ).
fof(f93,plain,
connection(in1(h2(f)),in1(and2(h2(f)))),
inference(resolution,[],[f34,f82]) ).
fof(f95,plain,
connection(in2(h2(f)),in2(and2(h2(f)))),
inference(resolution,[],[f35,f82]) ).
fof(f96,plain,
connection(outs(h1(f)),out1(and1(h1(f)))),
inference(resolution,[],[f36,f81]) ).
fof(f97,plain,
connection(outs(h2(f)),out1(and1(h2(f)))),
inference(resolution,[],[f36,f82]) ).
fof(f99,plain,
connection(outc(h2(f)),out1(and2(h2(f)))),
inference(resolution,[],[f37,f82]) ).
fof(f100,plain,
connection(in1(f),in1(h2(f))),
inference(resolution,[],[f47,f52]) ).
fof(f102,plain,
( ~ zero(in1(h2(f)))
| zero(in1(f)) ),
inference(resolution,[],[f100,f3]) ).
fof(f106,definition,
( spl0_4
<=> zero(in1(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f107,plain,
( ~ zero(in1(h2(f)))
| spl0_4 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl0_5
<=> zero(in1(f)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f111,plain,
( zero(in1(f))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f115,plain,
( spl0_5
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f102,f106,f110]) ).
fof(f116,plain,
connection(in2(f),in1(h1(f))),
inference(resolution,[],[f48,f52]) ).
fof(f117,plain,
connection(inc(f),in2(h1(f))),
inference(resolution,[],[f49,f52]) ).
fof(f118,plain,
connection(outs(f),outs(h2(f))),
inference(resolution,[],[f50,f52]) ).
fof(f119,plain,
connection(outc(f),out1(or1(f))),
inference(resolution,[],[f51,f52]) ).
fof(f123,plain,
( ~ zero(in2(f))
| zero(in1(h1(f))) ),
inference(resolution,[],[f116,f1]) ).
fof(f124,plain,
zero(in1(h1(f))),
inference(forward_subsumption_resolution,[],[f123,f54]) ).
fof(f126,plain,
connection(out1(or1(h1(f))),in1(and1(h1(f)))),
inference(resolution,[],[f38,f81]) ).
fof(f129,plain,
connection(out1(and2(h1(f))),in1(not1(h1(f)))),
inference(resolution,[],[f39,f81]) ).
fof(f130,plain,
connection(out1(and2(h2(f))),in1(not1(h2(f)))),
inference(resolution,[],[f39,f82]) ).
fof(f131,plain,
connection(out1(not1(h1(f))),in2(and1(h1(f)))),
inference(resolution,[],[f40,f81]) ).
fof(f132,plain,
connection(out1(not1(h2(f))),in2(and1(h2(f)))),
inference(resolution,[],[f40,f82]) ).
fof(f135,plain,
( ~ one(inc(f))
| one(in2(h1(f))) ),
inference(resolution,[],[f117,f2]) ).
fof(f146,plain,
one(in2(h1(f))),
inference(forward_subsumption_resolution,[],[f135,f55]) ).
fof(f148,plain,
connection(outs(h1(f)),in2(h2(f))),
inference(resolution,[],[f44,f52]) ).
fof(f150,plain,
connection(outc(h2(f)),in1(or1(f))),
inference(resolution,[],[f46,f52]) ).
fof(f153,plain,
( ~ one(outs(f))
| one(outs(h2(f))) ),
inference(resolution,[],[f118,f2]) ).
fof(f164,plain,
one(outs(h2(f))),
inference(forward_subsumption_resolution,[],[f153,f56]) ).
fof(f169,plain,
( ~ zero(outc(f))
| zero(out1(or1(f))) ),
inference(resolution,[],[f119,f1]) ).
fof(f170,plain,
zero(out1(or1(f))),
inference(forward_subsumption_resolution,[],[f169,f57]) ).
fof(f175,plain,
( ~ one(outs(h1(f)))
| one(in2(h2(f))) ),
inference(resolution,[],[f148,f2]) ).
fof(f187,definition,
( spl0_12
<=> one(in2(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f189,plain,
( one(in2(h2(f)))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f191,definition,
( spl0_13
<=> one(outs(h1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f193,plain,
( ~ one(outs(h1(f)))
| spl0_13 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f175,f191,f187]) ).
fof(f222,plain,
( ~ zero(in1(or1(f)))
| zero(outc(h2(f))) ),
inference(resolution,[],[f150,f3]) ).
fof(f226,definition,
( spl0_18
<=> zero(in1(or1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f227,plain,
( ~ zero(in1(or1(f)))
| spl0_18 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f230,definition,
( spl0_19
<=> zero(outc(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f231,plain,
( zero(outc(h2(f)))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f243,plain,
( spl0_19
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f222,f226,f230]) ).
fof(f246,plain,
! [X0] :
( abnormal(and1(X0))
| ~ halfadder(X0)
| ~ one(in1(and1(X0)))
| ~ one(in2(and1(X0)))
| one(out1(and1(X0))) ),
inference(resolution,[],[f83,f8]) ).
fof(f247,plain,
! [X0] :
( abnormal(and1(X0))
| ~ halfadder(X0)
| ~ one(out1(and1(X0)))
| one(in2(and1(X0))) ),
inference(resolution,[],[f83,f11]) ).
fof(f251,plain,
! [X0] :
( abnormal(and2(X0))
| ~ halfadder(X0)
| ~ zero(out1(and2(X0)))
| zero(in1(and2(X0)))
| zero(in2(and2(X0))) ),
inference(resolution,[],[f84,f9]) ).
fof(f256,plain,
! [X0] :
( abnormal(and2(X0))
| ~ halfadder(X0)
| ~ zero(in1(and2(X0)))
| zero(out1(and2(X0))) ),
inference(resolution,[],[f84,f6]) ).
fof(f260,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(or1(X0))
| ~ zero(out1(or1(X0)))
| zero(in1(or1(X0))) ),
inference(resolution,[],[f85,f18]) ).
fof(f267,plain,
! [X0] :
( abnormal(or1(X0))
| ~ halfadder(X0)
| ~ one(in2(or1(X0)))
| one(out1(or1(X0))) ),
inference(resolution,[],[f86,f15]) ).
fof(f269,plain,
! [X0] :
( abnormal(not1(X0))
| ~ halfadder(X0)
| ~ one(out1(not1(X0)))
| zero(in1(not1(X0))) ),
inference(resolution,[],[f87,f25]) ).
fof(f272,plain,
! [X0] :
( abnormal(not1(X0))
| ~ halfadder(X0)
| ~ zero(in1(not1(X0)))
| one(out1(not1(X0))) ),
inference(resolution,[],[f87,f22]) ).
fof(f288,plain,
( ~ one(in2(h1(f)))
| one(in2(or1(h1(f)))) ),
inference(resolution,[],[f90,f2]) ).
fof(f290,plain,
one(in2(or1(h1(f)))),
inference(forward_subsumption_resolution,[],[f288,f146]) ).
fof(f301,plain,
( ~ zero(in1(h1(f)))
| zero(in1(and2(h1(f)))) ),
inference(resolution,[],[f92,f1]) ).
fof(f302,plain,
zero(in1(and2(h1(f)))),
inference(forward_subsumption_resolution,[],[f301,f124]) ).
fof(f305,plain,
( ~ zero(in1(and2(h2(f))))
| zero(in1(h2(f))) ),
inference(resolution,[],[f93,f3]) ).
fof(f309,plain,
( ~ zero(in1(and2(h2(f))))
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f305,f107]) ).
fof(f318,plain,
( ~ one(in2(h2(f)))
| one(in2(and2(h2(f)))) ),
inference(resolution,[],[f95,f2]) ).
fof(f322,plain,
( ~ one(out1(and1(h1(f))))
| one(outs(h1(f))) ),
inference(resolution,[],[f96,f4]) ).
fof(f327,plain,
( ~ one(out1(and1(h1(f))))
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f322,f193]) ).
fof(f330,plain,
( ~ one(outs(h2(f)))
| one(out1(and1(h2(f)))) ),
inference(resolution,[],[f97,f2]) ).
fof(f332,plain,
one(out1(and1(h2(f)))),
inference(forward_subsumption_resolution,[],[f330,f164]) ).
fof(f344,plain,
( ~ zero(outc(h2(f)))
| zero(out1(and2(h2(f)))) ),
inference(resolution,[],[f99,f1]) ).
fof(f349,plain,
( ~ one(out1(or1(h1(f))))
| one(in1(and1(h1(f)))) ),
inference(resolution,[],[f126,f2]) ).
fof(f361,definition,
( spl0_24
<=> one(in1(and1(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f363,plain,
( one(in1(and1(h1(f))))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f365,definition,
( spl0_25
<=> one(out1(or1(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f367,plain,
( ~ one(out1(or1(h1(f))))
| spl0_25 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f368,plain,
( spl0_24
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f349,f365,f361]) ).
fof(f398,plain,
( ~ zero(out1(and2(h1(f))))
| zero(in1(not1(h1(f)))) ),
inference(resolution,[],[f129,f1]) ).
fof(f402,plain,
( ~ zero(in1(not1(h2(f))))
| zero(out1(and2(h2(f)))) ),
inference(resolution,[],[f130,f3]) ).
fof(f409,plain,
( ~ one(out1(not1(h1(f))))
| one(in2(and1(h1(f)))) ),
inference(resolution,[],[f131,f2]) ).
fof(f421,definition,
( spl0_32
<=> one(in2(and1(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f423,plain,
( one(in2(and1(h1(f))))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f425,definition,
( spl0_33
<=> one(out1(not1(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f427,plain,
( ~ one(out1(not1(h1(f))))
| spl0_33 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f428,plain,
( spl0_32
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f409,f425,f421]) ).
fof(f431,plain,
( ~ one(in2(and1(h2(f))))
| one(out1(not1(h2(f)))) ),
inference(resolution,[],[f132,f4]) ).
fof(f445,definition,
( spl0_36
<=> one(in2(and1(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f446,plain,
( ~ one(in2(and1(h2(f))))
| spl0_36 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f449,definition,
( spl0_37
<=> one(out1(not1(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f450,plain,
( one(out1(not1(h2(f))))
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f454,plain,
( spl0_37
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f431,f445,f449]) ).
fof(f466,plain,
( ~ halfadder(h1(f))
| ~ zero(in1(and2(h1(f))))
| zero(out1(and2(h1(f)))) ),
inference(resolution,[],[f256,f63]) ).
fof(f467,plain,
( ~ zero(in1(and2(h1(f))))
| zero(out1(and2(h1(f)))) ),
inference(forward_subsumption_resolution,[],[f466,f81]) ).
fof(f468,plain,
zero(out1(and2(h1(f)))),
inference(forward_subsumption_resolution,[],[f467,f302]) ).
fof(f473,definition,
( spl0_38
<=> zero(in1(not1(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f475,plain,
( zero(in1(not1(h1(f))))
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f477,definition,
( spl0_39
<=> zero(out1(and2(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f480,plain,
( spl0_38
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f398,f477,f473]) ).
fof(f482,plain,
spl0_39,
inference(avatar_split_clause,[],[f468,f477]) ).
fof(f487,plain,
( abnormal(or1(f))
| ~ zero(out1(or1(f)))
| zero(in1(or1(f))) ),
inference(resolution,[],[f260,f52]) ).
fof(f488,plain,
( ~ zero(out1(or1(f)))
| zero(in1(or1(f)))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f487,f72]) ).
fof(f489,plain,
( zero(in1(or1(f)))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f488,f170]) ).
fof(f490,plain,
( $false
| spl0_2
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f489,f227]) ).
fof(f491,plain,
( spl0_2
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f495,plain,
( ~ halfadder(h2(f))
| ~ one(out1(and1(h2(f))))
| one(in2(and1(h2(f))))
| spl0_1 ),
inference(resolution,[],[f68,f247]) ).
fof(f496,plain,
( ~ one(out1(and1(h2(f))))
| one(in2(and1(h2(f))))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f495,f82]) ).
fof(f498,plain,
( one(in2(and1(h2(f))))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f496,f332]) ).
fof(f500,plain,
( $false
| spl0_1
| spl0_36 ),
inference(forward_subsumption_resolution,[],[f498,f446]) ).
fof(f501,plain,
( spl0_1
| spl0_36 ),
inference(avatar_contradiction_clause,[],[f500]) ).
fof(f508,plain,
( ~ halfadder(h1(f))
| ~ one(in2(or1(h1(f))))
| one(out1(or1(h1(f)))) ),
inference(resolution,[],[f267,f61]) ).
fof(f509,plain,
( ~ one(in2(or1(h1(f))))
| one(out1(or1(h1(f)))) ),
inference(forward_subsumption_resolution,[],[f508,f81]) ).
fof(f510,plain,
one(out1(or1(h1(f)))),
inference(forward_subsumption_resolution,[],[f509,f290]) ).
fof(f511,plain,
( $false
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f510,f367]) ).
fof(f512,plain,
spl0_25,
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f515,plain,
( ~ halfadder(h2(f))
| ~ one(out1(not1(h2(f))))
| zero(in1(not1(h2(f))))
| spl0_3 ),
inference(resolution,[],[f269,f77]) ).
fof(f516,plain,
( ~ one(out1(not1(h2(f))))
| zero(in1(not1(h2(f))))
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f515,f82]) ).
fof(f517,plain,
( zero(in1(not1(h2(f))))
| spl0_3
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f516,f450]) ).
fof(f520,plain,
( zero(out1(and2(h2(f))))
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f344,f231]) ).
fof(f522,definition,
( spl0_40
<=> zero(in1(not1(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f526,definition,
( spl0_41
<=> zero(out1(and2(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f527,plain,
( zero(out1(and2(h2(f))))
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f530,plain,
( spl0_41
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f402,f522,f526]) ).
fof(f531,plain,
( spl0_40
| spl0_3
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f517,f449,f75,f522]) ).
fof(f532,plain,
( spl0_41
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f520,f230,f526]) ).
fof(f539,plain,
( ~ halfadder(h1(f))
| ~ zero(in1(not1(h1(f))))
| one(out1(not1(h1(f)))) ),
inference(resolution,[],[f272,f62]) ).
fof(f541,plain,
( ~ zero(in1(not1(h1(f))))
| one(out1(not1(h1(f)))) ),
inference(forward_subsumption_resolution,[],[f539,f81]) ).
fof(f542,plain,
( one(out1(not1(h1(f))))
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f541,f475]) ).
fof(f543,plain,
( $false
| spl0_33
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f542,f427]) ).
fof(f544,plain,
( spl0_33
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[],[f543]) ).
fof(f547,plain,
( ~ halfadder(h1(f))
| ~ one(in1(and1(h1(f))))
| ~ one(in2(and1(h1(f))))
| one(out1(and1(h1(f)))) ),
inference(resolution,[],[f246,f64]) ).
fof(f549,plain,
( ~ one(in1(and1(h1(f))))
| ~ one(in2(and1(h1(f))))
| one(out1(and1(h1(f)))) ),
inference(forward_subsumption_resolution,[],[f547,f81]) ).
fof(f550,plain,
( ~ one(in2(and1(h1(f))))
| one(out1(and1(h1(f))))
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f549,f363]) ).
fof(f551,plain,
( one(out1(and1(h1(f))))
| ~ spl0_24
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f550,f423]) ).
fof(f552,plain,
( $false
| spl0_13
| ~ spl0_24
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f551,f327]) ).
fof(f553,plain,
( spl0_13
| ~ spl0_24
| ~ spl0_32 ),
inference(avatar_contradiction_clause,[],[f552]) ).
fof(f556,plain,
( one(in2(and2(h2(f))))
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f318,f189]) ).
fof(f557,plain,
( ~ halfadder(h2(f))
| ~ zero(out1(and2(h2(f))))
| zero(in1(and2(h2(f))))
| zero(in2(and2(h2(f)))) ),
inference(resolution,[],[f251,f59]) ).
fof(f559,plain,
( ~ zero(out1(and2(h2(f))))
| zero(in1(and2(h2(f))))
| zero(in2(and2(h2(f)))) ),
inference(forward_subsumption_resolution,[],[f557,f82]) ).
fof(f560,plain,
( zero(in1(and2(h2(f))))
| zero(in2(and2(h2(f))))
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f559,f527]) ).
fof(f561,plain,
( zero(in2(and2(h2(f))))
| spl0_4
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f560,f309]) ).
fof(f579,definition,
( spl0_42
<=> zero(in2(and2(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f580,plain,
( ~ zero(in2(and2(h2(f))))
| spl0_42 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f581,plain,
( zero(in2(and2(h2(f))))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f589,plain,
( ~ one(in1(f))
| ~ spl0_5 ),
inference(resolution,[],[f111,f5]) ).
fof(f590,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f589,f53]) ).
fof(f591,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f590]) ).
fof(f592,plain,
( $false
| spl0_4
| ~ spl0_41
| spl0_42 ),
inference(forward_subsumption_resolution,[],[f561,f580]) ).
fof(f593,plain,
( spl0_4
| ~ spl0_41
| spl0_42 ),
inference(avatar_contradiction_clause,[],[f592]) ).
fof(f636,plain,
( ~ one(in2(and2(h2(f))))
| ~ spl0_42 ),
inference(resolution,[],[f581,f5]) ).
fof(f637,plain,
( $false
| ~ spl0_12
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f636,f556]) ).
fof(f638,plain,
( ~ spl0_12
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f637]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f73]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f78]) ).
cnf(s4,plain,
( ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f115]) ).
cnf(s10,plain,
( spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f194]) ).
cnf(s19,plain,
( ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f243]) ).
cnf(s22,plain,
( spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f368]) ).
cnf(s30,plain,
( spl0_32
| ~ spl0_33 ),
inference(sat_conversion,[],[f428]) ).
cnf(s36,plain,
( ~ spl0_36
| spl0_37 ),
inference(sat_conversion,[],[f454]) ).
cnf(s38,plain,
( spl0_38
| ~ spl0_39 ),
inference(sat_conversion,[],[f480]) ).
cnf(s40,plain,
spl0_39,
inference(sat_conversion,[],[f482]) ).
cnf(s42,plain,
( spl0_2
| spl0_18 ),
inference(sat_conversion,[],[f491]) ).
cnf(s43,plain,
( spl0_1
| spl0_36 ),
inference(sat_conversion,[],[f501]) ).
cnf(s45,plain,
spl0_25,
inference(sat_conversion,[],[f512]) ).
cnf(s48,plain,
( ~ spl0_40
| spl0_41 ),
inference(sat_conversion,[],[f530]) ).
cnf(s49,plain,
( spl0_3
| ~ spl0_37
| spl0_40 ),
inference(sat_conversion,[],[f531]) ).
cnf(s50,plain,
( ~ spl0_19
| spl0_41 ),
inference(sat_conversion,[],[f532]) ).
cnf(s51,plain,
( spl0_33
| ~ spl0_38 ),
inference(sat_conversion,[],[f544]) ).
cnf(s52,plain,
( spl0_13
| ~ spl0_24
| ~ spl0_32 ),
inference(sat_conversion,[],[f553]) ).
cnf(s58,plain,
~ spl0_5,
inference(sat_conversion,[],[f591]) ).
cnf(s59,plain,
( spl0_4
| ~ spl0_41
| spl0_42 ),
inference(sat_conversion,[],[f593]) ).
cnf(s72,plain,
( ~ spl0_12
| ~ spl0_42 ),
inference(sat_conversion,[],[f638]) ).
cnf(s76,plain,
spl0_38,
inference(rat,[],[s38,s40]) ).
cnf(s77,plain,
spl0_33,
inference(rat,[],[s51,s76]) ).
cnf(s79,plain,
spl0_32,
inference(rat,[],[s30,s77]) ).
cnf(s80,plain,
spl0_24,
inference(rat,[],[s22,s45]) ).
cnf(s81,plain,
spl0_13,
inference(rat,[],[s52,s79,s80]) ).
cnf(s84,plain,
spl0_12,
inference(rat,[],[s10,s81]) ).
cnf(s85,plain,
~ spl0_42,
inference(rat,[],[s72,s84]) ).
cnf(s88,plain,
~ spl0_4,
inference(rat,[],[s4,s58]) ).
cnf(s90,plain,
~ spl0_41,
inference(rat,[],[s59,s85,s88]) ).
cnf(s91,plain,
~ spl0_19,
inference(rat,[],[s50,s90]) ).
cnf(s92,plain,
~ spl0_40,
inference(rat,[],[s48,s90]) ).
cnf(s93,plain,
~ spl0_18,
inference(rat,[],[s19,s91]) ).
cnf(s94,plain,
spl0_2,
inference(rat,[],[s42,s93]) ).
cnf(s95,plain,
~ spl0_3,
inference(rat,[],[s2,s94]) ).
cnf(s96,plain,
~ spl0_37,
inference(rat,[],[s49,s92,s95]) ).
cnf(s97,plain,
~ spl0_36,
inference(rat,[],[s36,s96]) ).
cnf(s98,plain,
spl0_1,
inference(rat,[],[s43,s97]) ).
cnf(s99,plain,
$false,
inference(rat,[],[s1,s94,s98]) ).
fof(f639,plain,
$false,
inference(avatar_sat_refutation,[],[s99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWV006-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.35 % Computer : n004.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 27 10:53:07 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 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
% 0.13/0.43 % (3342884)Will run a generic schedule for satisfiability detection.
% 0.13/0.43 % (3342893)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2408488323:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.43 % (3342890)% WARNING: option uhcvi not known.
% 0.13/0.43 % (3342893) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3342884-3342893"...
% 0.13/0.43 % (3342893)...printing done.
% 0.13/0.43 % (3342893)Refutation found. Thanks to Tanya!
% 0.13/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.43 % (3342893)------------------------------
% 0.13/0.43 % (3342893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.43 % (3342893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.43 % (3342893)CaDiCaL version: 2.1.3
% 0.13/0.43 % (3342893)Termination reason: Refutation
% 0.13/0.43 % (3342893)Time elapsed: 0.006 s
% 0.13/0.43 % (3342893)Peak memory usage: 12 MB
% 0.13/0.43 % (3342893)Instructions burned: 15 (million)
% 0.13/0.43 % (3342884)Success in time 0.032 s
% 0.13/0.43 % Vampire exiting
%------------------------------------------------------------------------------