%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HWV007-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 10:20:10 AM UTC 2026
% Result : Unsatisfiable 3.20s 1.36s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 82
% Syntax : Number of formulae : 252 ( 68 unt; 34 def)
% Number of atoms : 495 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 446 ( 203 ~; 209 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 47 ( 46 usr; 35 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ connection(X0,X1)
| ~ zero(X0)
| zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',value_propagation_zero1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ connection(X0,X1)
| ~ one(X0)
| one(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',value_propagation_one1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ connection(X0,X1)
| ~ zero(X1)
| zero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',value_propagation_zero2) ).
fof(f4,axiom,
! [X0,X1] :
( ~ connection(X0,X1)
| ~ one(X1)
| one(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',value_propagation_one2) ).
fof(f5,axiom,
! [X0] :
( ~ zero(X0)
| ~ one(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_value) ).
fof(f6,axiom,
! [X0] :
( ~ and_ok(X0)
| ~ zero(in1(X0))
| zero(out1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_0x_0) ).
fof(f7,axiom,
! [X0] :
( ~ and_ok(X0)
| ~ zero(in2(X0))
| zero(out1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_x0_0) ).
fof(f8,axiom,
! [X0] :
( ~ and_ok(X0)
| ~ one(in1(X0))
| ~ one(in2(X0))
| one(out1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_11_1) ).
fof(f13,axiom,
! [X0] :
( ~ logic_and(X0)
| and_ok(X0)
| abnormal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_ok_or_abnormal) ).
fof(f15,axiom,
! [X0] :
( ~ or_ok(X0)
| ~ one(in2(X0))
| one(out1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_x1_1) ).
fof(f16,axiom,
! [X0] :
( ~ or_ok(X0)
| ~ zero(in1(X0))
| ~ zero(in2(X0))
| zero(out1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_00_0) ).
fof(f21,axiom,
! [X0] :
( ~ logic_or(X0)
| or_ok(X0)
| abnormal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_ok_or_abnormal) ).
fof(f23,axiom,
! [X0] :
( ~ not_ok(X0)
| ~ one(in1(X0))
| zero(out1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_1_0_fw) ).
fof(f27,axiom,
! [X0] :
( ~ logic_not(X0)
| not_ok(X0)
| abnormal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_ok_or_abnormal) ).
fof(f28,axiom,
! [X0] :
( logic_and(and1(X0))
| ~ halfadder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_and1) ).
fof(f29,axiom,
! [X0] :
( logic_and(and2(X0))
| ~ halfadder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_and2) ).
fof(f30,axiom,
! [X0] :
( logic_not(not1(X0))
| ~ halfadder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_not1) ).
fof(f31,axiom,
! [X0] :
( logic_or(or1(X0))
| ~ halfadder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_or1) ).
fof(f32,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(in1(X0),in1(or1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_connection_in1_in1or1) ).
fof(f33,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(in2(X0),in2(or1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_connection_in2_in2or1) ).
fof(f34,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(in1(X0),in1(and2(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_connection_in1_in1and2) ).
fof(f35,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(in2(X0),in2(and2(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_connection_in2_in2and2) ).
fof(f36,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(outs(X0),out1(and1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_connection_outs_out1and1) ).
fof(f37,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(outc(X0),out1(and2(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_connection_outc_out1and2) ).
fof(f38,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(out1(or1(X0)),in1(and1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_connection_out1or1_in1_and1) ).
fof(f39,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(out1(and2(X0)),in1(not1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_connection_out1and2_in1not1) ).
fof(f40,axiom,
! [X0] :
( ~ halfadder(X0)
| connection(out1(not1(X0)),in2(and1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halfadder_connection_out1not1_in2and1) ).
fof(f41,axiom,
! [X0] :
( ~ fulladder(X0)
| halfadder(h1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_halfadder1) ).
fof(f42,axiom,
! [X0] :
( ~ fulladder(X0)
| halfadder(h2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_halfadder2) ).
fof(f43,axiom,
! [X0] :
( logic_or(or1(X0))
| ~ fulladder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_or1) ).
fof(f44,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(outs(h1(X0)),in2(h2(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_connection_outsh1_in2h2) ).
fof(f45,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(outc(h1(X0)),in2(or1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_connection_outch1_in2or1) ).
fof(f47,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(in1(X0),in1(h2(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_connection_in1_in1h2) ).
fof(f48,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(in2(X0),in1(h1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_connection_in2_in1h1) ).
fof(f49,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(inc(X0),in2(h1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_connection_inc_in2h1) ).
fof(f50,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(outs(X0),outs(h2(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_connection_outs_outsh2) ).
fof(f51,axiom,
! [X0] :
( ~ fulladder(X0)
| connection(outc(X0),out1(or1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fulladder_connection_outc_out1or1) ).
fof(f52,axiom,
fulladder(f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_isa_fulladder) ).
fof(f53,axiom,
zero(in1(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in1_1) ).
fof(f54,axiom,
one(in2(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in2_0) ).
fof(f55,axiom,
one(inc(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inc_1) ).
fof(f56,axiom,
one(outs(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outs_1) ).
fof(f57,axiom,
zero(outc(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outc_0) ).
fof(f58,negated_conjecture,
~ abnormal(and2(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_and2h1) ).
fof(f59,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h1(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_and1h1) ).
fof(f60,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(not1(h1(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_not1h1) ).
fof(f61,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_and1h2) ).
fof(f62,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(or1(h2(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_or1h2) ).
fof(f64,definition,
( spl0_1
<=> abnormal(or1(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f67,definition,
( spl0_2
<=> abnormal(or1(f)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f69,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f62,f67,f64]) ).
fof(f71,definition,
( spl0_3
<=> abnormal(and1(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f73,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f61,f67,f71]) ).
fof(f75,definition,
( spl0_4
<=> abnormal(not1(h1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f77,plain,
( ~ spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f60,f67,f75]) ).
fof(f79,definition,
( spl0_5
<=> abnormal(and1(h1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f81,plain,
( ~ spl0_5
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f59,f67,f79]) ).
fof(f84,plain,
halfadder(h1(f)),
inference(resolution,[],[f41,f52]) ).
fof(f85,plain,
halfadder(h2(f)),
inference(resolution,[],[f42,f52]) ).
fof(f86,plain,
! [X0] :
( and_ok(and1(X0))
| abnormal(and1(X0))
| ~ halfadder(X0) ),
inference(resolution,[],[f13,f28]) ).
fof(f87,plain,
! [X0] :
( and_ok(and2(X0))
| abnormal(and2(X0))
| ~ halfadder(X0) ),
inference(resolution,[],[f13,f29]) ).
fof(f88,plain,
! [X0] :
( or_ok(or1(X0))
| abnormal(or1(X0))
| ~ fulladder(X0) ),
inference(resolution,[],[f21,f43]) ).
fof(f89,plain,
! [X0] :
( or_ok(or1(X0))
| abnormal(or1(X0))
| ~ halfadder(X0) ),
inference(resolution,[],[f21,f31]) ).
fof(f90,plain,
! [X0] :
( not_ok(not1(X0))
| abnormal(not1(X0))
| ~ halfadder(X0) ),
inference(resolution,[],[f27,f30]) ).
fof(f92,plain,
connection(in1(h2(f)),in1(or1(h2(f)))),
inference(resolution,[],[f32,f85]) ).
fof(f94,plain,
connection(in2(h2(f)),in2(or1(h2(f)))),
inference(resolution,[],[f33,f85]) ).
fof(f95,plain,
connection(in1(h1(f)),in1(and2(h1(f)))),
inference(resolution,[],[f34,f84]) ).
fof(f97,plain,
connection(in2(h1(f)),in2(and2(h1(f)))),
inference(resolution,[],[f35,f84]) ).
fof(f99,plain,
connection(outs(h1(f)),out1(and1(h1(f)))),
inference(resolution,[],[f36,f84]) ).
fof(f100,plain,
connection(outs(h2(f)),out1(and1(h2(f)))),
inference(resolution,[],[f36,f85]) ).
fof(f101,plain,
connection(outc(h1(f)),out1(and2(h1(f)))),
inference(resolution,[],[f37,f84]) ).
fof(f103,plain,
connection(in1(f),in1(h2(f))),
inference(resolution,[],[f47,f52]) ).
fof(f107,plain,
( ~ zero(in1(f))
| zero(in1(h2(f))) ),
inference(resolution,[],[f103,f1]) ).
fof(f109,definition,
( spl0_6
<=> zero(in1(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f112,definition,
( spl0_7
<=> zero(in1(f)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f113,plain,
( ~ zero(in1(f))
| spl0_7 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f107,f112,f109]) ).
fof(f122,plain,
( $false
| spl0_7 ),
inference(resolution,[],[f113,f53]) ).
fof(f123,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f122]) ).
fof(f124,plain,
connection(in2(f),in1(h1(f))),
inference(resolution,[],[f48,f52]) ).
fof(f129,plain,
( ~ one(in2(f))
| one(in1(h1(f))) ),
inference(resolution,[],[f124,f2]) ).
fof(f139,definition,
( spl0_12
<=> one(in1(h1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f142,definition,
( spl0_13
<=> one(in2(f)) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f143,plain,
( ~ one(in2(f))
| spl0_13 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f144,plain,
( spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f129,f142,f139]) ).
fof(f148,plain,
( $false
| spl0_13 ),
inference(resolution,[],[f143,f54]) ).
fof(f149,plain,
spl0_13,
inference(avatar_contradiction_clause,[],[f148]) ).
fof(f150,plain,
connection(inc(f),in2(h1(f))),
inference(resolution,[],[f49,f52]) ).
fof(f153,plain,
( ~ one(inc(f))
| one(in2(h1(f))) ),
inference(resolution,[],[f150,f2]) ).
fof(f163,definition,
( spl0_16
<=> one(in2(h1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f166,definition,
( spl0_17
<=> one(inc(f)) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f167,plain,
( ~ one(inc(f))
| spl0_17 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f168,plain,
( spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f153,f166,f163]) ).
fof(f172,plain,
( $false
| spl0_17 ),
inference(resolution,[],[f167,f55]) ).
fof(f173,plain,
spl0_17,
inference(avatar_contradiction_clause,[],[f172]) ).
fof(f174,plain,
connection(outs(f),outs(h2(f))),
inference(resolution,[],[f50,f52]) ).
fof(f176,plain,
( ~ zero(outs(h2(f)))
| zero(outs(f)) ),
inference(resolution,[],[f174,f3]) ).
fof(f180,definition,
( spl0_18
<=> zero(outs(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f183,definition,
( spl0_19
<=> zero(outs(f)) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f190,definition,
( spl0_21
<=> one(outs(f)) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f191,plain,
( ~ one(outs(f))
| spl0_21 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( zero(outs(f))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f195,plain,
( spl0_19
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f176,f180,f183]) ).
fof(f196,plain,
connection(outc(f),out1(or1(f))),
inference(resolution,[],[f51,f52]) ).
fof(f197,plain,
( $false
| spl0_21 ),
inference(resolution,[],[f191,f56]) ).
fof(f198,plain,
spl0_21,
inference(avatar_contradiction_clause,[],[f197]) ).
fof(f202,plain,
( ~ zero(outc(f))
| zero(out1(or1(f))) ),
inference(resolution,[],[f196,f1]) ).
fof(f204,definition,
( spl0_22
<=> zero(out1(or1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f205,plain,
( zero(out1(or1(f)))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,definition,
( spl0_23
<=> zero(outc(f)) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f208,plain,
( ~ zero(outc(f))
| spl0_23 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f209,plain,
( spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f202,f207,f204]) ).
fof(f214,definition,
( spl0_25
<=> one(out1(or1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f217,plain,
( $false
| spl0_23 ),
inference(resolution,[],[f208,f57]) ).
fof(f218,plain,
spl0_23,
inference(avatar_contradiction_clause,[],[f217]) ).
fof(f219,plain,
( ~ one(out1(or1(f)))
| ~ spl0_22 ),
inference(resolution,[],[f205,f5]) ).
fof(f220,plain,
( ~ spl0_25
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f219,f204,f214]) ).
fof(f222,plain,
connection(out1(or1(h2(f))),in1(and1(h2(f)))),
inference(resolution,[],[f38,f85]) ).
fof(f225,plain,
! [X0] :
( ~ halfadder(X0)
| abnormal(and1(X0))
| ~ zero(in2(and1(X0)))
| zero(out1(and1(X0))) ),
inference(resolution,[],[f86,f7]) ).
fof(f226,plain,
! [X0] :
( ~ halfadder(X0)
| abnormal(and1(X0))
| ~ zero(in1(and1(X0)))
| zero(out1(and1(X0))) ),
inference(resolution,[],[f86,f6]) ).
fof(f228,plain,
connection(out1(and2(h1(f))),in1(not1(h1(f)))),
inference(resolution,[],[f39,f84]) ).
fof(f235,plain,
connection(out1(not1(h1(f))),in2(and1(h1(f)))),
inference(resolution,[],[f40,f84]) ).
fof(f239,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(or1(X0))
| ~ one(in2(or1(X0)))
| one(out1(or1(X0))) ),
inference(resolution,[],[f88,f15]) ).
fof(f242,plain,
connection(outs(h1(f)),in2(h2(f))),
inference(resolution,[],[f44,f52]) ).
fof(f246,plain,
( ~ zero(outs(h1(f)))
| zero(in2(h2(f))) ),
inference(resolution,[],[f242,f1]) ).
fof(f248,definition,
( spl0_26
<=> zero(in2(h2(f))) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f251,definition,
( spl0_27
<=> zero(outs(h1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f253,plain,
( spl0_26
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f246,f251,f248]) ).
fof(f267,plain,
connection(outc(h1(f)),in2(or1(f))),
inference(resolution,[],[f45,f52]) ).
fof(f270,plain,
( ~ one(outc(h1(f)))
| one(in2(or1(f))) ),
inference(resolution,[],[f267,f2]) ).
fof(f280,definition,
( spl0_32
<=> one(in2(or1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f283,definition,
( spl0_33
<=> one(outc(h1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f285,plain,
( spl0_32
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f270,f283,f280]) ).
fof(f318,plain,
! [X0] :
( ~ halfadder(X0)
| ~ one(in2(and2(X0)))
| one(out1(and2(X0)))
| abnormal(and2(X0))
| ~ one(in1(and2(X0))) ),
inference(resolution,[],[f8,f87]) ).
fof(f328,plain,
! [X0] :
( ~ halfadder(X0)
| abnormal(not1(X0))
| ~ one(in1(not1(X0)))
| zero(out1(not1(X0))) ),
inference(resolution,[],[f90,f23]) ).
fof(f331,plain,
! [X0] :
( ~ halfadder(X0)
| ~ zero(in2(or1(X0)))
| zero(out1(or1(X0)))
| abnormal(or1(X0))
| ~ zero(in1(or1(X0))) ),
inference(resolution,[],[f16,f89]) ).
fof(f351,plain,
( ~ zero(in1(h2(f)))
| zero(in1(or1(h2(f)))) ),
inference(resolution,[],[f92,f1]) ).
fof(f353,definition,
( spl0_40
<=> zero(in1(or1(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f356,plain,
( spl0_40
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f351,f109,f353]) ).
fof(f380,plain,
( ~ zero(in2(h2(f)))
| zero(in2(or1(h2(f)))) ),
inference(resolution,[],[f94,f1]) ).
fof(f382,definition,
( spl0_44
<=> zero(in2(or1(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f391,plain,
( ~ one(in1(h1(f)))
| one(in1(and2(h1(f)))) ),
inference(resolution,[],[f95,f2]) ).
fof(f394,definition,
( spl0_46
<=> one(in1(and2(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
fof(f396,plain,
( spl0_46
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f391,f139,f394]) ).
fof(f417,plain,
( ~ one(in2(h1(f)))
| one(in2(and2(h1(f)))) ),
inference(resolution,[],[f97,f2]) ).
fof(f420,definition,
( spl0_50
<=> one(in2(and2(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f422,plain,
( spl0_50
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f417,f163,f420]) ).
fof(f440,plain,
( ~ zero(out1(and1(h1(f))))
| zero(outs(h1(f))) ),
inference(resolution,[],[f99,f3]) ).
fof(f444,definition,
( spl0_54
<=> zero(out1(and1(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f446,plain,
( spl0_27
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f440,f444,f251]) ).
fof(f452,plain,
( ~ zero(out1(and1(h2(f))))
| zero(outs(h2(f))) ),
inference(resolution,[],[f100,f3]) ).
fof(f461,definition,
( spl0_57
<=> zero(out1(and1(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_57])],[avatar_definition]) ).
fof(f463,plain,
( spl0_18
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f452,f461,f180]) ).
fof(f464,plain,
( ~ one(out1(and2(h1(f))))
| one(outc(h1(f))) ),
inference(resolution,[],[f101,f4]) ).
fof(f473,definition,
( spl0_59
<=> one(out1(and2(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_59])],[avatar_definition]) ).
fof(f475,plain,
( spl0_33
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f464,f473,f283]) ).
fof(f515,plain,
( ~ zero(out1(or1(h2(f))))
| zero(in1(and1(h2(f)))) ),
inference(resolution,[],[f222,f1]) ).
fof(f517,definition,
( spl0_66
<=> zero(in1(and1(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_66])],[avatar_definition]) ).
fof(f520,definition,
( spl0_67
<=> zero(out1(or1(h2(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_67])],[avatar_definition]) ).
fof(f522,plain,
( spl0_66
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f515,f520,f517]) ).
fof(f538,plain,
( ~ one(out1(and2(h1(f))))
| one(in1(not1(h1(f)))) ),
inference(resolution,[],[f228,f2]) ).
fof(f547,definition,
( spl0_71
<=> one(in1(not1(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_71])],[avatar_definition]) ).
fof(f567,plain,
( ~ zero(out1(not1(h1(f))))
| zero(in2(and1(h1(f)))) ),
inference(resolution,[],[f235,f1]) ).
fof(f569,definition,
( spl0_74
<=> zero(in2(and1(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_74])],[avatar_definition]) ).
fof(f572,definition,
( spl0_75
<=> zero(out1(not1(h1(f)))) ),
introduced(definition,[new_symbols(definition,[spl0_75])],[avatar_definition]) ).
fof(f574,plain,
( spl0_74
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f567,f572,f569]) ).
fof(f619,plain,
( abnormal(and1(h1(f)))
| ~ zero(in2(and1(h1(f))))
| zero(out1(and1(h1(f)))) ),
inference(resolution,[],[f225,f84]) ).
fof(f622,plain,
( abnormal(and1(h2(f)))
| ~ zero(in1(and1(h2(f))))
| zero(out1(and1(h2(f)))) ),
inference(resolution,[],[f226,f85]) ).
fof(f649,plain,
( abnormal(or1(f))
| ~ one(in2(or1(f)))
| one(out1(or1(f))) ),
inference(resolution,[],[f239,f52]) ).
fof(f668,plain,
( abnormal(not1(h1(f)))
| ~ one(in1(not1(h1(f))))
| zero(out1(not1(h1(f)))) ),
inference(resolution,[],[f328,f84]) ).
fof(f674,plain,
( ~ one(in2(and2(h1(f))))
| one(out1(and2(h1(f))))
| abnormal(and2(h1(f)))
| ~ one(in1(and2(h1(f)))) ),
inference(resolution,[],[f318,f84]) ).
fof(f678,definition,
( spl0_84
<=> abnormal(and2(h1(f))) ),
introduced(definition,[new_symbols(definition,[spl0_84])],[avatar_definition]) ).
fof(f679,plain,
( abnormal(and2(h1(f)))
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f681,plain,
( ~ spl0_46
| spl0_84
| spl0_59
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f674,f420,f473,f678,f394]) ).
fof(f683,plain,
( spl0_71
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f538,f473,f547]) ).
fof(f686,plain,
( spl0_75
| ~ spl0_71
| spl0_4 ),
inference(avatar_split_clause,[],[f668,f75,f547,f572]) ).
fof(f690,plain,
( spl0_54
| ~ spl0_74
| spl0_5 ),
inference(avatar_split_clause,[],[f619,f79,f569,f444]) ).
fof(f693,plain,
( spl0_44
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f380,f248,f382]) ).
fof(f708,plain,
( ~ zero(in2(or1(h2(f))))
| zero(out1(or1(h2(f))))
| abnormal(or1(h2(f)))
| ~ zero(in1(or1(h2(f)))) ),
inference(resolution,[],[f331,f85]) ).
fof(f711,plain,
( ~ spl0_40
| spl0_1
| spl0_67
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f708,f382,f520,f64,f353]) ).
fof(f714,plain,
( spl0_25
| ~ spl0_32
| spl0_2 ),
inference(avatar_split_clause,[],[f649,f67,f280,f214]) ).
fof(f716,plain,
( spl0_57
| ~ spl0_66
| spl0_3 ),
inference(avatar_split_clause,[],[f622,f71,f517,f461]) ).
fof(f731,plain,
( ~ one(outs(f))
| ~ spl0_19 ),
inference(resolution,[],[f193,f5]) ).
fof(f732,plain,
( ~ spl0_21
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f731,f183,f190]) ).
fof(f735,plain,
( $false
| ~ spl0_84 ),
inference(resolution,[],[f679,f58]) ).
fof(f736,plain,
~ spl0_84,
inference(avatar_contradiction_clause,[],[f735]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f73]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f77]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f81]) ).
cnf(s5,plain,
( spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f114]) ).
cnf(s7,plain,
spl0_7,
inference(sat_conversion,[],[f123]) ).
cnf(s10,plain,
( spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s12,plain,
spl0_13,
inference(sat_conversion,[],[f149]) ).
cnf(s14,plain,
( spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f168]) ).
cnf(s16,plain,
spl0_17,
inference(sat_conversion,[],[f173]) ).
cnf(s19,plain,
( ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f195]) ).
cnf(s20,plain,
spl0_21,
inference(sat_conversion,[],[f198]) ).
cnf(s21,plain,
( spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f209]) ).
cnf(s23,plain,
spl0_23,
inference(sat_conversion,[],[f218]) ).
cnf(s24,plain,
( ~ spl0_22
| ~ spl0_25 ),
inference(sat_conversion,[],[f220]) ).
cnf(s25,plain,
( spl0_26
| ~ spl0_27 ),
inference(sat_conversion,[],[f253]) ).
cnf(s30,plain,
( spl0_32
| ~ spl0_33 ),
inference(sat_conversion,[],[f285]) ).
cnf(s39,plain,
( ~ spl0_6
| spl0_40 ),
inference(sat_conversion,[],[f356]) ).
cnf(s46,plain,
( ~ spl0_12
| spl0_46 ),
inference(sat_conversion,[],[f396]) ).
cnf(s51,plain,
( ~ spl0_16
| spl0_50 ),
inference(sat_conversion,[],[f422]) ).
cnf(s55,plain,
( spl0_27
| ~ spl0_54 ),
inference(sat_conversion,[],[f446]) ).
cnf(s58,plain,
( spl0_18
| ~ spl0_57 ),
inference(sat_conversion,[],[f463]) ).
cnf(s60,plain,
( spl0_33
| ~ spl0_59 ),
inference(sat_conversion,[],[f475]) ).
cnf(s67,plain,
( spl0_66
| ~ spl0_67 ),
inference(sat_conversion,[],[f522]) ).
cnf(s75,plain,
( spl0_74
| ~ spl0_75 ),
inference(sat_conversion,[],[f574]) ).
cnf(s90,plain,
( ~ spl0_46
| ~ spl0_50
| spl0_59
| spl0_84 ),
inference(sat_conversion,[],[f681]) ).
cnf(s91,plain,
( ~ spl0_59
| spl0_71 ),
inference(sat_conversion,[],[f683]) ).
cnf(s93,plain,
( spl0_4
| ~ spl0_71
| spl0_75 ),
inference(sat_conversion,[],[f686]) ).
cnf(s95,plain,
( spl0_5
| spl0_54
| ~ spl0_74 ),
inference(sat_conversion,[],[f690]) ).
cnf(s97,plain,
( ~ spl0_26
| spl0_44 ),
inference(sat_conversion,[],[f693]) ).
cnf(s99,plain,
( spl0_1
| ~ spl0_40
| ~ spl0_44
| spl0_67 ),
inference(sat_conversion,[],[f711]) ).
cnf(s101,plain,
( spl0_2
| spl0_25
| ~ spl0_32 ),
inference(sat_conversion,[],[f714]) ).
cnf(s102,plain,
( spl0_3
| spl0_57
| ~ spl0_66 ),
inference(sat_conversion,[],[f716]) ).
cnf(s112,plain,
( ~ spl0_19
| ~ spl0_21 ),
inference(sat_conversion,[],[f732]) ).
cnf(s115,plain,
~ spl0_84,
inference(sat_conversion,[],[f736]) ).
cnf(s117,plain,
( ~ spl0_46
| ~ spl0_50
| spl0_59 ),
inference(rat,[],[s90,s115]) ).
cnf(s118,plain,
spl0_22,
inference(rat,[],[s21,s23]) ).
cnf(s119,plain,
~ spl0_25,
inference(rat,[],[s24,s118]) ).
cnf(s120,plain,
~ spl0_19,
inference(rat,[],[s112,s20]) ).
cnf(s121,plain,
~ spl0_18,
inference(rat,[],[s19,s120]) ).
cnf(s122,plain,
~ spl0_57,
inference(rat,[],[s58,s121]) ).
cnf(s125,plain,
spl0_16,
inference(rat,[],[s14,s16]) ).
cnf(s126,plain,
spl0_50,
inference(rat,[],[s51,s125]) ).
cnf(s128,plain,
spl0_12,
inference(rat,[],[s10,s12]) ).
cnf(s129,plain,
spl0_46,
inference(rat,[],[s46,s128]) ).
cnf(s131,plain,
spl0_59,
inference(rat,[],[s117,s126,s129]) ).
cnf(s132,plain,
spl0_71,
inference(rat,[],[s91,s131]) ).
cnf(s133,plain,
spl0_33,
inference(rat,[],[s60,s131]) ).
cnf(s134,plain,
spl0_32,
inference(rat,[],[s30,s133]) ).
cnf(s135,plain,
spl0_2,
inference(rat,[],[s101,s119,s134]) ).
cnf(s136,plain,
spl0_6,
inference(rat,[],[s5,s7]) ).
cnf(s138,plain,
spl0_40,
inference(rat,[],[s39,s136]) ).
cnf(s142,plain,
~ spl0_5,
inference(rat,[],[s4,s135]) ).
cnf(s143,plain,
~ spl0_4,
inference(rat,[],[s3,s135]) ).
cnf(s144,plain,
spl0_75,
inference(rat,[],[s93,s132,s143]) ).
cnf(s146,plain,
spl0_74,
inference(rat,[],[s75,s144]) ).
cnf(s149,plain,
spl0_54,
inference(rat,[],[s95,s142,s146]) ).
cnf(s151,plain,
spl0_27,
inference(rat,[],[s55,s149]) ).
cnf(s153,plain,
spl0_26,
inference(rat,[],[s25,s151]) ).
cnf(s156,plain,
spl0_44,
inference(rat,[],[s97,s153]) ).
cnf(s157,plain,
~ spl0_3,
inference(rat,[],[s2,s135]) ).
cnf(s158,plain,
~ spl0_66,
inference(rat,[],[s102,s122,s157]) ).
cnf(s161,plain,
~ spl0_67,
inference(rat,[],[s67,s158]) ).
cnf(s164,plain,
spl0_1,
inference(rat,[],[s99,s156,s138,s161]) ).
cnf(s165,plain,
$false,
inference(rat,[],[s1,s135,s164]) ).
fof(f737,plain,
$false,
inference(avatar_sat_refutation,[],[s165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV007-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:57:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.20/1.36 % (2449959)Input is clausal, will run a generic CNF schedule.
% 3.20/1.36 % (2449980)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2454903224:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.20/1.36 % (2449985)dis-21_1_sil=8000:lcm=predicate:random_seed=1452018722:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.20/1.36 % (2449985)First to succeed.
% 3.20/1.36 % (2449985)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2449959"
% 3.20/1.36 % (2449983)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1709104438:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.20/1.36 % (2449982)lrs+10_1_sil=8000:sp=occurrence:random_seed=225066038:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.20/1.36 % (2449984)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2419680686:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.20/1.36 % (2449979)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2085883178:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.20/1.36 % (2449981)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3525561081:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.20/1.36 % (2449983)Refutation not found, incomplete strategy
% 3.20/1.36 % (2449983)------------------------------
% 3.20/1.36 % (2449983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.36 % (2449983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.36 % (2449983)CaDiCaL version: 2.1.3
% 3.20/1.36 % (2449983)Termination reason: Refutation not found, incomplete strategy
% 3.20/1.36 % (2449983)Time elapsed: 0.008 s
% 3.20/1.36 % (2449983)Peak memory usage: 87 MB
% 3.20/1.36 % (2449983)Instructions burned: 7 (million)
% 3.20/1.36 % (2449984)Also succeeded, but the first one will report.
% 3.20/1.36 % (2449982)Instruction limit reached!
% 3.20/1.36 % (2449982)------------------------------
% 3.20/1.36 % (2449982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.36 % (2449982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.36 % (2449982)CaDiCaL version: 2.1.3
% 3.20/1.36 % (2449982)Termination reason: Instruction limit
% 3.20/1.36 % (2449982)Termination phase: Saturation
% 3.20/1.36 % (2449982)Time elapsed: 0.073 s
% 3.20/1.36 % (2449982)Peak memory usage: 88 MB
% 3.20/1.36 % (2449982)Instructions burned: 109 (million)
% 3.20/1.36 % (2449994)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1738564159:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.20/1.36 % (2449994)Refutation not found, incomplete strategy
% 3.20/1.36 % (2449994)------------------------------
% 3.20/1.36 % (2449994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.36 % (2449994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.36 % (2449994)CaDiCaL version: 2.1.3
% 3.20/1.36 % (2449994)Termination reason: Refutation not found, incomplete strategy
% 3.20/1.36 % (2449994)Time elapsed: 0.002 s
% 3.20/1.36 % (2449994)Peak memory usage: 88 MB
% 3.20/1.36 % (2449994)Instructions burned: 1 (million)
% 3.20/1.36 % (2449985)Refutation found. Thanks to Tanya!
% 3.20/1.36 % SZS status Unsatisfiable for theBenchmark
% 3.20/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.56 % (2449985)------------------------------
% 3.91/1.56 % (2449985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.56 % (2449985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.56 % (2449985)CaDiCaL version: 2.1.3
% 3.91/1.56 % (2449985)Termination reason: Refutation
% 3.91/1.56 % (2449985)Time elapsed: 0.018 s
% 3.91/1.56 % (2449985)Peak memory usage: 89 MB
% 3.91/1.56 % (2449985)Instructions burned: 15 (million)
% 3.91/1.56 % (2449985)------------------------------
% 3.91/1.56 % (2449985)------------------------------
% 3.91/1.56 % (2449959)Success in time 0.463 s
% 3.91/1.56 % Vampire exiting
%------------------------------------------------------------------------------