%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC182-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:02:50 PM UTC 2026
% Result : Unsatisfiable 2.73s 1.27s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 82 ( 24 unt; 9 def)
% Number of atoms : 182 ( 21 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 198 ( 98 ~; 91 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f98,axiom,
! [X0,X1] :
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
fof(f99,plain,
! [X0,X1] :
( nil != cons(X0,X1)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(reorient_equations,[],[f98]) ).
fof(f121,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
inference(reorient_equations,[],[f121]) ).
fof(f123,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
inference(reorient_equations,[],[f123]) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f204,negated_conjecture,
nil = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f206,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,plain,
sk1 = app(app(sk6,cons(sk5,nil)),sk7),
inference(reorient_equations,[],[f210]) ).
fof(f215,plain,
sk3 = app(app(sk6,cons(sk5,sk3)),sk7),
inference(definition_unfolding,[],[f211,f206,f204]) ).
fof(f218,plain,
! [X0,X1] :
( app(X0,X1) != sk3
| ~ ssList(X1)
| ~ ssList(X0)
| sk3 = X1 ),
inference(definition_unfolding,[],[f124,f204,f204]) ).
fof(f219,plain,
! [X0,X1] :
( app(X0,X1) != sk3
| ~ ssList(X1)
| ~ ssList(X0)
| sk3 = X0 ),
inference(definition_unfolding,[],[f122,f204,f204]) ).
fof(f220,plain,
! [X0,X1] :
( cons(X0,X1) != sk3
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(definition_unfolding,[],[f99,f204]) ).
fof(f279,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f280,plain,
sQ0_eqProxy(sk3,app(app(sk6,cons(sk5,sk3)),sk7)),
inference(equality_proxy_replacement,[],[f215,f279]) ).
fof(f289,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(app(X0,X1),sk3)
| ~ ssList(X1)
| ~ ssList(X0)
| sQ0_eqProxy(sk3,X1) ),
inference(equality_proxy_replacement,[],[f218,f279,f279]) ).
fof(f290,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(app(X0,X1),sk3)
| ~ ssList(X1)
| ~ ssList(X0)
| sQ0_eqProxy(sk3,X0) ),
inference(equality_proxy_replacement,[],[f219,f279,f279]) ).
fof(f292,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(cons(X0,X1),sk3)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(equality_proxy_replacement,[],[f220,f279]) ).
fof(f332,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f279]) ).
fof(f341,definition,
( spl1_2
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f342,plain,
( ~ ssList(sk3)
| spl1_2 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f371,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f342,f202]) ).
fof(f372,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f389,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(sk3,cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(resolution,[],[f332,f292]) ).
fof(f390,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(sk3,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| sQ0_eqProxy(sk3,X0) ),
inference(resolution,[],[f332,f290]) ).
fof(f391,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(sk3,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| sQ0_eqProxy(sk3,X1) ),
inference(resolution,[],[f332,f289]) ).
fof(f406,plain,
( ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,sk3)))
| sQ0_eqProxy(sk3,app(sk6,cons(sk5,sk3))) ),
inference(resolution,[],[f390,f280]) ).
fof(f421,definition,
( spl1_11
<=> sQ0_eqProxy(sk3,app(sk6,cons(sk5,sk3))) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f422,plain,
( sQ0_eqProxy(sk3,app(sk6,cons(sk5,sk3)))
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f424,definition,
( spl1_12
<=> ssList(app(sk6,cons(sk5,sk3))) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f425,plain,
( ~ ssList(app(sk6,cons(sk5,sk3)))
| spl1_12 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f427,definition,
( spl1_13
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f428,plain,
( ~ ssList(sk7)
| spl1_13 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f429,plain,
( spl1_11
| ~ spl1_12
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f406,f427,f424,f421]) ).
fof(f430,plain,
( ~ ssList(sk6)
| ~ ssList(cons(sk5,sk3))
| spl1_12 ),
inference(resolution,[],[f425,f85]) ).
fof(f432,definition,
( spl1_14
<=> ssList(cons(sk5,sk3)) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f433,plain,
( ~ ssList(cons(sk5,sk3))
| spl1_14 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f435,definition,
( spl1_15
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f436,plain,
( ~ ssList(sk6)
| spl1_15 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f437,plain,
( ~ spl1_14
| ~ spl1_15
| spl1_12 ),
inference(avatar_split_clause,[],[f430,f424,f435,f432]) ).
fof(f448,plain,
! [X0] :
( ssList(cons(sk5,X0))
| ~ ssList(X0) ),
inference(resolution,[],[f86,f207]) ).
fof(f449,plain,
( ~ ssList(sk3)
| spl1_14 ),
inference(resolution,[],[f448,f433]) ).
fof(f450,plain,
( ~ spl1_2
| spl1_14 ),
inference(avatar_split_clause,[],[f449,f432,f341]) ).
fof(f451,plain,
( $false
| spl1_15 ),
inference(resolution,[],[f436,f208]) ).
fof(f452,plain,
spl1_15,
inference(avatar_contradiction_clause,[],[f451]) ).
fof(f453,plain,
( $false
| spl1_13 ),
inference(resolution,[],[f428,f209]) ).
fof(f454,plain,
spl1_13,
inference(avatar_contradiction_clause,[],[f453]) ).
fof(f462,plain,
( ~ ssList(cons(sk5,sk3))
| ~ ssList(sk6)
| sQ0_eqProxy(sk3,cons(sk5,sk3))
| ~ spl1_11 ),
inference(resolution,[],[f391,f422]) ).
fof(f477,definition,
( spl1_17
<=> sQ0_eqProxy(sk3,cons(sk5,sk3)) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f478,plain,
( sQ0_eqProxy(sk3,cons(sk5,sk3))
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f479,plain,
( spl1_17
| ~ spl1_15
| ~ spl1_14
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f462,f421,f432,f435,f477]) ).
fof(f484,plain,
( ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ spl1_17 ),
inference(resolution,[],[f478,f389]) ).
fof(f486,definition,
( spl1_19
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
fof(f487,plain,
( ~ ssItem(sk5)
| spl1_19 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f488,plain,
( ~ spl1_2
| ~ spl1_19
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f484,f477,f486,f341]) ).
fof(f489,plain,
( $false
| spl1_19 ),
inference(resolution,[],[f487,f207]) ).
fof(f490,plain,
spl1_19,
inference(avatar_contradiction_clause,[],[f489]) ).
cnf(s8,plain,
spl1_2,
inference(sat_conversion,[],[f372]) ).
cnf(s11,plain,
( spl1_11
| ~ spl1_12
| ~ spl1_13 ),
inference(sat_conversion,[],[f429]) ).
cnf(s12,plain,
( spl1_12
| ~ spl1_14
| ~ spl1_15 ),
inference(sat_conversion,[],[f437]) ).
cnf(s13,plain,
( ~ spl1_2
| spl1_14 ),
inference(sat_conversion,[],[f450]) ).
cnf(s14,plain,
spl1_15,
inference(sat_conversion,[],[f452]) ).
cnf(s15,plain,
spl1_13,
inference(sat_conversion,[],[f454]) ).
cnf(s17,plain,
( ~ spl1_11
| ~ spl1_14
| ~ spl1_15
| spl1_17 ),
inference(sat_conversion,[],[f479]) ).
cnf(s19,plain,
( ~ spl1_2
| ~ spl1_17
| ~ spl1_19 ),
inference(sat_conversion,[],[f488]) ).
cnf(s20,plain,
spl1_19,
inference(sat_conversion,[],[f490]) ).
cnf(s21,plain,
( ~ spl1_2
| ~ spl1_17 ),
inference(rat,[],[s19,s20]) ).
cnf(s22,plain,
( spl1_12
| ~ spl1_14 ),
inference(rat,[],[s12,s14]) ).
cnf(s23,plain,
( spl1_11
| ~ spl1_12 ),
inference(rat,[],[s11,s15]) ).
cnf(s24,plain,
~ spl1_17,
inference(rat,[],[s21,s8]) ).
cnf(s25,plain,
spl1_14,
inference(rat,[],[s13,s8]) ).
cnf(s27,plain,
~ spl1_11,
inference(rat,[],[s17,s24,s14,s25]) ).
cnf(s28,plain,
spl1_12,
inference(rat,[],[s22,s25]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s23,s28,s27]) ).
fof(f491,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC182-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 08:20:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.73/1.27 % (1627431)Input is clausal, will run a generic CNF schedule.
% 2.73/1.27 % (1627442)dis-21_1_sil=8000:lcm=predicate:random_seed=1453923032: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)
% 2.73/1.27 % (1627442)First to succeed.
% 2.73/1.27 % (1627442)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1627431"
% 2.73/1.27 % (1627438)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1778974063:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.73/1.27 % (1627437)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=228279685:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.73/1.27 % (1627436)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=2576608365:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.73/1.27 % (1627440)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2684018382:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.73/1.27 % (1627439)lrs+10_1_sil=8000:sp=occurrence:random_seed=1908548143:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.73/1.27 % (1627441)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4085018360:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.73/1.27 % (1627440)Also succeeded, but the first one will report.
% 2.73/1.27 % (1627439)Also succeeded, but the first one will report.
% 2.73/1.27 % (1627441)Also succeeded, but the first one will report.
% 2.73/1.27 % (1627442)Refutation found. Thanks to Tanya!
% 2.73/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.73/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.27 % (1627442)------------------------------
% 2.73/1.27 % (1627442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.27 % (1627442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.27 % (1627442)CaDiCaL version: 2.1.3
% 2.73/1.27 % (1627442)Termination reason: Refutation
% 2.73/1.27 % (1627442)Time elapsed: 0.004 s
% 2.73/1.27 % (1627442)Peak memory usage: 89 MB
% 2.73/1.27 % (1627442)Instructions burned: 10 (million)
% 2.73/1.27 % (1627442)------------------------------
% 2.73/1.27 % (1627442)------------------------------
% 2.73/1.27 % (1627431)Success in time 0.322 s
% 2.73/1.27 % Vampire exiting
%------------------------------------------------------------------------------