%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC004-1 : 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 : n019.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 01:02:00 PM UTC 2026
% Result : Unsatisfiable 3.50s 1.24s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 85 ( 17 unt; 10 def)
% Number of atoms : 227 ( 29 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 284 ( 142 ~; 132 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f100,axiom,
! [X0,X1] :
( cons(X0,X1) != X1
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f216,negated_conjecture,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) != sk2
| app(X0,X2) != sk1
| ~ neq(X1,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f217,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f218,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f219,negated_conjecture,
( ssList(sk7)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f220,negated_conjecture,
( app(app(sk6,cons(sk5,nil)),sk7) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
fof(f221,plain,
( sk4 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f220]) ).
fof(f222,negated_conjecture,
( app(sk6,sk7) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
fof(f223,plain,
( sk3 = app(sk6,sk7)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f222]) ).
fof(f226,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f206,f204,f204]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) != sk4
| app(X0,X2) != sk3
| ~ neq(X1,nil)
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f216,f204,f205]) ).
fof(f242,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f251,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f254,definition,
( spl0_4
<=> sk3 = app(sk6,sk7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f255,plain,
( sk3 = app(sk6,sk7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f223,f254,f251]) ).
fof(f258,definition,
( spl0_5
<=> sk4 = app(app(sk6,cons(sk5,nil)),sk7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f259,plain,
( sk4 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f260,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f221,f258,f251]) ).
fof(f262,definition,
( spl0_6
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f263,plain,
( ssList(sk7)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f264,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f219,f262,f251]) ).
fof(f266,definition,
( spl0_7
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f267,plain,
( ssList(sk6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f268,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f218,f266,f251]) ).
fof(f270,definition,
( spl0_8
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f271,plain,
( ssItem(sk5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f272,plain,
( ~ spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f217,f270,f251]) ).
fof(f274,definition,
( spl0_9
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ neq(X1,nil)
| app(X0,X2) != sk3
| app(app(X0,X1),X2) != sk4
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f275,plain,
( ! [X2,X0,X1] :
( app(app(X0,X1),X2) != sk4
| ~ neq(X1,nil)
| app(X0,X2) != sk3
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f276,plain,
( ~ spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f234,f274,f251]) ).
fof(f284,plain,
spl0_3,
inference(avatar_split_clause,[],[f242,f251]) ).
fof(f289,plain,
( sk4 != sk4
| ~ neq(cons(sk5,nil),nil)
| sk3 != app(sk6,sk7)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f275,f259]) ).
fof(f290,plain,
( ~ neq(cons(sk5,nil),nil)
| sk3 != app(sk6,sk7)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ spl0_5
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f289]) ).
fof(f291,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f290,f255]) ).
fof(f294,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f291,f267]) ).
fof(f306,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f294,f263]) ).
fof(f312,definition,
( spl0_14
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f313,plain,
( ~ ssList(cons(sk5,nil))
| spl0_14 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f315,definition,
( spl0_15
<=> neq(cons(sk5,nil),nil) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f316,plain,
( ~ neq(cons(sk5,nil),nil)
| spl0_15 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f317,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f306,f274,f266,f262,f258,f254,f315,f312]) ).
fof(f380,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| nil = cons(sk5,nil)
| spl0_15 ),
inference(resolution,[],[f102,f316]) ).
fof(f383,plain,
( ~ ssList(cons(sk5,nil))
| nil = cons(sk5,nil)
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f380,f8]) ).
fof(f386,definition,
( spl0_22
<=> nil = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f387,plain,
( nil = cons(sk5,nil)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f388,plain,
( spl0_22
| ~ spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f383,f315,f312,f386]) ).
fof(f428,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_14 ),
inference(resolution,[],[f313,f86]) ).
fof(f429,plain,
( ~ ssItem(sk5)
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f428,f8]) ).
fof(f430,plain,
( $false
| ~ spl0_8
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f429,f271]) ).
fof(f431,plain,
( ~ spl0_8
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f430]) ).
fof(f454,plain,
( nil != nil
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ spl0_22 ),
inference(superposition,[],[f100,f387]) ).
fof(f458,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f454]) ).
fof(f460,plain,
( ~ ssList(nil)
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f458,f271]) ).
fof(f464,plain,
( $false
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f460,f8]) ).
fof(f465,plain,
( ~ spl0_8
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f464]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f256]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f260]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f264]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f268]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f272]) ).
cnf(s7,plain,
( ~ spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f276]) ).
cnf(s14,plain,
spl0_3,
inference(sat_conversion,[],[f284]) ).
cnf(s18,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f317]) ).
cnf(s22,plain,
( ~ spl0_14
| spl0_15
| spl0_22 ),
inference(sat_conversion,[],[f388]) ).
cnf(s25,plain,
( ~ spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f431]) ).
cnf(s27,plain,
( ~ spl0_8
| ~ spl0_22 ),
inference(sat_conversion,[],[f465]) ).
cnf(s28,plain,
spl0_9,
inference(rat,[],[s7,s14]) ).
cnf(s29,plain,
spl0_8,
inference(rat,[],[s6,s14]) ).
cnf(s30,plain,
~ spl0_22,
inference(rat,[],[s27,s29]) ).
cnf(s31,plain,
spl0_14,
inference(rat,[],[s25,s29]) ).
cnf(s32,plain,
spl0_15,
inference(rat,[],[s22,s30,s31]) ).
cnf(s33,plain,
spl0_7,
inference(rat,[],[s5,s14]) ).
cnf(s34,plain,
spl0_6,
inference(rat,[],[s4,s14]) ).
cnf(s35,plain,
spl0_5,
inference(rat,[],[s3,s14]) ).
cnf(s36,plain,
~ spl0_4,
inference(rat,[],[s18,s32,s31,s28,s33,s34,s35]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s2,s36,s14]) ).
fof(f467,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC004-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.35 % Computer : n019.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 28 07:24:03 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 3.50/1.24 % (3824824)Input is clausal, will run a generic CNF schedule.
% 3.50/1.24 % (3824834)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1419144878:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.50/1.24 % (3824832)lrs+10_1_sil=8000:sp=occurrence:random_seed=2246199608:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.50/1.24 % (3824835)dis-21_1_sil=8000:lcm=predicate:random_seed=3835039842: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)
% 3.50/1.24 % (3824830)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1988591253:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.50/1.24 % (3824831)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3792897115:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.50/1.24 % (3824829)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=3206790049:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.50/1.24 % (3824833)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2588049503:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.50/1.24 % (3824833)First to succeed.
% 3.50/1.24 % (3824833)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3824824"
% 3.50/1.24 % (3824832)Also succeeded, but the first one will report.
% 3.50/1.24 % (3824834)Also succeeded, but the first one will report.
% 3.50/1.24 % (3824835)Also succeeded, but the first one will report.
% 3.50/1.24 % (3824833)Refutation found. Thanks to Tanya!
% 3.50/1.24 % SZS status Unsatisfiable for theBenchmark
% 3.50/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.24 % (3824833)------------------------------
% 3.50/1.24 % (3824833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.24 % (3824833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.24 % (3824833)CaDiCaL version: 2.1.3
% 3.50/1.24 % (3824833)Termination reason: Refutation
% 3.50/1.24 % (3824833)Time elapsed: 0.007 s
% 3.50/1.24 % (3824833)Peak memory usage: 90 MB
% 3.50/1.24 % (3824833)Instructions burned: 8 (million)
% 3.50/1.24 % (3824833)------------------------------
% 3.50/1.24 % (3824833)------------------------------
% 3.50/1.24 % (3824824)Success in time 0.445 s
% 3.50/1.24 % Vampire exiting
%------------------------------------------------------------------------------