%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC325-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 01:03:28 PM UTC 2026
% Result : Unsatisfiable 3.58s 1.28s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 75 ( 13 unt; 7 def)
% Number of atoms : 180 ( 43 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 215 ( 110 ~; 98 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != sk2
| app(X1,X0) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f211,plain,
( sk3 = app(cons(sk5,nil),sk6)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f213,plain,
( sk4 = app(sk6,cons(sk5,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f212]) ).
fof(f216,plain,
! [X0,X1] :
( app(X1,X0) != sk3
| ~ ssList(X1)
| app(X0,X1) != sk4
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f206,f204,f205]) ).
fof(f232,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f233,plain,
( ~ neq(sk4,nil)
| spl0_3 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,definition,
( spl0_4
<=> sk4 = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f236,plain,
( sk4 = app(sk6,cons(sk5,nil))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f237,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f213,f235,f232]) ).
fof(f239,definition,
( spl0_5
<=> sk3 = app(cons(sk5,nil),sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f240,plain,
( sk3 = app(cons(sk5,nil),sk6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f241,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f211,f239,f232]) ).
fof(f243,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f244,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f209,f243,f232]) ).
fof(f247,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f248,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f208,f247,f232]) ).
fof(f251,definition,
( spl0_8
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f252,plain,
( nil != sk4
| spl0_8 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,definition,
( spl0_9
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f255,plain,
( nil = sk3
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( ~ spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f207,f254,f251]) ).
fof(f259,plain,
! [X0] :
( sk3 != X0
| ~ ssList(X0)
| app(nil,X0) != sk4
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f216,f73]) ).
fof(f260,plain,
! [X0] :
( sk3 != X0
| ~ ssList(X0)
| app(nil,X0) != sk4
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f259]) ).
fof(f261,plain,
! [X0] :
( app(nil,X0) != sk4
| ~ ssList(X0)
| sk3 != X0 ),
inference(forward_subsumption_resolution,[],[f260,f8]) ).
fof(f265,plain,
! [X0] :
( sk4 != X0
| ~ ssList(X0)
| sk3 != X0
| ~ ssList(X0) ),
inference(superposition,[],[f261,f74]) ).
fof(f266,plain,
! [X0] :
( sk4 != X0
| ~ ssList(X0)
| sk3 != X0 ),
inference(duplicate_literal_removal,[],[f265]) ).
fof(f273,plain,
( ~ ssList(sk4)
| sk3 != sk4 ),
inference(equality_resolution,[],[f266]) ).
fof(f274,plain,
sk3 != sk4,
inference(forward_subsumption_resolution,[],[f273,f203]) ).
fof(f277,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| nil = sk4
| spl0_3 ),
inference(resolution,[],[f102,f233]) ).
fof(f282,plain,
( ~ ssList(nil)
| nil = sk4
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f277,f203]) ).
fof(f283,plain,
( nil = sk4
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f282,f8]) ).
fof(f284,plain,
( $false
| spl0_3
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f283,f252]) ).
fof(f285,plain,
( spl0_3
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f284]) ).
fof(f286,plain,
( nil != sk4
| ~ spl0_9 ),
inference(superposition,[],[f274,f255]) ).
fof(f289,plain,
( ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f286,f254,f251]) ).
fof(f293,plain,
( sk3 != sk3
| ~ ssList(cons(sk5,nil))
| sk4 != app(sk6,cons(sk5,nil))
| ~ ssList(sk6)
| ~ spl0_5 ),
inference(superposition,[],[f216,f240]) ).
fof(f294,plain,
( ~ ssList(cons(sk5,nil))
| sk4 != app(sk6,cons(sk5,nil))
| ~ ssList(sk6)
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f293]) ).
fof(f295,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f294,f236]) ).
fof(f296,plain,
( ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f295,f244]) ).
fof(f301,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(resolution,[],[f296,f86]) ).
fof(f302,plain,
( ~ ssItem(sk5)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f301,f8]) ).
fof(f303,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f302,f248]) ).
fof(f304,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f303]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f237]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f241]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f245]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f249]) ).
cnf(s6,plain,
( ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f256]) ).
cnf(s8,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f285]) ).
cnf(s9,plain,
( ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f289]) ).
cnf(s10,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f304]) ).
cnf(s12,plain,
~ spl0_8,
inference(rat,[],[s6,s9]) ).
cnf(s13,plain,
spl0_3,
inference(rat,[],[s8,s12]) ).
cnf(s14,plain,
spl0_7,
inference(rat,[],[s5,s13]) ).
cnf(s15,plain,
spl0_6,
inference(rat,[],[s4,s13]) ).
cnf(s16,plain,
spl0_5,
inference(rat,[],[s3,s13]) ).
cnf(s17,plain,
spl0_4,
inference(rat,[],[s2,s13]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s10,s14,s15,s16,s17]) ).
fof(f305,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC325-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:08:24 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.58/1.28 % (3242567)Input is clausal, will run a generic CNF schedule.
% 3.58/1.28 % (3242669)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=452873013:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.58/1.28 % (3242666)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=2652293978:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.58/1.28 % (3242674)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2365411116:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.58/1.28 % (3242667)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=351264009:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.58/1.28 % (3242672)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1180958779:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.58/1.28 % (3242671)lrs+10_1_sil=8000:sp=occurrence:random_seed=1823943272:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.58/1.28 % (3242675)dis-21_1_sil=8000:lcm=predicate:random_seed=1663823604: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)
% 3.58/1.28 % (3242672)First to succeed.
% 3.58/1.28 % (3242671)Also succeeded, but the first one will report.
% 3.58/1.28 % (3242672)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3242567"
% 3.58/1.28 % (3242674)Also succeeded, but the first one will report.
% 3.58/1.28 % (3242675)Instruction limit reached!
% 3.58/1.28 % (3242675)------------------------------
% 3.58/1.28 % (3242675)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.28 % (3242675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.28 % (3242675)CaDiCaL version: 2.1.3
% 3.58/1.28 % (3242675)Termination reason: Instruction limit
% 3.58/1.28 % (3242675)Termination phase: Saturation
% 3.58/1.28 % (3242675)Time elapsed: 0.060 s
% 3.58/1.28 % (3242675)Peak memory usage: 89 MB
% 3.58/1.28 % (3242675)Instructions burned: 118 (million)
% 3.58/1.28 % (3242756)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=3282477071:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.58/1.28 % (3242756)Also succeeded, but the first one will report.
% 3.58/1.28 % (3242672)Refutation found. Thanks to Tanya!
% 3.58/1.28 % SZS status Unsatisfiable for theBenchmark
% 3.58/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.28 % (3242672)------------------------------
% 3.58/1.28 % (3242672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.28 % (3242672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.28 % (3242672)CaDiCaL version: 2.1.3
% 3.58/1.28 % (3242672)Termination reason: Refutation
% 3.58/1.28 % (3242672)Time elapsed: 0.005 s
% 3.58/1.28 % (3242672)Peak memory usage: 90 MB
% 3.58/1.28 % (3242672)Instructions burned: 5 (million)
% 3.58/1.28 % (3242672)------------------------------
% 3.58/1.28 % (3242672)------------------------------
% 3.58/1.28 % (3242567)Success in time 0.416 s
% 3.58/1.28 % Vampire exiting
%------------------------------------------------------------------------------