%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC029-1 : 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 : n006.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 01:02:07 PM UTC 2026
% Result : Unsatisfiable 1.96s 1.05s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 25
% Syntax : Number of formulae : 88 ( 9 unt; 9 def)
% Number of atoms : 243 ( 54 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 290 ( 135 ~; 146 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
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(f121,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
inference(reorient_equations,[],[f123]) ).
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,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f211]) ).
fof(f213,negated_conjecture,
( nil = sk2
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f216,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f219,plain,
( nil = sk4
| nil = sk3 ),
inference(definition_unfolding,[],[f213,f204,f205]) ).
fof(f222,plain,
( nil != sk3
| nil != sk4 ),
inference(definition_unfolding,[],[f216,f205,f204]) ).
fof(f231,definition,
( spl0_1
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f233,plain,
( nil != sk4
| spl0_1 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f235,definition,
( spl0_2
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f236,plain,
( nil = sk3
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f222,f235,f231]) ).
fof(f239,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f219,f231,f235]) ).
fof(f241,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f243,plain,
( ~ neq(sk4,nil)
| spl0_3 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f245,definition,
( spl0_4
<=> sk3 = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f247,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f212,f245,f241]) ).
fof(f250,definition,
( spl0_5
<=> sk4 = app(cons(sk5,nil),sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f252,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f210,f250,f241]) ).
fof(f255,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f257,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f258,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f208,f255,f241]) ).
fof(f260,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f262,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f263,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f207,f260,f241]) ).
fof(f264,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f206,f235,f231]) ).
fof(f268,plain,
nil = app(nil,nil),
inference(resolution,[],[f73,f8]) ).
fof(f282,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| nil = sk4
| spl0_3 ),
inference(resolution,[],[f102,f243]) ).
fof(f287,plain,
( ~ ssList(nil)
| nil = sk4
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f282,f203]) ).
fof(f288,plain,
( nil = sk4
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f287,f8]) ).
fof(f289,plain,
( $false
| spl0_1
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f288,f233]) ).
fof(f290,plain,
( spl0_1
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f289]) ).
fof(f291,plain,
( nil = app(sk6,cons(sk5,nil))
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f247,f236]) ).
fof(f304,plain,
( nil != nil
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| nil = sk6
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f122,f291]) ).
fof(f306,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| nil = sk6
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f304]) ).
fof(f307,plain,
( ~ ssList(cons(sk5,nil))
| nil = sk6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f306,f257]) ).
fof(f309,definition,
( spl0_8
<=> nil = sk6 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f311,plain,
( nil = sk6
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f313,definition,
( spl0_9
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f314,plain,
( ssList(cons(sk5,nil))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f315,plain,
( ~ ssList(cons(sk5,nil))
| spl0_9 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f316,plain,
( spl0_8
| ~ spl0_9
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f307,f255,f245,f235,f313,f309]) ).
fof(f320,plain,
( nil != nil
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| nil = cons(sk5,nil)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f124,f291]) ).
fof(f321,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| nil = cons(sk5,nil)
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f320]) ).
fof(f322,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_9 ),
inference(resolution,[],[f315,f86]) ).
fof(f323,plain,
( ~ ssItem(sk5)
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f322,f8]) ).
fof(f324,plain,
( $false
| ~ spl0_7
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f323,f262]) ).
fof(f325,plain,
( ~ spl0_7
| spl0_9 ),
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f326,plain,
( ~ ssList(sk6)
| nil = cons(sk5,nil)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f321,f314]) ).
fof(f327,plain,
( nil = cons(sk5,nil)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f326,f257]) ).
fof(f333,plain,
( sk4 = app(cons(sk5,nil),nil)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f252,f311]) ).
fof(f335,plain,
( sk4 = app(nil,nil)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f333,f327]) ).
fof(f337,plain,
( nil = sk4
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f335,f268]) ).
fof(f338,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f337,f233]) ).
fof(f339,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f338]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f238]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f239]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f253]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f258]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f263]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f264]) ).
cnf(s8,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f290]) ).
cnf(s9,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f316]) ).
cnf(s10,plain,
( ~ spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f325]) ).
cnf(s11,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f339]) ).
cnf(s12,plain,
spl0_1,
inference(rat,[],[s11,s9,s10,s3,s4,s5,s6,s2,s8]) ).
cnf(s13,plain,
spl0_2,
inference(rat,[],[s7,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s13,s12]) ).
fof(f340,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC029-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 07:30:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 1.96/1.05 % (3798492)Input is clausal, will run a generic CNF schedule.
% 1.96/1.05 % (3798497)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=2995320372:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.96/1.05 % (3798502)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3067758865:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.96/1.05 % (3798500)lrs+10_1_sil=8000:sp=occurrence:random_seed=57641500:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.96/1.05 % (3798503)dis-21_1_sil=8000:lcm=predicate:random_seed=3612334057: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)
% 1.96/1.05 % (3798499)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3670316784:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.96/1.05 % (3798501)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=211557899:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.96/1.05 % (3798498)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1406869228:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.96/1.05 % (3798500)First to succeed.
% 1.96/1.05 % (3798501)Also succeeded, but the first one will report.
% 1.96/1.05 % (3798500)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3798492"
% 1.96/1.05 % (3798502)Also succeeded, but the first one will report.
% 1.96/1.05 % (3798503)Instruction limit reached!
% 1.96/1.05 % (3798503)------------------------------
% 1.96/1.05 % (3798503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.96/1.05 % (3798503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.96/1.05 % (3798503)CaDiCaL version: 2.1.3
% 1.96/1.05 % (3798503)Termination reason: Instruction limit
% 1.96/1.05 % (3798503)Termination phase: Saturation
% 1.96/1.05 % (3798503)Time elapsed: 0.068 s
% 1.96/1.05 % (3798503)Peak memory usage: 90 MB
% 1.96/1.05 % (3798503)Instructions burned: 117 (million)
% 1.96/1.05 % (3798511)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=2174644772:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.96/1.05 % (3798511)Also succeeded, but the first one will report.
% 1.96/1.05 % (3798500)Refutation found. Thanks to Tanya!
% 1.96/1.05 % SZS status Unsatisfiable for theBenchmark
% 1.96/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.25 % (3798500)------------------------------
% 3.51/1.25 % (3798500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.25 % (3798500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.25 % (3798500)CaDiCaL version: 2.1.3
% 3.51/1.25 % (3798500)Termination reason: Refutation
% 3.51/1.25 % (3798500)Time elapsed: 0.006 s
% 3.51/1.25 % (3798500)Peak memory usage: 89 MB
% 3.51/1.25 % (3798500)Instructions burned: 5 (million)
% 3.51/1.25 % (3798500)------------------------------
% 3.51/1.25 % (3798500)------------------------------
% 3.51/1.25 % (3798492)Success in time 0.441 s
% 3.51/1.25 % Vampire exiting
%------------------------------------------------------------------------------