%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC392-1 : 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 : n007.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 01:03:47 PM UTC 2026
% Result : Unsatisfiable 3.80s 1.32s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 66 ( 14 unt; 5 def)
% Number of atoms : 161 ( 32 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 179 ( 84 ~; 90 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 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(f71,axiom,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f98,axiom,
! [X0,X1] :
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
fof(f99,plain,
! [X0,X1] :
( nil != cons(X0,X1)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(reorient_equations,[],[f98]) ).
fof(f173,axiom,
! [X2,X0,X1] :
( ~ memberP(cons(X0,X1),X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X2)
| memberP(X1,X2)
| X2 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X0,X1),X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X2)
| memberP(X1,X2)
| X0 = X2 ),
inference(reorient_equations,[],[f173]) ).
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,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
memberP(sk1,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
~ memberP(sk2,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( ssItem(sk6)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
( ssItem(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f212,plain,
( sk3 = cons(sk6,nil)
| nil = sk4 ),
inference(reorient_equations,[],[f211]) ).
fof(f215,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f216,plain,
( sk3 = cons(sk6,nil)
| nil = sk3 ),
inference(reorient_equations,[],[f215]) ).
fof(f217,negated_conjecture,
( memberP(sk4,sk6)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f221,plain,
memberP(sk3,sk5),
inference(definition_unfolding,[],[f207,f205]) ).
fof(f222,plain,
~ memberP(sk4,sk5),
inference(definition_unfolding,[],[f208,f204]) ).
fof(f230,definition,
( spl0_1
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f232,plain,
( nil = sk3
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f238,definition,
( spl0_3
<=> memberP(sk4,sk6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f240,plain,
( memberP(sk4,sk6)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f241,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f217,f238,f230]) ).
fof(f243,definition,
( spl0_4
<=> sk3 = cons(sk6,nil) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f245,plain,
( sk3 = cons(sk6,nil)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f246,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f216,f243,f230]) ).
fof(f248,definition,
( spl0_5
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f250,plain,
( nil = sk4
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f253,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f212,f243,f248]) ).
fof(f255,definition,
( spl0_6
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f257,plain,
( ssItem(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f258,plain,
( spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f210,f255,f230]) ).
fof(f259,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f209,f255,f248]) ).
fof(f275,plain,
( nil != sk3
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ spl0_4 ),
inference(superposition,[],[f99,f245]) ).
fof(f276,plain,
( nil != sk3
| ~ ssList(nil)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f275,f257]) ).
fof(f277,plain,
( nil != sk3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f276,f8]) ).
fof(f278,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f277,f255,f243,f230]) ).
fof(f522,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssItem(X0)
| memberP(nil,X0)
| sk6 = X0 )
| ~ spl0_4 ),
inference(superposition,[],[f174,f245]) ).
fof(f525,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(sk6)
| ~ ssItem(X0)
| memberP(nil,X0)
| sk6 = X0 )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f522,f8]) ).
fof(f526,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0)
| memberP(nil,X0)
| sk6 = X0 )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f525,f257]) ).
fof(f527,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0)
| sk6 = X0 )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f526,f71]) ).
fof(f528,plain,
( ~ ssItem(sk5)
| sk5 = sk6
| ~ spl0_4
| ~ spl0_6 ),
inference(resolution,[],[f527,f221]) ).
fof(f530,plain,
( sk5 = sk6
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f528,f206]) ).
fof(f541,plain,
( memberP(sk4,sk5)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f240,f530]) ).
fof(f552,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f541,f222]) ).
fof(f553,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f552]) ).
fof(f555,plain,
( memberP(nil,sk5)
| ~ spl0_1 ),
inference(superposition,[],[f221,f232]) ).
fof(f559,plain,
( ~ memberP(nil,sk5)
| ~ spl0_5 ),
inference(superposition,[],[f222,f250]) ).
fof(f565,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f559,f555]) ).
fof(f566,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f565]) ).
cnf(s2,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f241]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f246]) ).
cnf(s6,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f253]) ).
cnf(s7,plain,
( spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f258]) ).
cnf(s8,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f259]) ).
cnf(s9,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f278]) ).
cnf(s12,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f553]) ).
cnf(s13,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f566]) ).
cnf(s15,plain,
spl0_1,
inference(rat,[],[s12,s2,s3,s7]) ).
cnf(s16,plain,
~ spl0_5,
inference(rat,[],[s13,s15]) ).
cnf(s17,plain,
spl0_6,
inference(rat,[],[s8,s16]) ).
cnf(s18,plain,
spl0_4,
inference(rat,[],[s6,s16]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s9,s15,s17,s18]) ).
fof(f569,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC392-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 09:24:25 UTC 2026
% 0.08/0.18 % 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
% 3.80/1.32 % (2265286)Input is clausal, will run a generic CNF schedule.
% 3.80/1.32 % (2265291)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=2736184820:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.80/1.32 % (2265296)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2783090466:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.80/1.32 % (2265295)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=396126916:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.80/1.32 % (2265292)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2941063145:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.80/1.32 % (2265297)dis-21_1_sil=8000:lcm=predicate:random_seed=735546939: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)
% 3.80/1.32 % (2265293)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1245433702:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.80/1.32 % (2265294)lrs+10_1_sil=8000:sp=occurrence:random_seed=1684611509:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.80/1.32 % (2265294)First to succeed.
% 3.80/1.32 % (2265294)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2265286"
% 3.80/1.32 % (2265295)Also succeeded, but the first one will report.
% 3.80/1.32 % (2265296)Also succeeded, but the first one will report.
% 3.80/1.32 % (2265297)Instruction limit reached!
% 3.80/1.32 % (2265297)------------------------------
% 3.80/1.32 % (2265297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.32 % (2265297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.32 % (2265297)CaDiCaL version: 2.1.3
% 3.80/1.32 % (2265297)Termination reason: Instruction limit
% 3.80/1.32 % (2265297)Termination phase: Saturation
% 3.80/1.32 % (2265297)Time elapsed: 0.054 s
% 3.80/1.32 % (2265297)Peak memory usage: 89 MB
% 3.80/1.32 % (2265297)Instructions burned: 118 (million)
% 3.80/1.32 % (2265305)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=3424894298:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.80/1.32 % (2265305)Also succeeded, but the first one will report.
% 3.80/1.32 % (2265294)Refutation found. Thanks to Tanya!
% 3.80/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.80/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.32 % (2265294)------------------------------
% 3.80/1.32 % (2265294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.32 % (2265294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.32 % (2265294)CaDiCaL version: 2.1.3
% 3.80/1.32 % (2265294)Termination reason: Refutation
% 3.80/1.32 % (2265294)Time elapsed: 0.011 s
% 3.80/1.32 % (2265294)Peak memory usage: 89 MB
% 3.80/1.32 % (2265294)Instructions burned: 14 (million)
% 3.80/1.32 % (2265294)------------------------------
% 3.80/1.32 % (2265294)------------------------------
% 3.80/1.32 % (2265286)Success in time 0.448 s
% 3.80/1.32 % Vampire exiting
%------------------------------------------------------------------------------