%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC229-1 : 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 : n026.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 01:03:02 PM UTC 2026
% Result : Unsatisfiable 3.42s 1.17s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 61 ( 16 unt; 2 def)
% Number of atoms : 165 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 203 ( 99 ~; 102 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
fof(f71,axiom,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f80,axiom,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
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(f103,axiom,
! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| ssItem(sk5(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk1 != app(app(X1,cons(X0,nil)),X2)
| ssItem(sk5(X2,X1,X0)) ),
inference(reorient_equations,[],[f208]) ).
fof(f210,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| memberP(X1,sk5(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk1 != app(app(X1,cons(X0,nil)),X2)
| memberP(X1,sk5(X2,X1,X0)) ),
inference(reorient_equations,[],[f210]) ).
fof(f218,negated_conjecture,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f221,plain,
nil != sk3,
inference(definition_unfolding,[],[f207,f205]) ).
fof(f222,plain,
! [X2,X0,X1] :
( sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| ssItem(sk5(X2,X1,X0)) ),
inference(definition_unfolding,[],[f209,f205]) ).
fof(f223,plain,
! [X2,X0,X1] :
( sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| memberP(X1,sk5(X2,X1,X0)) ),
inference(definition_unfolding,[],[f211,f205]) ).
fof(f241,definition,
( spl0_1
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f243,plain,
( ~ neq(sk4,nil)
| spl0_1 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f245,definition,
( spl0_2
<=> singletonP(sk3) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f247,plain,
( singletonP(sk3)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f218,f245,f241]) ).
fof(f249,plain,
sk3 = app(sk3,nil),
inference(resolution,[],[f73,f202]) ).
fof(f252,plain,
sk3 = app(nil,sk3),
inference(resolution,[],[f74,f202]) ).
fof(f269,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| nil = sk4
| spl0_1 ),
inference(resolution,[],[f102,f243]) ).
fof(f274,plain,
( ~ ssList(nil)
| nil = sk4
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f269,f203]) ).
fof(f275,plain,
( nil = sk4
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f274,f8]) ).
fof(f279,plain,
( segmentP(nil,sk3)
| spl0_1 ),
inference(superposition,[],[f206,f275]) ).
fof(f293,plain,
( ~ ssList(sk3)
| nil = sk3
| spl0_1 ),
inference(resolution,[],[f279,f80]) ).
fof(f294,plain,
( nil = sk3
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f293,f202]) ).
fof(f295,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f294,f221]) ).
fof(f296,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f295]) ).
fof(f297,plain,
( ~ ssList(sk3)
| sk3 = cons(skaf44(sk3),nil)
| ~ spl0_2 ),
inference(resolution,[],[f247,f103]) ).
fof(f298,plain,
( sk3 = cons(skaf44(sk3),nil)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f297,f202]) ).
fof(f305,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(skaf44(sk3))
| memberP(X0,sk5(X1,X0,skaf44(sk3))) )
| ~ spl0_2 ),
inference(superposition,[],[f223,f298]) ).
fof(f306,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(skaf44(sk3))
| ssItem(sk5(X1,X0,skaf44(sk3))) )
| ~ spl0_2 ),
inference(superposition,[],[f222,f298]) ).
fof(f312,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ssItem(sk5(X1,X0,skaf44(sk3))) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f306,f47]) ).
fof(f313,plain,
( ! [X0,X1] :
( sk3 != app(app(X0,sk3),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X0,sk5(X1,X0,skaf44(sk3))) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f305,f47]) ).
fof(f321,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ssItem(sk5(X0,nil,skaf44(sk3))) )
| ~ spl0_2 ),
inference(superposition,[],[f312,f252]) ).
fof(f322,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(X0)
| ssItem(sk5(X0,nil,skaf44(sk3))) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f321,f8]) ).
fof(f341,plain,
( sk3 != sk3
| ~ ssList(nil)
| ssItem(sk5(nil,nil,skaf44(sk3)))
| ~ spl0_2 ),
inference(superposition,[],[f322,f249]) ).
fof(f342,plain,
( ~ ssList(nil)
| ssItem(sk5(nil,nil,skaf44(sk3)))
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f341]) ).
fof(f343,plain,
( ssItem(sk5(nil,nil,skaf44(sk3)))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f342,f8]) ).
fof(f352,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(nil,sk5(X0,nil,skaf44(sk3))) )
| ~ spl0_2 ),
inference(superposition,[],[f313,f252]) ).
fof(f353,plain,
( ! [X0] :
( sk3 != app(sk3,X0)
| ~ ssList(X0)
| memberP(nil,sk5(X0,nil,skaf44(sk3))) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f352,f8]) ).
fof(f360,plain,
( sk3 != sk3
| ~ ssList(nil)
| memberP(nil,sk5(nil,nil,skaf44(sk3)))
| ~ spl0_2 ),
inference(superposition,[],[f353,f249]) ).
fof(f361,plain,
( ~ ssList(nil)
| memberP(nil,sk5(nil,nil,skaf44(sk3)))
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f360]) ).
fof(f362,plain,
( memberP(nil,sk5(nil,nil,skaf44(sk3)))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f361,f8]) ).
fof(f370,plain,
( ~ ssItem(sk5(nil,nil,skaf44(sk3)))
| ~ spl0_2 ),
inference(resolution,[],[f362,f71]) ).
fof(f371,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f370,f343]) ).
fof(f372,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f371]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f248]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f296]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f372]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f373,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC229-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.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 08:37:57 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
% 3.42/1.17 % (3700696)Input is clausal, will run a generic CNF schedule.
% 3.42/1.17 % (3700705)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3414659807:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.42/1.17 % (3700702)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=978390345:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.42/1.17 % (3700703)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2017068537:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.42/1.17 % (3700705)Instruction limit reached!
% 3.42/1.17 % (3700705)------------------------------
% 3.42/1.17 % (3700705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.17 % (3700705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.17 % (3700705)CaDiCaL version: 2.1.3
% 3.42/1.17 % (3700705)Termination reason: Instruction limit
% 3.42/1.17 % (3700705)Termination phase: Saturation
% 3.42/1.17 % (3700705)Time elapsed: 0.034 s
% 3.42/1.17 % (3700705)Peak memory usage: 88 MB
% 3.42/1.17 % (3700705)Instructions burned: 118 (million)
% 3.42/1.17 % (3700701)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=1363221394:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.42/1.17 % (3700706)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2455362000:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.42/1.17 % (3700704)lrs+10_1_sil=8000:sp=occurrence:random_seed=3079558232:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.42/1.17 % (3700707)dis-21_1_sil=8000:lcm=predicate:random_seed=563122766: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)
% 3.42/1.17 % (3700704)First to succeed.
% 3.42/1.17 % (3700704)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3700696"
% 3.42/1.17 % (3700706)Also succeeded, but the first one will report.
% 3.42/1.17 % (3700707)Instruction limit reached!
% 3.42/1.17 % (3700707)------------------------------
% 3.42/1.17 % (3700707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.17 % (3700707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.17 % (3700707)CaDiCaL version: 2.1.3
% 3.42/1.17 % (3700707)Termination reason: Instruction limit
% 3.42/1.17 % (3700707)Termination phase: Saturation
% 3.42/1.17 % (3700707)Time elapsed: 0.055 s
% 3.42/1.17 % (3700707)Peak memory usage: 89 MB
% 3.42/1.17 % (3700707)Instructions burned: 118 (million)
% 3.42/1.17 % (3700712)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=3371747432:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.42/1.17 % (3700712)Also succeeded, but the first one will report.
% 3.42/1.17 % (3700716)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=695415222:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.42/1.17 % (3700704)Refutation found. Thanks to Tanya!
% 3.42/1.17 % SZS status Unsatisfiable for theBenchmark
% 3.42/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.17 % (3700704)------------------------------
% 3.42/1.17 % (3700704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.17 % (3700704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.17 % (3700704)CaDiCaL version: 2.1.3
% 3.42/1.17 % (3700704)Termination reason: Refutation
% 3.42/1.17 % (3700704)Time elapsed: 0.007 s
% 3.42/1.17 % (3700704)Peak memory usage: 89 MB
% 3.42/1.17 % (3700704)Instructions burned: 8 (million)
% 3.42/1.17 % (3700704)------------------------------
% 3.42/1.17 % (3700704)------------------------------
% 3.42/1.17 % (3700696)Success in time 0.416 s
% 3.42/1.17 % Vampire exiting
%------------------------------------------------------------------------------