%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC258+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 : n010.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 01:03:10 PM UTC 2026
% Result : Theorem 2.64s 1.14s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 14 unt; 4 def)
% Number of atoms : 186 ( 51 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 218 ( 78 ~; 70 |; 53 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 25 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( nil = X1
| ( nil != X1
& totalorderedP(X1)
& leq(X0,hd(X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| totalorderedP(X0)
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X5,X4) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| totalorderedP(X0)
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X5,X4) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ totalorderedP(X0)
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X5,X4) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ totalorderedP(X0)
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X5,X4) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ( totalorderedP(cons(X0,X1))
<=> ( nil = X1
| ( nil != X1
& totalorderedP(X1)
& leq(X0,hd(X1)) ) ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f120,plain,
( sK1 = sK3
& sK0 = sK2
& ~ totalorderedP(sK0)
& ( ( sK2 = cons(sK4,nil)
& memberP(sK3,sK4)
& ! [X5] :
( ~ ssItem(X5)
| sK4 = X5
| ~ memberP(sK3,X5)
| ~ leq(X5,sK4) )
& ssItem(sK4) )
| ( nil = sK3
& nil = sK2 ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( ( totalorderedP(cons(X0,X1))
| ( nil != X1
& ( nil = X1
| ~ totalorderedP(X1)
| ~ leq(X0,hd(X1)) ) ) )
& ( nil = X1
| ( nil != X1
& totalorderedP(X1)
& leq(X0,hd(X1)) )
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f116]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( ( totalorderedP(cons(X0,X1))
| ( nil != X1
& ( nil = X1
| ~ totalorderedP(X1)
| ~ leq(X0,hd(X1)) ) ) )
& ( nil = X1
| ( nil != X1
& totalorderedP(X1)
& leq(X0,hd(X1)) )
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f130]) ).
fof(f139,plain,
( ssItem(sK4)
| nil = sK2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f145,plain,
( sK2 = cons(sK4,nil)
| nil = sK2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f147,plain,
~ totalorderedP(sK0),
inference(cnf_transformation,[],[f120]) ).
fof(f148,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f120]) ).
fof(f161,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f180,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| nil != X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f181,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f191,plain,
~ totalorderedP(sK2),
inference(definition_unfolding,[],[f147,f148]) ).
fof(f198,definition,
~ sP18(nil),
introduced(definition,[new_symbols(definition,[sP18])],[inequality_splitting_name_introduction]) ).
fof(f199,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| sP18(X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(inequality_splitting,[],[f180,f198]) ).
fof(f207,definition,
( spl20_1
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f209,plain,
( nil = sK2
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f211,definition,
( spl20_2
<=> ssItem(sK4) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f213,plain,
( ssItem(sK4)
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,plain,
( spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f139,f211,f207]) ).
fof(f232,definition,
( spl20_6
<=> sK2 = cons(sK4,nil) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
fof(f234,plain,
( sK2 = cons(sK4,nil)
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,plain,
( spl20_1
| spl20_6 ),
inference(avatar_split_clause,[],[f145,f232,f207]) ).
fof(f238,plain,
( ~ totalorderedP(cons(sK4,nil))
| ~ spl20_6 ),
inference(superposition,[],[f191,f234]) ).
fof(f242,plain,
( sP18(nil)
| ~ ssList(nil)
| ~ ssItem(sK4)
| ~ spl20_6 ),
inference(resolution,[],[f238,f199]) ).
fof(f243,plain,
( ~ ssList(nil)
| ~ ssItem(sK4)
| ~ spl20_6 ),
inference(forward_subsumption_resolution,[],[f242,f198]) ).
fof(f246,plain,
( ~ ssItem(sK4)
| ~ spl20_6 ),
inference(forward_subsumption_resolution,[],[f243,f161]) ).
fof(f247,plain,
( $false
| ~ spl20_2
| ~ spl20_6 ),
inference(forward_subsumption_resolution,[],[f246,f213]) ).
fof(f248,plain,
( ~ spl20_2
| ~ spl20_6 ),
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f252,plain,
( ~ totalorderedP(nil)
| ~ spl20_1 ),
inference(superposition,[],[f191,f209]) ).
fof(f253,plain,
( $false
| ~ spl20_1 ),
inference(forward_subsumption_resolution,[],[f252,f181]) ).
fof(f254,plain,
~ spl20_1,
inference(avatar_contradiction_clause,[],[f253]) ).
cnf(s1,plain,
( spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f214]) ).
cnf(s7,plain,
( spl20_1
| spl20_6 ),
inference(sat_conversion,[],[f235]) ).
cnf(s10,plain,
( ~ spl20_2
| ~ spl20_6 ),
inference(sat_conversion,[],[f248]) ).
cnf(s11,plain,
~ spl20_1,
inference(sat_conversion,[],[f254]) ).
cnf(s12,plain,
spl20_6,
inference(rat,[],[s7,s11]) ).
cnf(s13,plain,
~ spl20_2,
inference(rat,[],[s10,s12]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s13,s11]) ).
fof(f255,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC258+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 08:44:53 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.64/1.14 % (1778916)Detected formulas, will run a generic FOF schedule.
% 2.64/1.14 % (1779021)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2319526346:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.14 % (1779021)First to succeed.
% 2.64/1.14 % (1779021)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1778916"
% 2.64/1.14 % (1779017)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=662196861:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.14 % (1779020)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4092241000:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.14 % (1779018)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3269635757:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.14 % (1779026)dis-21_1_sil=8000:lcm=predicate:random_seed=84670847:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.64/1.14 % (1779023)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3893419909:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.14 % (1779024)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2819490437:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.14 % (1779023)Also succeeded, but the first one will report.
% 2.64/1.14 % (1779024)Also succeeded, but the first one will report.
% 2.64/1.14 % (1779026)Instruction limit reached!
% 2.64/1.14 % (1779026)------------------------------
% 2.64/1.14 % (1779026)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.14 % (1779026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.14 % (1779026)CaDiCaL version: 2.1.3
% 2.64/1.14 % (1779026)Termination reason: Instruction limit
% 2.64/1.14 % (1779026)Termination phase: Saturation
% 2.64/1.14 % (1779026)Time elapsed: 0.071 s
% 2.64/1.14 % (1779026)Peak memory usage: 91 MB
% 2.64/1.14 % (1779026)Instructions burned: 130 (million)
% 2.64/1.14 % (1779021)Refutation found. Thanks to Tanya!
% 2.64/1.14 % SZS status Theorem for theBenchmark
% 2.64/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.15 % (1779021)------------------------------
% 2.64/1.15 % (1779021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.15 % (1779021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.15 % (1779021)CaDiCaL version: 2.1.3
% 2.64/1.15 % (1779021)Termination reason: Refutation
% 2.64/1.15 % (1779021)Time elapsed: 0.003 s
% 2.64/1.15 % (1779021)Peak memory usage: 90 MB
% 2.64/1.15 % (1779021)Instructions burned: 6 (million)
% 2.64/1.15 % (1779021)------------------------------
% 2.64/1.15 % (1779021)------------------------------
% 2.64/1.15 % (1778916)Success in time 0.275 s
% 2.64/1.15 % Vampire exiting
%------------------------------------------------------------------------------