%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC386-1 : 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 : n015.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 01:03:45 PM UTC 2026
% Result : Unsatisfiable 2.45s 1.05s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 77 ( 12 unt; 7 def)
% Number of atoms : 180 ( 33 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 197 ( 94 ~; 96 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 11 !; 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(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
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)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( ssItem(sk5)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,plain,
( sk3 = cons(sk5,nil)
| nil = sk4 ),
inference(reorient_equations,[],[f208]) ).
fof(f210,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f211,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,plain,
( sk3 = cons(sk5,nil)
| nil = sk3 ),
inference(reorient_equations,[],[f211]) ).
fof(f213,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f215,negated_conjecture,
! [X0] :
( nil = sk2
| ~ ssItem(X0)
| cons(X0,nil) != sk1
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f216,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f217,negated_conjecture,
! [X0] :
( nil != sk1
| ~ ssItem(X0)
| cons(X0,nil) != sk1
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f221,plain,
! [X0] :
( nil = sk4
| ~ ssItem(X0)
| cons(X0,nil) != sk3
| ~ memberP(sk4,X0) ),
inference(definition_unfolding,[],[f215,f204,f205,f204]) ).
fof(f222,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f216,f205,f204]) ).
fof(f223,plain,
! [X0] :
( nil != sk3
| ~ ssItem(X0)
| cons(X0,nil) != sk3
| ~ memberP(sk4,X0) ),
inference(definition_unfolding,[],[f217,f205,f205,f204]) ).
fof(f227,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f231,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f227]) ).
fof(f235,definition,
( spl0_1
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk4,X0)
| cons(X0,nil) != sk3 ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f236,plain,
( ! [X0] :
( cons(X0,nil) != sk3
| ~ memberP(sk4,X0)
| ~ ssItem(X0) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,definition,
( spl0_2
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f241,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f223,f238,f235]) ).
fof(f243,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f245,plain,
( neq(sk4,nil)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f246,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f222,f238,f243]) ).
fof(f248,definition,
( spl0_4
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f250,plain,
( nil = sk4
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f221,f248,f235]) ).
fof(f254,definition,
( spl0_5
<=> memberP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f256,plain,
( memberP(sk4,sk5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f257,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f213,f254,f238]) ).
fof(f259,definition,
( spl0_6
<=> sk3 = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f261,plain,
( sk3 = cons(sk5,nil)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,plain,
( spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f212,f259,f238]) ).
fof(f263,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f210,f254,f248]) ).
fof(f264,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f209,f259,f248]) ).
fof(f266,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f268,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f269,plain,
( spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f207,f266,f238]) ).
fof(f270,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f206,f266,f248]) ).
fof(f271,plain,
( memberP(nil,sk5)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f256,f250]) ).
fof(f273,plain,
( ~ ssItem(sk5)
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f71,f271]) ).
fof(f274,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f273,f268]) ).
fof(f275,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f274]) ).
fof(f277,plain,
( neq(nil,nil)
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f245,f250]) ).
fof(f279,plain,
( ~ ssList(nil)
| ~ spl0_3
| ~ spl0_4 ),
inference(resolution,[],[f231,f277]) ).
fof(f280,plain,
( $false
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f279,f8]) ).
fof(f281,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f288,plain,
( sk3 != sk3
| ~ memberP(sk4,sk5)
| ~ ssItem(sk5)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f236,f261]) ).
fof(f289,plain,
( ~ memberP(sk4,sk5)
| ~ ssItem(sk5)
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f288]) ).
fof(f290,plain,
( ~ ssItem(sk5)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f289,f256]) ).
fof(f291,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f290,f268]) ).
fof(f292,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f291]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f241]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f246]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f251]) ).
cnf(s5,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f257]) ).
cnf(s6,plain,
( spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f262]) ).
cnf(s7,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f263]) ).
cnf(s8,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f264]) ).
cnf(s9,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f269]) ).
cnf(s10,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f270]) ).
cnf(s11,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f275]) ).
cnf(s12,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f281]) ).
cnf(s14,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f292]) ).
cnf(s15,plain,
spl0_1,
inference(rat,[],[s11,s5,s9,s1,s3]) ).
cnf(s16,plain,
spl0_2,
inference(rat,[],[s14,s5,s6,s9,s15]) ).
cnf(s17,plain,
spl0_3,
inference(rat,[],[s2,s16]) ).
cnf(s18,plain,
~ spl0_4,
inference(rat,[],[s12,s17]) ).
cnf(s19,plain,
spl0_7,
inference(rat,[],[s10,s18]) ).
cnf(s20,plain,
spl0_6,
inference(rat,[],[s8,s18]) ).
cnf(s21,plain,
spl0_5,
inference(rat,[],[s7,s18]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s14,s19,s15,s20,s21]) ).
fof(f293,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC386-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n015.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 09:28:46 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 2.45/1.05 % (2497204)Input is clausal, will run a generic CNF schedule.
% 2.45/1.05 % (2497212)lrs+10_1_sil=8000:sp=occurrence:random_seed=58493165:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.45/1.05 % (2497212)First to succeed.
% 2.45/1.05 % (2497212)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2497204"
% 2.45/1.05 % (2497214)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4021648812:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.45/1.05 % (2497209)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=1484697194:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.45/1.05 % (2497210)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3422182923:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.45/1.05 % (2497215)dis-21_1_sil=8000:lcm=predicate:random_seed=4264533234: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)
% 2.45/1.05 % (2497211)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2483889407:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.45/1.05 % (2497213)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2238007974:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.45/1.05 % (2497213)Also succeeded, but the first one will report.
% 2.45/1.05 % (2497214)Also succeeded, but the first one will report.
% 2.45/1.05 % (2497215)Instruction limit reached!
% 2.45/1.05 % (2497215)------------------------------
% 2.45/1.05 % (2497215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.05 % (2497215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.05 % (2497215)CaDiCaL version: 2.1.3
% 2.45/1.05 % (2497215)Termination reason: Instruction limit
% 2.45/1.05 % (2497215)Termination phase: Saturation
% 2.45/1.05 % (2497215)Time elapsed: 0.049 s
% 2.45/1.05 % (2497215)Peak memory usage: 88 MB
% 2.45/1.05 % (2497215)Instructions burned: 118 (million)
% 2.45/1.05 % (2497212)Refutation found. Thanks to Tanya!
% 2.45/1.05 % SZS status Unsatisfiable for theBenchmark
% 2.45/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.45/1.05 % (2497212)------------------------------
% 2.45/1.05 % (2497212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.05 % (2497212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.05 % (2497212)CaDiCaL version: 2.1.3
% 2.45/1.05 % (2497212)Termination reason: Refutation
% 2.45/1.05 % (2497212)Time elapsed: 0.003 s
% 2.45/1.05 % (2497212)Peak memory usage: 90 MB
% 2.45/1.05 % (2497212)Instructions burned: 4 (million)
% 2.45/1.05 % (2497212)------------------------------
% 2.45/1.05 % (2497212)------------------------------
% 2.45/1.05 % (2497204)Success in time 0.275 s
% 2.45/1.05 % Vampire exiting
%------------------------------------------------------------------------------