%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC027-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 01:02:06 PM UTC 2026
% Result : Unsatisfiable 3.49s 1.45s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 76 ( 13 unt; 8 def)
% Number of atoms : 160 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 160 ( 76 ~; 76 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f71,axiom,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
fof(f98,axiom,
! [X0,X1] :
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
fof(f99,plain,
! [X0,X1] :
( nil != cons(X0,X1)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(reorient_equations,[],[f98]) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
( ssItem(sk5)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( ssItem(sk5)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,plain,
( sk3 = cons(sk5,nil)
| nil = sk4 ),
inference(reorient_equations,[],[f208]) ).
fof(f214,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f216,negated_conjecture,
( nil = sk2
| nil = sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f219,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f251,definition,
( spl0_1
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f252,plain,
( nil = sk2
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f253,plain,
( nil != sk2
| spl0_1 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f255,definition,
( spl0_2
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f256,plain,
( nil = sk1
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( nil != sk1
| spl0_2 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f258,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f219,f255,f251]) ).
fof(f259,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f216,f251,f255]) ).
fof(f261,definition,
( spl0_3
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f263,plain,
( nil = sk3
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f269,definition,
( spl0_5
<=> memberP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f271,plain,
( memberP(sk4,sk5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f272,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f214,f269,f261]) ).
fof(f274,definition,
( spl0_6
<=> sk3 = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f276,plain,
( sk3 = cons(sk5,nil)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f279,definition,
( spl0_7
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f281,plain,
( nil = sk4
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f284,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f209,f274,f279]) ).
fof(f286,definition,
( spl0_8
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f288,plain,
( ssItem(sk5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f289,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f207,f286,f261]) ).
fof(f290,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f206,f286,f279]) ).
fof(f296,definition,
( spl0_10
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f297,plain,
( ssList(nil)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f332,plain,
spl0_10,
inference(avatar_split_clause,[],[f8,f296]) ).
fof(f335,plain,
( nil != sk4
| spl0_1 ),
inference(forward_demodulation,[],[f253,f204]) ).
fof(f336,plain,
( ~ spl0_7
| spl0_1 ),
inference(avatar_split_clause,[],[f335,f251,f279]) ).
fof(f337,plain,
( nil != sk3
| spl0_2 ),
inference(forward_demodulation,[],[f257,f205]) ).
fof(f338,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f337,f255,f261]) ).
fof(f340,plain,
( nil = sk4
| ~ spl0_1 ),
inference(superposition,[],[f204,f252]) ).
fof(f343,plain,
( spl0_7
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f340,f251,f279]) ).
fof(f344,plain,
( memberP(nil,sk5)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f271,f281]) ).
fof(f355,plain,
( ~ ssItem(sk5)
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[],[f71,f344]) ).
fof(f356,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f355,f288]) ).
fof(f357,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f356]) ).
fof(f360,plain,
( nil = sk3
| ~ spl0_2 ),
inference(superposition,[],[f205,f256]) ).
fof(f366,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f360,f255,f261]) ).
fof(f412,plain,
( nil != sk3
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ spl0_6 ),
inference(superposition,[],[f99,f276]) ).
fof(f413,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f412,f263]) ).
fof(f414,plain,
( ~ ssList(nil)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f413,f288]) ).
fof(f415,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f414,f297]) ).
fof(f416,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f415]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f258]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f259]) ).
cnf(s4,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f272]) ).
cnf(s8,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f284]) ).
cnf(s9,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f289]) ).
cnf(s10,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f290]) ).
cnf(s20,plain,
spl0_10,
inference(sat_conversion,[],[f332]) ).
cnf(s21,plain,
( spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f336]) ).
cnf(s22,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f338]) ).
cnf(s24,plain,
( ~ spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f343]) ).
cnf(s28,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f357]) ).
cnf(s33,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f366]) ).
cnf(s35,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f416]) ).
cnf(s40,plain,
spl0_1,
inference(rat,[],[s35,s33,s8,s10,s2,s21,s20]) ).
cnf(s41,plain,
spl0_7,
inference(rat,[],[s24,s40]) ).
cnf(s42,plain,
~ spl0_2,
inference(rat,[],[s1,s40]) ).
cnf(s43,plain,
~ spl0_3,
inference(rat,[],[s22,s42]) ).
cnf(s44,plain,
spl0_8,
inference(rat,[],[s9,s43]) ).
cnf(s46,plain,
spl0_5,
inference(rat,[],[s4,s43]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s28,s41,s44,s46]) ).
fof(f417,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC027-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 07:30:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.49/1.45 % (180419)Input is clausal, will run a generic CNF schedule.
% 3.49/1.45 % (180424)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=2849826796:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.49/1.45 % (180425)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=367774002:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.49/1.45 % (180426)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2971424526:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.49/1.45 % (180429)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=35235171:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.49/1.45 % (180427)lrs+10_1_sil=8000:sp=occurrence:random_seed=1269837956:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.49/1.45 % (180428)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=326625270:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.49/1.45 % (180430)dis-21_1_sil=8000:lcm=predicate:random_seed=2117310663: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)
% 3.49/1.45 % (180429)First to succeed.
% 3.49/1.45 % (180429)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-180419"
% 3.49/1.45 % (180428)Also succeeded, but the first one will report.
% 3.49/1.45 % (180427)Also succeeded, but the first one will report.
% 3.49/1.45 % (180430)Instruction limit reached!
% 3.49/1.45 % (180430)------------------------------
% 3.49/1.45 % (180430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.45 % (180430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.45 % (180430)CaDiCaL version: 2.1.3
% 3.49/1.45 % (180430)Termination reason: Instruction limit
% 3.49/1.45 % (180430)Termination phase: Saturation
% 3.49/1.45 % (180430)Time elapsed: 0.054 s
% 3.49/1.45 % (180430)Peak memory usage: 89 MB
% 3.49/1.45 % (180430)Instructions burned: 117 (million)
% 3.49/1.45 % (180438)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=191727867:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.49/1.45 % (180438)Also succeeded, but the first one will report.
% 3.49/1.45 % (180429)Refutation found. Thanks to Tanya!
% 3.49/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.49/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.45 % (180429)------------------------------
% 3.49/1.45 % (180429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.45 % (180429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.45 % (180429)CaDiCaL version: 2.1.3
% 3.49/1.45 % (180429)Termination reason: Refutation
% 3.49/1.45 % (180429)Time elapsed: 0.009 s
% 3.49/1.45 % (180429)Peak memory usage: 90 MB
% 3.49/1.45 % (180429)Instructions burned: 11 (million)
% 3.49/1.45 % (180429)------------------------------
% 3.49/1.45 % (180429)------------------------------
% 3.49/1.45 % (180419)Success in time 0.413 s
% 3.49/1.45 % Vampire exiting
%------------------------------------------------------------------------------