%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC366-1 : 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 : n020.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 01:03:39 PM UTC 2026
% Result : Unsatisfiable 0.81s 0.93s
% Output : Refutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 87 ( 16 unt; 7 def)
% Number of atoms : 230 ( 24 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 269 ( 126 ~; 136 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f76,axiom,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause76) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
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(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f154,axiom,
! [X2,X0,X1] :
( app(X0,X1) != X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
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(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,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f210,negated_conjecture,
! [X2,X0,X1] :
( ~ ssList(X0)
| sk4 = X0
| ~ ssList(X1)
| app(X1,sk3) != X0
| ~ ssItem(X2)
| cons(X2,nil) != X1
| hd(sk4) != X2
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
( ~ rearsegP(sk2,sk1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f214,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f206,f204,f204]) ).
fof(f218,plain,
( ~ rearsegP(sk4,sk3)
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f211,f204,f205]) ).
fof(f222,plain,
! [X2,X1] :
( ~ ssList(app(X1,sk3))
| sk4 = app(X1,sk3)
| ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,nil) != X1
| hd(sk4) != X2
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f210]) ).
fof(f223,plain,
! [X2] :
( ~ ssList(app(cons(X2,nil),sk3))
| sk4 = app(cons(X2,nil),sk3)
| ~ ssList(cons(X2,nil))
| ~ ssItem(X2)
| hd(sk4) != X2
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f222]) ).
fof(f224,plain,
( ~ ssList(app(cons(hd(sk4),nil),sk3))
| sk4 = app(cons(hd(sk4),nil),sk3)
| ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f223]) ).
fof(f226,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f229,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f232,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f234,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f214]) ).
fof(f236,definition,
( spl0_1
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f237,plain,
( neq(sk4,nil)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f240,definition,
( spl0_2
<=> rearsegP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f242,plain,
( ~ rearsegP(sk4,sk3)
| spl0_2 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f243,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f218,f240,f236]) ).
fof(f245,definition,
( spl0_3
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f246,plain,
( neq(nil,sk4)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f247,plain,
( ~ neq(nil,sk4)
| spl0_3 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f249,definition,
( spl0_4
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f250,plain,
( ssItem(hd(sk4))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( ~ ssItem(hd(sk4))
| spl0_4 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f253,definition,
( spl0_5
<=> ssList(cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f254,plain,
( ssList(cons(hd(sk4),nil))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f255,plain,
( ~ ssList(cons(hd(sk4),nil))
| spl0_5 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f257,definition,
( spl0_6
<=> sk4 = app(cons(hd(sk4),nil),sk3) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f259,plain,
( sk4 = app(cons(hd(sk4),nil),sk3)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f261,definition,
( spl0_7
<=> ssList(app(cons(hd(sk4),nil),sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f263,plain,
( ~ ssList(app(cons(hd(sk4),nil),sk3))
| spl0_7 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f264,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f224,f261,f257,f253,f249,f245,f236]) ).
fof(f267,plain,
spl0_1,
inference(avatar_split_clause,[],[f234,f236]) ).
fof(f289,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| nil = sk4
| spl0_3 ),
inference(resolution,[],[f102,f247]) ).
fof(f294,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f289,f8]) ).
fof(f295,plain,
( nil = sk4
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f294,f203]) ).
fof(f302,plain,
( neq(nil,nil)
| ~ spl0_1
| spl0_3 ),
inference(superposition,[],[f237,f295]) ).
fof(f304,plain,
( ~ neq(nil,nil)
| spl0_3 ),
inference(superposition,[],[f247,f295]) ).
fof(f307,plain,
( $false
| ~ spl0_1
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f302,f304]) ).
fof(f308,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f309,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_4 ),
inference(resolution,[],[f251,f76]) ).
fof(f310,plain,
( nil = sk4
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f309,f203]) ).
fof(f316,plain,
( neq(nil,nil)
| ~ spl0_3
| spl0_4 ),
inference(superposition,[],[f246,f310]) ).
fof(f324,plain,
( ~ ssList(nil)
| ~ spl0_3
| spl0_4 ),
inference(resolution,[],[f316,f232]) ).
fof(f325,plain,
( $false
| ~ spl0_3
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f324,f8]) ).
fof(f326,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f329,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| spl0_5 ),
inference(resolution,[],[f255,f86]) ).
fof(f330,plain,
( ~ ssItem(hd(sk4))
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f329,f8]) ).
fof(f331,plain,
( $false
| ~ spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f330,f250]) ).
fof(f332,plain,
( ~ spl0_4
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f331]) ).
fof(f335,plain,
( ~ ssList(cons(hd(sk4),nil))
| ~ ssList(sk3)
| spl0_7 ),
inference(resolution,[],[f263,f85]) ).
fof(f336,plain,
( ~ ssList(sk3)
| ~ spl0_5
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f335,f254]) ).
fof(f337,plain,
( $false
| ~ spl0_5
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f336,f202]) ).
fof(f338,plain,
( ~ spl0_5
| spl0_7 ),
inference(avatar_contradiction_clause,[],[f337]) ).
fof(f376,plain,
( rearsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(cons(hd(sk4),nil))
| ~ spl0_6 ),
inference(superposition,[],[f229,f259]) ).
fof(f384,plain,
( ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(cons(hd(sk4),nil))
| spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f376,f242]) ).
fof(f386,plain,
( ~ ssList(sk4)
| ~ ssList(cons(hd(sk4),nil))
| spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f384,f202]) ).
fof(f387,plain,
( ~ ssList(cons(hd(sk4),nil))
| spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f386,f203]) ).
fof(f388,plain,
( $false
| spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f387,f254]) ).
fof(f389,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f388]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f243]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f264]) ).
cnf(s5,plain,
spl0_1,
inference(sat_conversion,[],[f267]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f308]) ).
cnf(s7,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f326]) ).
cnf(s8,plain,
( ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f332]) ).
cnf(s9,plain,
( ~ spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f338]) ).
cnf(s12,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f389]) ).
cnf(s13,plain,
spl0_3,
inference(rat,[],[s6,s5]) ).
cnf(s14,plain,
spl0_4,
inference(rat,[],[s7,s13]) ).
cnf(s15,plain,
spl0_5,
inference(rat,[],[s8,s14]) ).
cnf(s16,plain,
spl0_7,
inference(rat,[],[s9,s15]) ).
cnf(s17,plain,
spl0_6,
inference(rat,[],[s2,s16,s15,s14,s13,s5]) ).
cnf(s18,plain,
spl0_2,
inference(rat,[],[s12,s15,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s18,s5]) ).
fof(f390,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC366-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % 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 09:21:11 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
% 0.81/0.93 % (50483)Input is clausal, will run a generic CNF schedule.
% 0.81/0.93 % (50491)lrs+10_1_sil=8000:sp=occurrence:random_seed=2442879902:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.81/0.93 % (50491)First to succeed.
% 0.81/0.93 % (50491)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-50483"
% 0.81/0.93 % (50493)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=36596722:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.81/0.93 % (50489)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=786521122:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.81/0.93 % (50488)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=4105878947:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.81/0.93 % (50492)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1239616601:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.81/0.93 % (50494)dis-21_1_sil=8000:lcm=predicate:random_seed=2306362978: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)
% 0.81/0.93 % (50490)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=979193055:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.81/0.93 % (50492)Also succeeded, but the first one will report.
% 0.81/0.93 % (50493)Also succeeded, but the first one will report.
% 0.81/0.93 % (50494)Instruction limit reached!
% 0.81/0.93 % (50494)------------------------------
% 0.81/0.93 % (50494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.81/0.93 % (50494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.93 % (50494)CaDiCaL version: 2.1.3
% 0.81/0.93 % (50494)Termination reason: Instruction limit
% 0.81/0.93 % (50494)Termination phase: Saturation
% 0.81/0.93 % (50494)Time elapsed: 0.050 s
% 0.81/0.93 % (50494)Peak memory usage: 89 MB
% 0.81/0.93 % (50494)Instructions burned: 118 (million)
% 0.81/0.93 % (50491)Refutation found. Thanks to Tanya!
% 0.81/0.93 % SZS status Unsatisfiable for theBenchmark
% 0.81/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.49/1.12 % (50491)------------------------------
% 2.49/1.12 % (50491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.12 % (50491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.12 % (50491)CaDiCaL version: 2.1.3
% 2.49/1.12 % (50491)Termination reason: Refutation
% 2.49/1.12 % (50491)Time elapsed: 0.004 s
% 2.49/1.12 % (50491)Peak memory usage: 90 MB
% 2.49/1.12 % (50491)Instructions burned: 7 (million)
% 2.49/1.12 % (50491)------------------------------
% 2.49/1.12 % (50491)------------------------------
% 2.49/1.12 % (50483)Success in time 0.275 s
% 2.49/1.12 % Vampire exiting
%------------------------------------------------------------------------------