%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC010-1 : 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 : 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 01:02:01 PM UTC 2026
% Result : Unsatisfiable 2.31s 1.06s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 64 ( 14 unt; 8 def)
% Number of atoms : 164 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 203 ( 103 ~; 92 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f218,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk2
| app(X1,X2) != sk1
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk2 != app(app(X1,cons(X0,nil)),X2)
| app(X1,X2) != sk1
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f218]) ).
fof(f220,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f221,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f222,negated_conjecture,
( ssList(sk7)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f223,negated_conjecture,
( app(app(sk6,cons(sk5,nil)),sk7) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
fof(f224,plain,
( sk4 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f223]) ).
fof(f225,negated_conjecture,
( app(sk6,sk7) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_21) ).
fof(f226,plain,
( sk3 = app(sk6,sk7)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f225]) ).
fof(f252,plain,
neq(sk2,nil),
inference(duplicate_literal_removal,[],[f206]) ).
fof(f260,definition,
( spl0_1
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f262,plain,
( ~ neq(sk4,nil)
| spl0_1 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f268,definition,
( spl0_3
<=> sk3 = app(sk6,sk7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f270,plain,
( sk3 = app(sk6,sk7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f271,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f226,f268,f260]) ).
fof(f273,definition,
( spl0_4
<=> sk4 = app(app(sk6,cons(sk5,nil)),sk7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f275,plain,
( sk4 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f276,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f224,f273,f260]) ).
fof(f278,definition,
( spl0_5
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f280,plain,
( ssList(sk7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f281,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f222,f278,f260]) ).
fof(f283,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f285,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f286,plain,
( ~ spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f221,f283,f260]) ).
fof(f288,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f290,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f291,plain,
( ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f220,f288,f260]) ).
fof(f293,definition,
( spl0_8
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| app(X1,X2) != sk1
| sk2 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f294,plain,
( ! [X2,X0,X1] :
( sk2 != app(app(X1,cons(X0,nil)),X2)
| app(X1,X2) != sk1
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f295,plain,
( ~ spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f219,f293,f260]) ).
fof(f297,definition,
( spl0_9
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f308,plain,
spl0_9,
inference(avatar_split_clause,[],[f252,f297]) ).
fof(f353,plain,
( ~ neq(sk2,nil)
| spl0_1 ),
inference(forward_demodulation,[],[f262,f204]) ).
fof(f354,plain,
( ~ spl0_9
| spl0_1 ),
inference(avatar_split_clause,[],[f353,f260,f297]) ).
fof(f357,plain,
( sk1 = app(sk6,sk7)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f270,f205]) ).
fof(f358,plain,
( sk2 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ spl0_4 ),
inference(forward_demodulation,[],[f275,f204]) ).
fof(f360,plain,
( sk2 != sk2
| sk1 != app(sk6,sk7)
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f294,f358]) ).
fof(f361,plain,
( sk1 != app(sk6,sk7)
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f360]) ).
fof(f362,plain,
( ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f361,f357]) ).
fof(f363,plain,
( ~ ssList(sk7)
| ~ ssList(sk6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f362,f290]) ).
fof(f364,plain,
( ~ ssList(sk6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f363,f280]) ).
fof(f365,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f364,f285]) ).
fof(f366,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f365]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f271]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f276]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f281]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f286]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f291]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f295]) ).
cnf(s16,plain,
spl0_9,
inference(sat_conversion,[],[f308]) ).
cnf(s27,plain,
( spl0_1
| ~ spl0_9 ),
inference(sat_conversion,[],[f354]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f366]) ).
cnf(s34,plain,
spl0_1,
inference(rat,[],[s27,s16]) ).
cnf(s35,plain,
spl0_8,
inference(rat,[],[s7,s34]) ).
cnf(s36,plain,
spl0_7,
inference(rat,[],[s6,s34]) ).
cnf(s37,plain,
spl0_6,
inference(rat,[],[s5,s34]) ).
cnf(s38,plain,
spl0_5,
inference(rat,[],[s4,s34]) ).
cnf(s39,plain,
spl0_4,
inference(rat,[],[s3,s34]) ).
cnf(s40,plain,
~ spl0_3,
inference(rat,[],[s29,s35,s36,s37,s38,s39]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s2,s40,s34]) ).
fof(f367,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC010-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n004.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 28 07:25:10 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 2.31/1.06 % (177965)Input is clausal, will run a generic CNF schedule.
% 2.31/1.06 % (177975)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=824460070:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.31/1.06 % (177975)First to succeed.
% 2.31/1.06 % (177975)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-177965"
% 2.31/1.06 % (177973)lrs+10_1_sil=8000:sp=occurrence:random_seed=3146164583:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.31/1.06 % (177970)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=1585977784:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.31/1.06 % (177974)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4086589345:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.31/1.06 % (177971)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2962937438:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.31/1.06 % (177972)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=61596362:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.31/1.06 % (177976)dis-21_1_sil=8000:lcm=predicate:random_seed=3373882191: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)
% 2.31/1.06 % (177974)Also succeeded, but the first one will report.
% 2.31/1.06 % (177973)Also succeeded, but the first one will report.
% 2.31/1.06 % (177976)Also succeeded, but the first one will report.
% 2.31/1.06 % (177975)Refutation found. Thanks to Tanya!
% 2.31/1.06 % SZS status Unsatisfiable for theBenchmark
% 2.31/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 2.31/1.06 % (177975)------------------------------
% 2.31/1.06 % (177975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/1.06 % (177975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/1.06 % (177975)CaDiCaL version: 2.1.3
% 2.31/1.06 % (177975)Termination reason: Refutation
% 2.31/1.06 % (177975)Time elapsed: 0.003 s
% 2.31/1.06 % (177975)Peak memory usage: 89 MB
% 2.31/1.06 % (177975)Instructions burned: 8 (million)
% 2.31/1.06 % (177975)------------------------------
% 2.31/1.06 % (177975)------------------------------
% 2.31/1.06 % (177965)Success in time 0.271 s
% 2.31/1.06 % Vampire exiting
%------------------------------------------------------------------------------