%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC096-1 : 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 : n011.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 01:02:25 PM UTC 2026
% Result : Unsatisfiable 2.65s 1.35s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 51 ( 12 unt; 6 def)
% Number of atoms : 128 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 158 ( 81 ~; 71 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 10 !; 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(f216,negated_conjecture,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,nil) != sk1
| app(X1,cons(X0,nil)) != sk2
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f217,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,nil) != sk1
| sk2 != app(X1,cons(X0,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f216]) ).
fof(f218,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f219,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f220,negated_conjecture,
( cons(sk5,nil) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f221,plain,
( sk3 = cons(sk5,nil)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f220]) ).
fof(f222,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f223,plain,
( sk4 = app(sk6,cons(sk5,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f222]) ).
fof(f226,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f206,f204,f204]) ).
fof(f233,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,nil) != sk3
| sk4 != app(X1,cons(X0,nil))
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f217,f205,f204]) ).
fof(f241,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f250,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f253,definition,
( spl0_4
<=> sk4 = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f254,plain,
( sk4 = app(sk6,cons(sk5,nil))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f255,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f223,f253,f250]) ).
fof(f257,definition,
( spl0_5
<=> sk3 = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f258,plain,
( sk3 = cons(sk5,nil)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f221,f257,f250]) ).
fof(f261,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f262,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f219,f261,f250]) ).
fof(f265,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f266,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f267,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f218,f265,f250]) ).
fof(f269,definition,
( spl0_8
<=> ! [X0,X1] :
( ~ ssItem(X0)
| cons(X0,nil) != sk3
| ~ ssList(X1)
| sk4 != app(X1,cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f270,plain,
( ! [X0,X1] :
( sk4 != app(X1,cons(X0,nil))
| cons(X0,nil) != sk3
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f271,plain,
( ~ spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f233,f269,f250]) ).
fof(f278,plain,
spl0_3,
inference(avatar_split_clause,[],[f241,f250]) ).
fof(f281,plain,
( sk4 != sk4
| sk3 != cons(sk5,nil)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f270,f254]) ).
fof(f282,plain,
( sk3 != cons(sk5,nil)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f281]) ).
fof(f284,plain,
( ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f282,f258]) ).
fof(f286,plain,
( ~ ssItem(sk5)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f284,f262]) ).
fof(f287,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f286,f266]) ).
fof(f288,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f287]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f255]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f259]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f263]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f267]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f271]) ).
cnf(s12,plain,
spl0_3,
inference(sat_conversion,[],[f278]) ).
cnf(s13,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f288]) ).
cnf(s14,plain,
spl0_8,
inference(rat,[],[s6,s12]) ).
cnf(s15,plain,
spl0_7,
inference(rat,[],[s5,s12]) ).
cnf(s16,plain,
spl0_6,
inference(rat,[],[s4,s12]) ).
cnf(s17,plain,
spl0_5,
inference(rat,[],[s3,s12]) ).
cnf(s18,plain,
~ spl0_4,
inference(rat,[],[s13,s14,s15,s16,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s2,s18,s12]) ).
fof(f289,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC096-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n011.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 07:51:56 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.65/1.35 % (3236246)Input is clausal, will run a generic CNF schedule.
% 2.65/1.35 % (3236255)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1487659373:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.65/1.35 % (3236255)First to succeed.
% 2.65/1.35 % (3236255)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3236246"
% 2.65/1.35 % (3236254)lrs+10_1_sil=8000:sp=occurrence:random_seed=1357479200:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.65/1.35 % (3236252)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2154688168:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.65/1.35 % (3236251)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=743101483:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.65/1.35 % (3236253)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1283084896:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.65/1.35 % (3236256)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1587858960:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.65/1.35 % (3236257)dis-21_1_sil=8000:lcm=predicate:random_seed=2186877378: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)
% 2.65/1.35 % (3236254)Also succeeded, but the first one will report.
% 2.65/1.35 % (3236257)Also succeeded, but the first one will report.
% 2.65/1.35 % (3236256)Also succeeded, but the first one will report.
% 2.65/1.35 % (3236255)Refutation found. Thanks to Tanya!
% 2.65/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.35 % (3236255)------------------------------
% 2.65/1.35 % (3236255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.35 % (3236255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.35 % (3236255)CaDiCaL version: 2.1.3
% 2.65/1.35 % (3236255)Termination reason: Refutation
% 2.65/1.35 % (3236255)Time elapsed: 0.002 s
% 2.65/1.35 % (3236255)Peak memory usage: 90 MB
% 2.65/1.35 % (3236255)Instructions burned: 3 (million)
% 2.65/1.35 % (3236255)------------------------------
% 2.65/1.35 % (3236255)------------------------------
% 2.65/1.35 % (3236246)Success in time 0.293 s
% 2.65/1.35 % Vampire exiting
%------------------------------------------------------------------------------