%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC322-1 : 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 : n013.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 01:03:27 PM UTC 2026
% Result : Unsatisfiable 2.75s 1.18s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 68 ( 10 unt; 6 def)
% Number of atoms : 146 ( 51 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 142 ( 64 ~; 72 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn 4 !; 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,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = sk3
| app(X1,cons(X0,nil)) != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = sk3
| ~ ssList(X1)
| ~ ssItem(X0)
| sk4 != app(X1,cons(X0,nil)) ),
inference(reorient_equations,[],[f206]) ).
fof(f208,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f209,negated_conjecture,
( ssItem(sk5)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
( ssItem(sk5)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f211,negated_conjecture,
( ssList(sk6)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk2
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f213,plain,
( sk2 = app(sk6,cons(sk5,nil))
| nil = sk2 ),
inference(reorient_equations,[],[f212]) ).
fof(f214,negated_conjecture,
( app(cons(sk5,nil),sk6) != sk1
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f215,plain,
( sk1 != app(cons(sk5,nil),sk6)
| nil = sk2 ),
inference(reorient_equations,[],[f214]) ).
fof(f216,negated_conjecture,
( ssList(sk6)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f217,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk2
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f218,plain,
( sk2 = app(sk6,cons(sk5,nil))
| nil != sk1 ),
inference(reorient_equations,[],[f217]) ).
fof(f219,negated_conjecture,
( app(cons(sk5,nil),sk6) != sk1
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f220,plain,
( sk1 != app(cons(sk5,nil),sk6)
| nil != sk1 ),
inference(reorient_equations,[],[f219]) ).
fof(f223,plain,
( ssItem(sk5)
| nil = sk4 ),
inference(definition_unfolding,[],[f209,f204]) ).
fof(f224,plain,
( ssItem(sk5)
| nil != sk3 ),
inference(definition_unfolding,[],[f210,f205]) ).
fof(f225,plain,
( ssList(sk6)
| nil = sk4 ),
inference(definition_unfolding,[],[f211,f204]) ).
fof(f226,plain,
( sk4 = app(sk6,cons(sk5,nil))
| nil = sk4 ),
inference(definition_unfolding,[],[f213,f204,f204]) ).
fof(f227,plain,
( sk3 != app(cons(sk5,nil),sk6)
| nil = sk4 ),
inference(definition_unfolding,[],[f215,f205,f204]) ).
fof(f228,plain,
( ssList(sk6)
| nil != sk3 ),
inference(definition_unfolding,[],[f216,f205]) ).
fof(f229,plain,
( sk4 = app(sk6,cons(sk5,nil))
| nil != sk3 ),
inference(definition_unfolding,[],[f218,f204,f205]) ).
fof(f230,plain,
( sk3 != app(cons(sk5,nil),sk6)
| nil != sk3 ),
inference(definition_unfolding,[],[f220,f205,f205]) ).
fof(f242,definition,
( spl0_3
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f245,definition,
( spl0_4
<=> sk3 = app(cons(sk5,nil),sk6) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f246,plain,
( sk3 != app(cons(sk5,nil),sk6)
| spl0_4 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f247,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f230,f245,f242]) ).
fof(f249,definition,
( spl0_5
<=> sk4 = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f250,plain,
( sk4 = app(sk6,cons(sk5,nil))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f229,f249,f242]) ).
fof(f253,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f254,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f255,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f228,f253,f242]) ).
fof(f257,definition,
( spl0_7
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f259,plain,
( spl0_7
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f227,f245,f257]) ).
fof(f260,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f226,f249,f257]) ).
fof(f261,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f225,f253,f257]) ).
fof(f263,definition,
( spl0_8
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f264,plain,
( ssItem(sk5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f265,plain,
( ~ spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f224,f263,f242]) ).
fof(f266,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f223,f263,f257]) ).
fof(f269,plain,
( ~ spl0_7
| spl0_3 ),
inference(avatar_split_clause,[],[f208,f242,f257]) ).
fof(f274,plain,
( sk3 != sk3
| ~ ssList(sk6)
| ~ ssItem(sk5)
| sk4 != app(sk6,cons(sk5,nil))
| spl0_4 ),
inference(superposition,[],[f246,f207]) ).
fof(f277,plain,
( ~ ssList(sk6)
| ~ ssItem(sk5)
| sk4 != app(sk6,cons(sk5,nil))
| spl0_4 ),
inference(trivial_inequality_removal,[],[f274]) ).
fof(f278,plain,
( ~ ssItem(sk5)
| sk4 != app(sk6,cons(sk5,nil))
| spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f277,f254]) ).
fof(f279,plain,
( sk4 != app(sk6,cons(sk5,nil))
| spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f278,f264]) ).
fof(f280,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f279,f250]) ).
fof(f281,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f280]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f247]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f251]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f255]) ).
cnf(s5,plain,
( ~ spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f259]) ).
cnf(s6,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f260]) ).
cnf(s7,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f261]) ).
cnf(s8,plain,
( ~ spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f265]) ).
cnf(s9,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f266]) ).
cnf(s10,plain,
( spl0_3
| ~ spl0_7 ),
inference(sat_conversion,[],[f269]) ).
cnf(s11,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f281]) ).
cnf(s12,plain,
spl0_7,
inference(rat,[],[s11,s5,s6,s7,s9]) ).
cnf(s13,plain,
spl0_3,
inference(rat,[],[s10,s12]) ).
cnf(s14,plain,
spl0_8,
inference(rat,[],[s8,s13]) ).
cnf(s15,plain,
spl0_6,
inference(rat,[],[s4,s13]) ).
cnf(s16,plain,
spl0_5,
inference(rat,[],[s3,s13]) ).
cnf(s17,plain,
~ spl0_4,
inference(rat,[],[s2,s13]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s11,s14,s15,s16,s17]) ).
fof(f282,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC322-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n013.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 09:04:49 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 2.75/1.18 % (1039166)Input is clausal, will run a generic CNF schedule.
% 2.75/1.18 % (1039175)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2128570901:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.75/1.18 % (1039175)First to succeed.
% 2.75/1.18 % (1039175)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1039166"
% 2.75/1.18 % (1039171)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=654858350:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.75/1.18 % (1039177)dis-21_1_sil=8000:lcm=predicate:random_seed=1635202998: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)
% 2.75/1.18 % (1039173)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1703449973:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.75/1.18 % (1039172)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2990580838:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.75/1.18 % (1039174)lrs+10_1_sil=8000:sp=occurrence:random_seed=3742026421:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.75/1.18 % (1039174)Also succeeded, but the first one will report.
% 2.75/1.18 % (1039177)Also succeeded, but the first one will report.
% 2.75/1.18 % (1039176)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3735656100:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.75/1.18 % (1039176)Also succeeded, but the first one will report.
% 2.75/1.18 % (1039175)Refutation found. Thanks to Tanya!
% 2.75/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.75/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.18 % (1039175)------------------------------
% 2.75/1.18 % (1039175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.18 % (1039175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.18 % (1039175)CaDiCaL version: 2.1.3
% 2.75/1.18 % (1039175)Termination reason: Refutation
% 2.75/1.18 % (1039175)Time elapsed: 0.002 s
% 2.75/1.18 % (1039175)Peak memory usage: 90 MB
% 2.75/1.18 % (1039175)Instructions burned: 4 (million)
% 2.75/1.18 % (1039175)------------------------------
% 2.75/1.18 % (1039175)------------------------------
% 2.75/1.18 % (1039166)Success in time 0.3 s
% 2.75/1.18 % Vampire exiting
%------------------------------------------------------------------------------