%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC312-1 : 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 : n003.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 01:03:25 PM UTC 2026
% Result : Unsatisfiable 2.74s 1.15s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 66 ( 8 unt; 9 def)
% Number of atoms : 166 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 196 ( 96 ~; 91 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f212,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f211]) ).
fof(f213,negated_conjecture,
( nil = sk2
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f214,negated_conjecture,
! [X0,X1] :
( nil = sk2
| ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk2
| app(X1,cons(X0,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f215,plain,
! [X0,X1] :
( nil = sk2
| ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk2
| sk1 != app(X1,cons(X0,nil)) ),
inference(reorient_equations,[],[f214]) ).
fof(f216,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f217,negated_conjecture,
! [X0,X1] :
( nil != sk1
| ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk2
| app(X1,cons(X0,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f218,plain,
! [X0,X1] :
( nil != sk1
| ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk2
| sk1 != app(X1,cons(X0,nil)) ),
inference(reorient_equations,[],[f217]) ).
fof(f221,plain,
( nil = sk4
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f213,f204,f204]) ).
fof(f222,plain,
! [X0,X1] :
( nil = sk4
| ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk4
| sk3 != app(X1,cons(X0,nil)) ),
inference(definition_unfolding,[],[f215,f204,f204,f205]) ).
fof(f223,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f216,f205,f204]) ).
fof(f224,plain,
! [X0,X1] :
( nil != sk3
| ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk4
| sk3 != app(X1,cons(X0,nil)) ),
inference(definition_unfolding,[],[f218,f205,f204,f205]) ).
fof(f246,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f247,plain,
( sQ0_eqProxy(nil,sk3)
| ~ sQ0_eqProxy(nil,sk4) ),
inference(equality_proxy_replacement,[],[f206,f246,f246]) ).
fof(f248,plain,
( sQ0_eqProxy(sk4,app(cons(sk5,nil),sk6))
| ~ neq(sk4,nil) ),
inference(equality_proxy_replacement,[],[f210,f246]) ).
fof(f249,plain,
( sQ0_eqProxy(sk3,app(sk6,cons(sk5,nil)))
| ~ neq(sk4,nil) ),
inference(equality_proxy_replacement,[],[f212,f246]) ).
fof(f250,plain,
( sQ0_eqProxy(nil,sk4)
| neq(sk4,nil) ),
inference(equality_proxy_replacement,[],[f221,f246]) ).
fof(f251,plain,
! [X0,X1] :
( sQ0_eqProxy(nil,sk4)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ sQ0_eqProxy(app(cons(X0,nil),X1),sk4)
| ~ sQ0_eqProxy(sk3,app(X1,cons(X0,nil))) ),
inference(equality_proxy_replacement,[],[f222,f246,f246,f246]) ).
fof(f252,plain,
( ~ sQ0_eqProxy(nil,sk3)
| neq(sk4,nil) ),
inference(equality_proxy_replacement,[],[f223,f246]) ).
fof(f253,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(nil,sk3)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ sQ0_eqProxy(app(cons(X0,nil),X1),sk4)
| ~ sQ0_eqProxy(sk3,app(X1,cons(X0,nil))) ),
inference(equality_proxy_replacement,[],[f224,f246,f246,f246]) ).
fof(f307,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f246]) ).
fof(f342,definition,
( spl1_8
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ sQ0_eqProxy(sk3,app(X1,cons(X0,nil)))
| ~ sQ0_eqProxy(app(cons(X0,nil),X1),sk4)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f343,plain,
( ! [X0,X1] :
( ~ sQ0_eqProxy(app(cons(X0,nil),X1),sk4)
| ~ sQ0_eqProxy(sk3,app(X1,cons(X0,nil)))
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f345,definition,
( spl1_9
<=> sQ0_eqProxy(nil,sk3) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f347,plain,
( spl1_8
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f253,f345,f342]) ).
fof(f349,definition,
( spl1_10
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f351,plain,
( spl1_10
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f252,f345,f349]) ).
fof(f353,definition,
( spl1_11
<=> sQ0_eqProxy(nil,sk4) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f355,plain,
( spl1_8
| spl1_11 ),
inference(avatar_split_clause,[],[f251,f353,f342]) ).
fof(f356,plain,
( spl1_10
| spl1_11 ),
inference(avatar_split_clause,[],[f250,f353,f349]) ).
fof(f359,definition,
( spl1_12
<=> sQ0_eqProxy(sk3,app(sk6,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f360,plain,
( sQ0_eqProxy(sk3,app(sk6,cons(sk5,nil)))
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f361,plain,
( ~ spl1_10
| spl1_12 ),
inference(avatar_split_clause,[],[f249,f359,f349]) ).
fof(f363,definition,
( spl1_13
<=> sQ0_eqProxy(sk4,app(cons(sk5,nil),sk6)) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f365,plain,
( ~ spl1_10
| spl1_13 ),
inference(avatar_split_clause,[],[f248,f363,f349]) ).
fof(f367,definition,
( spl1_14
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f369,plain,
( ~ spl1_10
| spl1_14 ),
inference(avatar_split_clause,[],[f208,f367,f349]) ).
fof(f371,definition,
( spl1_15
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f373,plain,
( ~ spl1_10
| spl1_15 ),
inference(avatar_split_clause,[],[f207,f371,f349]) ).
fof(f376,plain,
( ~ spl1_11
| spl1_9 ),
inference(avatar_split_clause,[],[f247,f345,f353]) ).
fof(f379,plain,
( ! [X0,X1] :
( ~ sQ0_eqProxy(sk3,app(X1,cons(X0,nil)))
| ~ sQ0_eqProxy(sk4,app(cons(X0,nil),X1))
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl1_8 ),
inference(resolution,[],[f307,f343]) ).
fof(f380,plain,
( ~ sQ0_eqProxy(sk4,app(cons(sk5,nil),sk6))
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ spl1_8
| ~ spl1_12 ),
inference(resolution,[],[f379,f360]) ).
fof(f385,plain,
( ~ spl1_14
| ~ spl1_15
| ~ spl1_13
| ~ spl1_8
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f380,f359,f342,f363,f371,f367]) ).
cnf(s7,plain,
( spl1_8
| ~ spl1_9 ),
inference(sat_conversion,[],[f347]) ).
cnf(s8,plain,
( ~ spl1_9
| spl1_10 ),
inference(sat_conversion,[],[f351]) ).
cnf(s9,plain,
( spl1_8
| spl1_11 ),
inference(sat_conversion,[],[f355]) ).
cnf(s10,plain,
( spl1_10
| spl1_11 ),
inference(sat_conversion,[],[f356]) ).
cnf(s11,plain,
( ~ spl1_10
| spl1_12 ),
inference(sat_conversion,[],[f361]) ).
cnf(s12,plain,
( ~ spl1_10
| spl1_13 ),
inference(sat_conversion,[],[f365]) ).
cnf(s13,plain,
( ~ spl1_10
| spl1_14 ),
inference(sat_conversion,[],[f369]) ).
cnf(s14,plain,
( ~ spl1_10
| spl1_15 ),
inference(sat_conversion,[],[f373]) ).
cnf(s15,plain,
( spl1_9
| ~ spl1_11 ),
inference(sat_conversion,[],[f376]) ).
cnf(s17,plain,
( ~ spl1_8
| ~ spl1_12
| ~ spl1_13
| ~ spl1_14
| ~ spl1_15 ),
inference(sat_conversion,[],[f385]) ).
cnf(s24,plain,
spl1_8,
inference(rat,[],[s15,s7,s9]) ).
cnf(s25,plain,
~ spl1_10,
inference(rat,[],[s17,s11,s12,s13,s14,s24]) ).
cnf(s26,plain,
spl1_11,
inference(rat,[],[s10,s25]) ).
cnf(s27,plain,
~ spl1_9,
inference(rat,[],[s8,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s15,s26,s27]) ).
fof(f386,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC312-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.19 % Computer : n003.cluster.edu
% 0.14/0.19 % Model : x86_64 x86_64
% 0.14/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.19 % Memory : 8046.5625MB
% 0.14/0.19 % OS : Linux 6.8.0-71-generic
% 0.14/0.19 % CPULimit : 300
% 0.14/0.19 % WCLimit : 300
% 0.14/0.19 % DateTime : Mon Sep 28 09:02:42 UTC 2026
% 0.14/0.20 % CPUTime :
% 0.14/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.22 Running first-order theorem proving
% 0.14/0.22 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
% 2.74/1.15 % (1447046)Input is clausal, will run a generic CNF schedule.
% 2.74/1.15 % (1447057)dis-21_1_sil=8000:lcm=predicate:random_seed=4218077964: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)
% 2.74/1.15 % (1447057)First to succeed.
% 2.74/1.15 % (1447057)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1447046"
% 2.74/1.15 % (1447056)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3545622387:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.74/1.15 % (1447052)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1080720352:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.74/1.15 % (1447054)lrs+10_1_sil=8000:sp=occurrence:random_seed=29440344:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.74/1.15 % (1447055)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2846815162:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.74/1.15 % (1447053)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2712220826:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.74/1.15 % (1447051)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=137523391:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.74/1.15 % (1447055)Also succeeded, but the first one will report.
% 2.74/1.15 % (1447054)Also succeeded, but the first one will report.
% 2.74/1.15 % (1447056)Also succeeded, but the first one will report.
% 2.74/1.15 % (1447057)Refutation found. Thanks to Tanya!
% 2.74/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.15 % (1447057)------------------------------
% 2.74/1.15 % (1447057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.15 % (1447057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.15 % (1447057)CaDiCaL version: 2.1.3
% 2.74/1.15 % (1447057)Termination reason: Refutation
% 2.74/1.15 % (1447057)Time elapsed: 0.003 s
% 2.74/1.15 % (1447057)Peak memory usage: 89 MB
% 2.74/1.15 % (1447057)Instructions burned: 8 (million)
% 2.74/1.15 % (1447057)------------------------------
% 2.74/1.15 % (1447057)------------------------------
% 2.74/1.15 % (1447046)Success in time 0.298 s
% 2.74/1.15 % Vampire exiting
%------------------------------------------------------------------------------