%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC097+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 : n002.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 : Theorem 2.72s 1.33s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 10 unt; 5 def)
% Number of atoms : 137 ( 26 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 154 ( 58 ~; 47 |; 34 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 20 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& app(X0,cons(X4,nil)) = X1 )
| ! [X5] :
( ssItem(X5)
=> app(X2,cons(X5,nil)) != X3 ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& app(X0,cons(X4,nil)) = X1 )
| ! [X5] :
( ssItem(X5)
=> app(X2,cons(X5,nil)) != X3 ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| app(X0,cons(X4,nil)) != X1 )
& ? [X5] :
( app(X2,cons(X5,nil)) = X3
& ssItem(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| app(X0,cons(X4,nil)) != X1 )
& ? [X5] :
( app(X2,cons(X5,nil)) = X3
& ssItem(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f216,plain,
( sK7 = sK9
& sK6 = sK8
& ( ( neq(sK7,nil)
& ! [X4] :
( ~ ssItem(X4)
| sK7 != app(sK6,cons(X4,nil)) )
& sK9 = app(sK8,cons(sK10,nil))
& ssItem(sK10) )
| ( neq(sK7,nil)
& ~ neq(sK9,nil) ) )
& ssList(sK9)
& ssList(sK8)
& ssList(sK7)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9),skolemize(X5,sK10)],[f99]) ).
fof(f269,plain,
( ssItem(sK10)
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f216]) ).
fof(f271,plain,
( sK9 = app(sK8,cons(sK10,nil))
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f216]) ).
fof(f273,plain,
! [X4] :
( ~ ssItem(X4)
| sK7 != app(sK6,cons(X4,nil))
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f216]) ).
fof(f276,plain,
( neq(sK7,nil)
| neq(sK7,nil) ),
inference(cnf_transformation,[],[f216]) ).
fof(f277,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f216]) ).
fof(f278,plain,
sK7 = sK9,
inference(cnf_transformation,[],[f216]) ).
fof(f440,plain,
( neq(sK9,nil)
| neq(sK9,nil) ),
inference(definition_unfolding,[],[f276,f278,f278]) ).
fof(f443,plain,
! [X4] :
( ~ ssItem(X4)
| sK9 != app(sK8,cons(X4,nil))
| ~ neq(sK9,nil) ),
inference(definition_unfolding,[],[f273,f278,f277]) ).
fof(f469,definition,
! [X0,X1] :
( sQ46_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ46_eqProxy])],[equality_proxy_definition]) ).
fof(f471,plain,
! [X4] :
( ~ ssItem(X4)
| ~ sQ46_eqProxy(sK9,app(sK8,cons(X4,nil)))
| ~ neq(sK9,nil) ),
inference(equality_proxy_replacement,[],[f443,f469]) ).
fof(f473,plain,
( sQ46_eqProxy(sK9,app(sK8,cons(sK10,nil)))
| ~ neq(sK9,nil) ),
inference(equality_proxy_replacement,[],[f271,f469]) ).
fof(f540,plain,
neq(sK9,nil),
inference(duplicate_literal_removal,[],[f440]) ).
fof(f580,definition,
( spl47_11
<=> neq(sK9,nil) ),
introduced(definition,[new_symbols(definition,[spl47_11])],[avatar_definition]) ).
fof(f583,definition,
( spl47_12
<=> ssItem(sK10) ),
introduced(definition,[new_symbols(definition,[spl47_12])],[avatar_definition]) ).
fof(f584,plain,
( ssItem(sK10)
| ~ spl47_12 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f585,plain,
( ~ spl47_11
| spl47_12 ),
inference(avatar_split_clause,[],[f269,f583,f580]) ).
fof(f589,definition,
( spl47_13
<=> sQ46_eqProxy(sK9,app(sK8,cons(sK10,nil))) ),
introduced(definition,[new_symbols(definition,[spl47_13])],[avatar_definition]) ).
fof(f590,plain,
( sQ46_eqProxy(sK9,app(sK8,cons(sK10,nil)))
| ~ spl47_13 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f591,plain,
( ~ spl47_11
| spl47_13 ),
inference(avatar_split_clause,[],[f473,f589,f580]) ).
fof(f594,definition,
( spl47_14
<=> ! [X4] :
( ~ ssItem(X4)
| ~ sQ46_eqProxy(sK9,app(sK8,cons(X4,nil))) ) ),
introduced(definition,[new_symbols(definition,[spl47_14])],[avatar_definition]) ).
fof(f595,plain,
( ! [X4] :
( ~ sQ46_eqProxy(sK9,app(sK8,cons(X4,nil)))
| ~ ssItem(X4) )
| ~ spl47_14 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f596,plain,
( ~ spl47_11
| spl47_14 ),
inference(avatar_split_clause,[],[f471,f594,f580]) ).
fof(f598,plain,
spl47_11,
inference(avatar_split_clause,[],[f540,f580]) ).
fof(f599,plain,
( ~ ssItem(sK10)
| ~ spl47_13
| ~ spl47_14 ),
inference(resolution,[],[f595,f590]) ).
fof(f600,plain,
( $false
| ~ spl47_12
| ~ spl47_13
| ~ spl47_14 ),
inference(resolution,[],[f599,f584]) ).
fof(f601,plain,
( ~ spl47_12
| ~ spl47_13
| ~ spl47_14 ),
inference(avatar_contradiction_clause,[],[f600]) ).
cnf(s9,plain,
( ~ spl47_11
| spl47_12 ),
inference(sat_conversion,[],[f585]) ).
cnf(s11,plain,
( ~ spl47_11
| spl47_13 ),
inference(sat_conversion,[],[f591]) ).
cnf(s13,plain,
( ~ spl47_11
| spl47_14 ),
inference(sat_conversion,[],[f596]) ).
cnf(s15,plain,
spl47_11,
inference(sat_conversion,[],[f598]) ).
cnf(s16,plain,
( ~ spl47_12
| ~ spl47_13
| ~ spl47_14 ),
inference(sat_conversion,[],[f601]) ).
cnf(s17,plain,
spl47_14,
inference(rat,[],[s13,s15]) ).
cnf(s18,plain,
spl47_13,
inference(rat,[],[s11,s15]) ).
cnf(s19,plain,
~ spl47_12,
inference(rat,[],[s16,s17,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s9,s19,s15]) ).
fof(f602,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC097+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 07:54:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.72/1.33 % (197408)Detected formulas, will run a generic FOF schedule.
% 2.72/1.33 % (197419)dis-21_1_sil=8000:lcm=predicate:random_seed=3055291683:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.72/1.33 % (197419)First to succeed.
% 2.72/1.33 % (197419)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-197408"
% 2.72/1.33 % (197416)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=836632784:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.33 % (197415)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1745429166:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.33 % (197417)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1664291123:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.33 % (197413)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=2656452416:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.33 % (197414)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2945791839:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.33 % (197418)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2762534575:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.33 % (197417)Also succeeded, but the first one will report.
% 2.72/1.33 % (197416)Also succeeded, but the first one will report.
% 2.72/1.33 % (197418)Also succeeded, but the first one will report.
% 2.72/1.33 % (197419)Refutation found. Thanks to Tanya!
% 2.72/1.33 % SZS status Theorem for theBenchmark
% 2.72/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.34 % (197419)------------------------------
% 2.72/1.34 % (197419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.34 % (197419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.34 % (197419)CaDiCaL version: 2.1.3
% 2.72/1.34 % (197419)Termination reason: Refutation
% 2.72/1.34 % (197419)Time elapsed: 0.004 s
% 2.72/1.34 % (197419)Peak memory usage: 90 MB
% 2.72/1.34 % (197419)Instructions burned: 9 (million)
% 2.72/1.34 % (197419)------------------------------
% 2.72/1.34 % (197419)------------------------------
% 2.72/1.34 % (197408)Success in time 0.306 s
% 2.72/1.34 % Vampire exiting
%------------------------------------------------------------------------------