%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC018-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 01:04:18 PM UTC 2026
% Result : Unsatisfiable 0.06s 0.38s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 84 ( 17 unt; 6 def)
% Number of atoms : 247 ( 38 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 326 ( 163 ~; 157 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f61,axiom,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause61) ).
fof(f83,axiom,
! [X0] :
( nil != X0
| ~ ssList(X0)
| frontsegP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause83) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f121,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
inference(reorient_equations,[],[f121]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( app(X0,X1) != X2
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| frontsegP(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
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,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
sk4 = app(sk3,sk5),
inference(reorient_equations,[],[f207]) ).
fof(f212,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f214,negated_conjecture,
! [X0] :
( nil = sk2
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk2,X0)
| ~ frontsegP(sk1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f215,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f216,negated_conjecture,
! [X0] :
( nil != sk1
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk2,X0)
| ~ frontsegP(sk1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f220,plain,
! [X0] :
( nil = sk4
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(definition_unfolding,[],[f214,f204,f204,f205]) ).
fof(f221,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f215,f205,f204]) ).
fof(f222,plain,
! [X0] :
( nil != sk3
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(definition_unfolding,[],[f216,f205,f204,f205]) ).
fof(f225,plain,
( ~ ssList(nil)
| frontsegP(nil,nil) ),
inference(equality_resolution,[],[f83]) ).
fof(f234,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| frontsegP(app(X0,X1),X0) ),
inference(equality_resolution,[],[f155]) ).
fof(f254,definition,
( spl0_1
<=> ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ neq(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f255,plain,
( ! [X0] :
( ~ neq(X0,nil)
| ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ ssList(X0) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f257,definition,
( spl0_2
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f258,plain,
( nil = sk3
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( nil != sk3
| spl0_2 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f260,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f222,f257,f254]) ).
fof(f262,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f264,plain,
( neq(sk4,nil)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f221,f257,f262]) ).
fof(f267,definition,
( spl0_4
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f269,plain,
( nil = sk4
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f270,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f220,f267,f254]) ).
fof(f272,plain,
( ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f212,f267,f257]) ).
fof(f278,definition,
( spl0_6
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f279,plain,
( ssList(nil)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f291,definition,
( spl0_9
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f293,plain,
( frontsegP(nil,nil)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f294,plain,
( spl0_9
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f225,f278,f291]) ).
fof(f314,plain,
spl0_6,
inference(avatar_split_clause,[],[f8,f278]) ).
fof(f637,plain,
( ! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(sk3,X0)
| ~ neq(X0,nil) )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f255,f269]) ).
fof(f638,plain,
( neq(nil,nil)
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f264,f269]) ).
fof(f659,plain,
( ! [X0] :
( ~ frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ neq(X0,nil) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f637,f258]) ).
fof(f660,plain,
( ! [X0] :
( ~ neq(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f659]) ).
fof(f662,plain,
( ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(resolution,[],[f660,f638]) ).
fof(f664,plain,
( ~ frontsegP(nil,nil)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f662,f279]) ).
fof(f665,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f664,f293]) ).
fof(f666,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f665]) ).
fof(f701,plain,
( ! [X0] :
( ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0 )
| ~ spl0_1 ),
inference(resolution,[],[f255,f102]) ).
fof(f703,plain,
( ! [X0] :
( ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0 )
| ~ spl0_1 ),
inference(duplicate_literal_removal,[],[f701]) ).
fof(f705,plain,
( ! [X0] :
( ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f703,f279]) ).
fof(f1001,plain,
( nil != sk4
| ~ ssList(sk5)
| ~ ssList(sk3)
| nil = sk3 ),
inference(superposition,[],[f122,f208]) ).
fof(f1245,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f234,f85]) ).
fof(f1267,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(superposition,[],[f1245,f208]) ).
fof(f1272,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk5) ),
inference(forward_subsumption_resolution,[],[f1267,f202]) ).
fof(f1274,plain,
frontsegP(sk4,sk3),
inference(forward_subsumption_resolution,[],[f1272,f206]) ).
fof(f1275,plain,
( ~ frontsegP(sk3,sk3)
| ~ ssList(sk3)
| nil = sk3
| ~ spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f1274,f705]) ).
fof(f1277,plain,
( ~ ssList(sk3)
| nil = sk3
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f1275,f61]) ).
fof(f1278,plain,
( nil = sk3
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f1277,f202]) ).
fof(f1279,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f1278,f259]) ).
fof(f1280,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f1279]) ).
fof(f1283,plain,
( nil != sk4
| ~ ssList(sk3)
| nil = sk3 ),
inference(forward_subsumption_resolution,[],[f1001,f206]) ).
fof(f1288,plain,
( nil != sk4
| nil = sk3 ),
inference(forward_subsumption_resolution,[],[f1283,f202]) ).
fof(f1293,plain,
( nil != sk4
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f1288,f259]) ).
fof(f1304,plain,
( ~ spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f1293,f257,f267]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f260]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f265]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f270]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f272]) ).
cnf(s9,plain,
( ~ spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f294]) ).
cnf(s15,plain,
spl0_6,
inference(sat_conversion,[],[f314]) ).
cnf(s25,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_9 ),
inference(sat_conversion,[],[f666]) ).
cnf(s61,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_6 ),
inference(sat_conversion,[],[f1280]) ).
cnf(s65,plain,
( spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f1304]) ).
cnf(s69,plain,
spl0_9,
inference(rat,[],[s9,s15]) ).
cnf(s71,plain,
spl0_1,
inference(rat,[],[s65,s1,s3]) ).
cnf(s72,plain,
spl0_2,
inference(rat,[],[s61,s15,s71]) ).
cnf(s73,plain,
spl0_4,
inference(rat,[],[s5,s72]) ).
cnf(s74,plain,
spl0_3,
inference(rat,[],[s2,s72]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s25,s69,s15,s72,s71,s73,s74]) ).
fof(f1306,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC018-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.32 % Computer : n012.cluster.edu
% 0.03/0.32 % Model : x86_64 x86_64
% 0.03/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.32 % Memory : 8046.5625MB
% 0.03/0.32 % OS : Linux 6.8.0-71-generic
% 0.03/0.32 % CPULimit : 300
% 0.03/0.32 % WCLimit : 300
% 0.03/0.32 % DateTime : Mon Sep 28 07:26:34 UTC 2026
% 0.03/0.32 % CPUTime :
% 0.03/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.33 Running first-order model finding
% 0.06/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.38 % (3213012)Will run a generic schedule for satisfiability detection.
% 0.06/0.38 % (3213018)% WARNING: option uhcvi not known.
% 0.06/0.38 % (3213018)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1971775658:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.38 % (3213022)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=562184424:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.38 % (3213017)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3286560492_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.38 % (3213020)dis+10_1_sil=32000:sp=arity:random_seed=4072740237:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.38 % (3213019)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2656944427:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.38 % (3213021)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2060021148:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.38 % (3213023)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=299178333:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.38 % TRYING [1]
% 0.06/0.38 % TRYING [2]
% 0.06/0.38 % TRYING [3]
% 0.06/0.38 % (3213020) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3213012-3213020"...
% 0.06/0.38 % (3213020)...printing done.
% 0.06/0.38 % (3213020)Refutation found. Thanks to Tanya!
% 0.06/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.06/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.38 % (3213020)------------------------------
% 0.06/0.38 % (3213020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.38 % (3213020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.38 % (3213020)CaDiCaL version: 2.1.3
% 0.06/0.38 % (3213020)Termination reason: Refutation
% 0.06/0.38 % (3213020)Time elapsed: 0.013 s
% 0.06/0.38 % (3213020)Peak memory usage: 13 MB
% 0.06/0.38 % (3213020)Instructions burned: 35 (million)
% 0.06/0.38 % (3213012)Success in time 0.041 s
% 0.06/0.38 % Vampire exiting
%------------------------------------------------------------------------------