%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC106+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 : n019.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 01:04:41 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 83 ( 19 unt; 8 def)
% Number of atoms : 258 ( 39 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 302 ( 127 ~; 113 |; 30 &)
% ( 12 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 56 ( 0 sgn 42 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X2,X1) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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)
=> ! [X5] :
( ssList(X5)
=> ( cons(X4,nil) != X2
| app(X5,cons(X4,nil)) != X3 ) ) )
| ( neq(X0,nil)
& rearsegP(X1,X0) ) )
& ( ~ 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)
=> ! [X5] :
( ssList(X5)
=> ( cons(X4,nil) != X2
| app(X5,cons(X4,nil)) != X3 ) ) )
| ( neq(X0,nil)
& rearsegP(X1,X0) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X2,X1) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ? [X4] :
( ? [X5] :
( cons(X4,nil) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
& ( ~ neq(X0,nil)
| ~ rearsegP(X1,X0) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ? [X4] :
( ? [X5] :
( cons(X4,nil) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
& ( ~ neq(X0,nil)
| ~ rearsegP(X1,X0) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f240,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f303,plain,
! [X0,X1] :
( neq(X0,X1)
| ~ ssList(X1)
| X0 = X1
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f307,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f318,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f414,plain,
( ~ neq(sK50,nil)
| ssList(sK52) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
( ~ neq(sK50,nil)
| sK50 = app(sK52,cons(sK51,nil)) ),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
( ~ neq(sK50,nil)
| sK49 = cons(sK51,nil) ),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
( ~ neq(sK50,nil)
| ~ rearsegP(sK48,sK47)
| ~ neq(sK47,nil) ),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f432,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f421,f425]) ).
fof(f434,plain,
( ~ neq(sK50,nil)
| ~ rearsegP(sK50,sK49)
| ~ neq(sK49,nil) ),
inference(definition_unfolding,[],[f419,f425,f424,f424]) ).
fof(f443,plain,
! [X2,X1] :
( ~ ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X2,X1),X1) ),
inference(equality_resolution,[],[f240]) ).
fof(f472,definition,
( spl53_1
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl53_1])],[avatar_definition]) ).
fof(f474,plain,
( ssList(sK52)
| ~ spl53_1 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f476,definition,
( spl53_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f481,definition,
( spl53_3
<=> sK50 = app(sK52,cons(sK51,nil)) ),
introduced(definition,[new_symbols(definition,[spl53_3])],[avatar_definition]) ).
fof(f483,plain,
( sK50 = app(sK52,cons(sK51,nil))
| ~ spl53_3 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f486,definition,
( spl53_4
<=> sK49 = cons(sK51,nil) ),
introduced(definition,[new_symbols(definition,[spl53_4])],[avatar_definition]) ).
fof(f488,plain,
( sK49 = cons(sK51,nil)
| ~ spl53_4 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f490,plain,
( spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f414,f476,f472]) ).
fof(f491,plain,
( spl53_3
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f415,f476,f481]) ).
fof(f492,plain,
( spl53_4
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f416,f476,f486]) ).
fof(f494,definition,
( spl53_5
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl53_5])],[avatar_definition]) ).
fof(f496,plain,
( ssItem(sK51)
| ~ spl53_5 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f497,plain,
( spl53_5
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f417,f476,f494]) ).
fof(f500,definition,
( spl53_6
<=> neq(sK49,nil) ),
introduced(definition,[new_symbols(definition,[spl53_6])],[avatar_definition]) ).
fof(f502,plain,
( ~ neq(sK49,nil)
| spl53_6 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f504,definition,
( spl53_7
<=> rearsegP(sK50,sK49) ),
introduced(definition,[new_symbols(definition,[spl53_7])],[avatar_definition]) ).
fof(f507,plain,
( ~ spl53_6
| ~ spl53_7
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f434,f476,f504,f500]) ).
fof(f509,plain,
spl53_2,
inference(avatar_split_clause,[],[f432,f476]) ).
fof(f511,definition,
( spl53_8
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl53_8])],[avatar_definition]) ).
fof(f512,plain,
( ssList(nil)
| ~ spl53_8 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f539,plain,
spl53_8,
inference(avatar_split_clause,[],[f306,f511]) ).
fof(f540,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f443,f318]) ).
fof(f542,plain,
( sK50 = app(sK52,sK49)
| ~ spl53_3
| ~ spl53_4 ),
inference(superposition,[],[f483,f488]) ).
fof(f662,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(sK51,X0) != X0 )
| ~ spl53_5 ),
inference(resolution,[],[f307,f496]) ).
fof(f665,plain,
( nil != cons(sK51,nil)
| ~ spl53_5
| ~ spl53_8 ),
inference(resolution,[],[f662,f512]) ).
fof(f672,plain,
( nil != sK49
| ~ spl53_4
| ~ spl53_5
| ~ spl53_8 ),
inference(forward_demodulation,[],[f665,f488]) ).
fof(f700,plain,
( rearsegP(sK50,sK49)
| ~ ssList(sK52)
| ~ ssList(sK49)
| ~ spl53_3
| ~ spl53_4 ),
inference(superposition,[],[f540,f542]) ).
fof(f702,plain,
( rearsegP(sK50,sK49)
| ~ ssList(sK49)
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4 ),
inference(forward_subsumption_resolution,[],[f700,f474]) ).
fof(f704,plain,
( rearsegP(sK50,sK49)
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4 ),
inference(forward_subsumption_resolution,[],[f702,f426]) ).
fof(f706,plain,
( spl53_7
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4 ),
inference(avatar_split_clause,[],[f704,f486,f481,f472,f504]) ).
fof(f748,plain,
( ~ ssList(nil)
| nil = sK49
| ~ ssList(sK49)
| spl53_6 ),
inference(resolution,[],[f303,f502]) ).
fof(f753,plain,
( nil = sK49
| ~ ssList(sK49)
| spl53_6
| ~ spl53_8 ),
inference(forward_subsumption_resolution,[],[f748,f512]) ).
fof(f754,plain,
( ~ ssList(sK49)
| ~ spl53_4
| ~ spl53_5
| spl53_6
| ~ spl53_8 ),
inference(forward_subsumption_resolution,[],[f753,f672]) ).
fof(f755,plain,
( $false
| ~ spl53_4
| ~ spl53_5
| spl53_6
| ~ spl53_8 ),
inference(forward_subsumption_resolution,[],[f754,f426]) ).
fof(f756,plain,
( ~ spl53_4
| ~ spl53_5
| spl53_6
| ~ spl53_8 ),
inference(avatar_contradiction_clause,[],[f755]) ).
cnf(s4,plain,
( spl53_1
| ~ spl53_2 ),
inference(sat_conversion,[],[f490]) ).
cnf(s5,plain,
( ~ spl53_2
| spl53_3 ),
inference(sat_conversion,[],[f491]) ).
cnf(s6,plain,
( ~ spl53_2
| spl53_4 ),
inference(sat_conversion,[],[f492]) ).
cnf(s7,plain,
( ~ spl53_2
| spl53_5 ),
inference(sat_conversion,[],[f497]) ).
cnf(s9,plain,
( ~ spl53_2
| ~ spl53_6
| ~ spl53_7 ),
inference(sat_conversion,[],[f507]) ).
cnf(s11,plain,
spl53_2,
inference(sat_conversion,[],[f509]) ).
cnf(s19,plain,
spl53_8,
inference(sat_conversion,[],[f539]) ).
cnf(s20,plain,
( ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| spl53_7 ),
inference(sat_conversion,[],[f706]) ).
cnf(s23,plain,
( ~ spl53_4
| ~ spl53_5
| spl53_6
| ~ spl53_8 ),
inference(sat_conversion,[],[f756]) ).
cnf(s27,plain,
( ~ spl53_6
| ~ spl53_7 ),
inference(rat,[],[s9,s11]) ).
cnf(s28,plain,
spl53_5,
inference(rat,[],[s7,s11]) ).
cnf(s29,plain,
spl53_4,
inference(rat,[],[s6,s11]) ).
cnf(s30,plain,
spl53_6,
inference(rat,[],[s23,s19,s28,s29]) ).
cnf(s31,plain,
~ spl53_7,
inference(rat,[],[s27,s30]) ).
cnf(s32,plain,
spl53_3,
inference(rat,[],[s5,s11]) ).
cnf(s33,plain,
~ spl53_1,
inference(rat,[],[s20,s31,s29,s32]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s4,s11,s33]) ).
fof(f757,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC106+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 28 07:54:03 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 Running first-order model finding
% 0.12/0.38 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
% 0.12/0.44 % (3842081)Will run a generic schedule for satisfiability detection.
% 0.12/0.44 % (3842088)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4234557328:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.44 % (3842087)% WARNING: option uhcvi not known.
% 0.12/0.44 % (3842086)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1588296275_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.44 % (3842090)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1927122288:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.44 % (3842087)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1814618804:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.44 % (3842089)dis+10_1_sil=32000:sp=arity:random_seed=308711686:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.44 % (3842091)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=376433065:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.44 % (3842092)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=420934084:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.44 % TRYING [1]
% 0.12/0.44 % TRYING [2]
% 0.12/0.44 % (3842090) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3842081-3842090"...
% 0.12/0.44 % (3842090)...printing done.
% 0.12/0.44 % (3842090)Refutation found. Thanks to Tanya!
% 0.12/0.44 % SZS status Theorem for theBenchmark
% 0.12/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (3842090)------------------------------
% 0.12/0.45 % (3842090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (3842090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (3842090)CaDiCaL version: 2.1.3
% 0.12/0.45 % (3842090)Termination reason: Refutation
% 0.12/0.45 % (3842090)Time elapsed: 0.017 s
% 0.12/0.45 % (3842090)Peak memory usage: 13 MB
% 0.12/0.45 % (3842090)Instructions burned: 28 (million)
% 0.12/0.45 % (3842081)Success in time 0.054 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------