%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC100+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 : n008.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 01:04:40 PM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 85 ( 18 unt; 6 def)
% Number of atoms : 297 ( 64 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 350 ( 138 ~; 137 |; 46 &)
% ( 12 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 44 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ strictorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& lt(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ( neq(X0,nil)
& frontsegP(X1,X0) ) ) ) ) ) ) ) ),
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
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ strictorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& lt(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ( neq(X0,nil)
& frontsegP(X1,X0) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f158,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& strictorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ lt(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ( ~ neq(X0,nil)
| ~ frontsegP(X1,X0) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& strictorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ lt(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ( ~ neq(X0,nil)
| ~ frontsegP(X1,X0) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f237,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
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(f318,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f347,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f412,plain,
( ~ frontsegP(sK48,sK47)
| ~ neq(sK47,nil)
| nil = sK48 ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
( ~ frontsegP(sK48,sK47)
| ~ neq(sK47,nil)
| nil != sK47 ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
ssList(sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
sK50 = app(sK49,sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
( neq(sK48,nil)
| nil != sK47 ),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
( nil != sK49
| nil = sK50 ),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f422,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f429,plain,
( neq(sK50,nil)
| nil != sK49 ),
inference(definition_unfolding,[],[f417,f422,f421]) ).
fof(f430,plain,
( ~ frontsegP(sK50,sK49)
| ~ neq(sK49,nil)
| nil != sK49 ),
inference(definition_unfolding,[],[f413,f422,f421,f421,f421]) ).
fof(f431,plain,
( ~ frontsegP(sK50,sK49)
| ~ neq(sK49,nil)
| nil = sK50 ),
inference(definition_unfolding,[],[f412,f422,f421,f421,f422]) ).
fof(f435,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f237]) ).
fof(f465,definition,
( spl52_1
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
fof(f467,plain,
( nil = sK50
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f469,definition,
( spl52_2
<=> neq(sK49,nil) ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
fof(f471,plain,
( ~ neq(sK49,nil)
| spl52_2 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f473,definition,
( spl52_3
<=> frontsegP(sK50,sK49) ),
introduced(definition,[new_symbols(definition,[spl52_3])],[avatar_definition]) ).
fof(f474,plain,
( frontsegP(sK50,sK49)
| ~ spl52_3 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f476,plain,
( spl52_1
| ~ spl52_2
| ~ spl52_3 ),
inference(avatar_split_clause,[],[f431,f473,f469,f465]) ).
fof(f478,definition,
( spl52_4
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl52_4])],[avatar_definition]) ).
fof(f479,plain,
( nil = sK49
| ~ spl52_4 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f480,plain,
( nil != sK49
| spl52_4 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f481,plain,
( ~ spl52_4
| ~ spl52_2
| ~ spl52_3 ),
inference(avatar_split_clause,[],[f430,f473,f469,f478]) ).
fof(f483,definition,
( spl52_5
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl52_5])],[avatar_definition]) ).
fof(f485,plain,
( neq(sK50,nil)
| ~ spl52_5 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f486,plain,
( ~ spl52_4
| spl52_5 ),
inference(avatar_split_clause,[],[f429,f483,f478]) ).
fof(f488,plain,
( spl52_1
| ~ spl52_4 ),
inference(avatar_split_clause,[],[f419,f478,f465]) ).
fof(f490,definition,
( spl52_6
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl52_6])],[avatar_definition]) ).
fof(f491,plain,
( ssList(nil)
| ~ spl52_6 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f518,plain,
spl52_6,
inference(avatar_split_clause,[],[f306,f490]) ).
fof(f520,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f435,f318]) ).
fof(f605,plain,
( frontsegP(sK50,sK49)
| ~ ssList(sK51)
| ~ ssList(sK49) ),
inference(superposition,[],[f520,f416]) ).
fof(f610,plain,
( frontsegP(sK50,sK49)
| ~ ssList(sK49) ),
inference(forward_subsumption_resolution,[],[f605,f414]) ).
fof(f611,plain,
frontsegP(sK50,sK49),
inference(forward_subsumption_resolution,[],[f610,f423]) ).
fof(f612,plain,
spl52_3,
inference(avatar_split_clause,[],[f611,f473]) ).
fof(f628,plain,
( ~ ssList(nil)
| nil = sK49
| ~ ssList(sK49)
| spl52_2 ),
inference(resolution,[],[f303,f471]) ).
fof(f633,plain,
( nil = sK49
| ~ ssList(sK49)
| spl52_2
| ~ spl52_6 ),
inference(forward_subsumption_resolution,[],[f628,f491]) ).
fof(f634,plain,
( ~ ssList(sK49)
| spl52_2
| spl52_4
| ~ spl52_6 ),
inference(forward_subsumption_resolution,[],[f633,f480]) ).
fof(f635,plain,
( $false
| spl52_2
| spl52_4
| ~ spl52_6 ),
inference(forward_subsumption_resolution,[],[f634,f423]) ).
fof(f636,plain,
( spl52_2
| spl52_4
| ~ spl52_6 ),
inference(avatar_contradiction_clause,[],[f635]) ).
fof(f638,plain,
( frontsegP(nil,sK49)
| ~ spl52_1
| ~ spl52_3 ),
inference(superposition,[],[f474,f467]) ).
fof(f639,plain,
( neq(nil,nil)
| ~ spl52_1
| ~ spl52_5 ),
inference(superposition,[],[f485,f467]) ).
fof(f648,plain,
( ~ neq(nil,nil)
| spl52_2
| ~ spl52_4 ),
inference(superposition,[],[f471,f479]) ).
fof(f656,plain,
( $false
| ~ spl52_1
| spl52_2
| ~ spl52_4
| ~ spl52_5 ),
inference(forward_subsumption_resolution,[],[f648,f639]) ).
fof(f657,plain,
( ~ spl52_1
| spl52_2
| ~ spl52_4
| ~ spl52_5 ),
inference(avatar_contradiction_clause,[],[f656]) ).
fof(f659,plain,
( nil = sK49
| ~ ssList(sK49)
| ~ spl52_1
| ~ spl52_3 ),
inference(resolution,[],[f638,f347]) ).
fof(f660,plain,
( ~ ssList(sK49)
| ~ spl52_1
| ~ spl52_3
| spl52_4 ),
inference(forward_subsumption_resolution,[],[f659,f480]) ).
fof(f661,plain,
( $false
| ~ spl52_1
| ~ spl52_3
| spl52_4 ),
inference(forward_subsumption_resolution,[],[f660,f423]) ).
fof(f662,plain,
( ~ spl52_1
| ~ spl52_3
| spl52_4 ),
inference(avatar_contradiction_clause,[],[f661]) ).
cnf(s1,plain,
( spl52_1
| ~ spl52_2
| ~ spl52_3 ),
inference(sat_conversion,[],[f476]) ).
cnf(s2,plain,
( ~ spl52_2
| ~ spl52_3
| ~ spl52_4 ),
inference(sat_conversion,[],[f481]) ).
cnf(s3,plain,
( ~ spl52_4
| spl52_5 ),
inference(sat_conversion,[],[f486]) ).
cnf(s5,plain,
( spl52_1
| ~ spl52_4 ),
inference(sat_conversion,[],[f488]) ).
cnf(s13,plain,
spl52_6,
inference(sat_conversion,[],[f518]) ).
cnf(s14,plain,
spl52_3,
inference(sat_conversion,[],[f612]) ).
cnf(s16,plain,
( spl52_2
| spl52_4
| ~ spl52_6 ),
inference(sat_conversion,[],[f636]) ).
cnf(s18,plain,
( ~ spl52_1
| spl52_2
| ~ spl52_4
| ~ spl52_5 ),
inference(sat_conversion,[],[f657]) ).
cnf(s19,plain,
( ~ spl52_1
| ~ spl52_3
| spl52_4 ),
inference(sat_conversion,[],[f662]) ).
cnf(s23,plain,
( ~ spl52_2
| ~ spl52_4 ),
inference(rat,[],[s2,s14]) ).
cnf(s24,plain,
( spl52_1
| ~ spl52_2 ),
inference(rat,[],[s1,s14]) ).
cnf(s25,plain,
spl52_1,
inference(rat,[],[s16,s24,s5,s13]) ).
cnf(s26,plain,
spl52_4,
inference(rat,[],[s19,s14,s25]) ).
cnf(s27,plain,
spl52_5,
inference(rat,[],[s3,s26]) ).
cnf(s28,plain,
~ spl52_2,
inference(rat,[],[s23,s26]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s18,s25,s26,s27,s28]) ).
fof(f663,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC100+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 07:53:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 Running first-order model finding
% 0.14/0.40 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
% 0.14/0.46 % (2087245)Will run a generic schedule for satisfiability detection.
% 0.14/0.46 % (2087254)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2664827344:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.46 % (2087251)% WARNING: option uhcvi not known.
% 0.14/0.46 % (2087252)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2722992633:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.46 % (2087250)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=268485626_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.46 % (2087251)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1983253301:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.46 % (2087253)dis+10_1_sil=32000:sp=arity:random_seed=330154083:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.46 % (2087254) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2087245-2087254"...
% 0.14/0.46 % (2087255)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3381269946:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.46 % (2087256)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=913079345:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.46 % (2087254)...printing done.
% 0.14/0.46 % (2087254)Refutation found. Thanks to Tanya!
% 0.14/0.46 % SZS status Theorem for theBenchmark
% 0.14/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.46 % (2087254)------------------------------
% 0.14/0.46 % (2087254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.46 % (2087254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.46 % (2087254)CaDiCaL version: 2.1.3
% 0.14/0.46 % (2087254)Termination reason: Refutation
% 0.14/0.46 % (2087254)Time elapsed: 0.008 s
% 0.14/0.46 % (2087254)Peak memory usage: 13 MB
% 0.14/0.46 % (2087254)Instructions burned: 25 (million)
% 0.14/0.46 % (2087245)Success in time 0.047 s
% 0.14/0.46 % Vampire exiting
%------------------------------------------------------------------------------