%------------------------------------------------------------------------------
% 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 : n005.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 : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 15 unt; 5 def)
% Number of atoms : 310 ( 65 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 388 ( 161 ~; 152 |; 46 &)
% ( 11 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 58 !; 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(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
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
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X8] :
( ssList(X8)
& neq(X8,nil)
& frontsegP(X1,X8)
& frontsegP(X0,X8) ) ) ) ) ) ) ) ),
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
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X8] :
( ssList(X8)
& neq(X8,nil)
& frontsegP(X1,X8)
& frontsegP(X0,X8) ) ) ) ) ) ) ) ),
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(f153,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
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
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X8] :
( ~ ssList(X8)
| ~ neq(X8,nil)
| ~ frontsegP(X1,X8)
| ~ frontsegP(X0,X8) ) ) )
& 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
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X8] :
( ~ ssList(X8)
| ~ neq(X8,nil)
| ~ frontsegP(X1,X8)
| ~ frontsegP(X0,X8) ) ) )
& 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(f304,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 != X1
| ~ neq(X0,X1) ),
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(f340,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f347,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f412,plain,
! [X8] :
( ~ frontsegP(sK47,X8)
| ~ frontsegP(sK48,X8)
| ~ neq(X8,nil)
| ~ ssList(X8)
| nil = sK48 ),
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(f431,plain,
! [X8] :
( ~ frontsegP(sK49,X8)
| ~ frontsegP(sK50,X8)
| ~ neq(X8,nil)
| ~ ssList(X8)
| nil = sK50 ),
inference(definition_unfolding,[],[f412,f421,f422,f422]) ).
fof(f435,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f237]) ).
fof(f446,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f304]) ).
fof(f461,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f446]) ).
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
<=> ! [X8] :
( ~ frontsegP(sK49,X8)
| ~ ssList(X8)
| ~ neq(X8,nil)
| ~ frontsegP(sK50,X8) ) ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
fof(f470,plain,
( ! [X8] :
( ~ neq(X8,nil)
| ~ ssList(X8)
| ~ frontsegP(sK49,X8)
| ~ frontsegP(sK50,X8) )
| ~ spl52_2 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f471,plain,
( spl52_1
| spl52_2 ),
inference(avatar_split_clause,[],[f431,f469,f465]) ).
fof(f473,definition,
( spl52_3
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl52_3])],[avatar_definition]) ).
fof(f475,plain,
( nil != sK49
| spl52_3 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f478,definition,
( spl52_4
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl52_4])],[avatar_definition]) ).
fof(f480,plain,
( neq(sK50,nil)
| ~ spl52_4 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f481,plain,
( ~ spl52_3
| spl52_4 ),
inference(avatar_split_clause,[],[f429,f478,f473]) ).
fof(f483,plain,
( spl52_1
| ~ spl52_3 ),
inference(avatar_split_clause,[],[f419,f473,f465]) ).
fof(f485,definition,
( spl52_5
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl52_5])],[avatar_definition]) ).
fof(f486,plain,
( ssList(nil)
| ~ spl52_5 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f513,plain,
spl52_5,
inference(avatar_split_clause,[],[f306,f485]) ).
fof(f515,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f435,f318]) ).
fof(f747,plain,
( frontsegP(sK50,sK49)
| ~ ssList(sK51)
| ~ ssList(sK49) ),
inference(superposition,[],[f515,f416]) ).
fof(f751,plain,
( frontsegP(sK50,sK49)
| ~ ssList(sK49) ),
inference(forward_subsumption_resolution,[],[f747,f414]) ).
fof(f752,plain,
frontsegP(sK50,sK49),
inference(forward_subsumption_resolution,[],[f751,f423]) ).
fof(f766,plain,
( ! [X0] :
( ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ ssList(X0)
| ~ frontsegP(sK49,X0)
| ~ frontsegP(sK50,X0) )
| ~ spl52_2 ),
inference(resolution,[],[f303,f470]) ).
fof(f771,plain,
( ! [X0] :
( ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ frontsegP(sK49,X0)
| ~ frontsegP(sK50,X0) )
| ~ spl52_2 ),
inference(duplicate_literal_removal,[],[f766]) ).
fof(f772,plain,
( ! [X0] :
( ~ frontsegP(sK50,X0)
| ~ ssList(X0)
| ~ frontsegP(sK49,X0)
| nil = X0 )
| ~ spl52_2
| ~ spl52_5 ),
inference(forward_subsumption_resolution,[],[f771,f486]) ).
fof(f779,plain,
( ~ ssList(sK49)
| ~ frontsegP(sK49,sK49)
| nil = sK49
| ~ spl52_2
| ~ spl52_5 ),
inference(resolution,[],[f772,f752]) ).
fof(f783,plain,
( ~ frontsegP(sK49,sK49)
| nil = sK49
| ~ spl52_2
| ~ spl52_5 ),
inference(forward_subsumption_resolution,[],[f779,f423]) ).
fof(f784,plain,
( ~ frontsegP(sK49,sK49)
| ~ spl52_2
| spl52_3
| ~ spl52_5 ),
inference(forward_subsumption_resolution,[],[f783,f475]) ).
fof(f790,plain,
( ~ ssList(sK49)
| ~ spl52_2
| spl52_3
| ~ spl52_5 ),
inference(resolution,[],[f784,f340]) ).
fof(f791,plain,
( $false
| ~ spl52_2
| spl52_3
| ~ spl52_5 ),
inference(forward_subsumption_resolution,[],[f790,f423]) ).
fof(f792,plain,
( ~ spl52_2
| spl52_3
| ~ spl52_5 ),
inference(avatar_contradiction_clause,[],[f791]) ).
fof(f794,plain,
( neq(nil,nil)
| ~ spl52_1
| ~ spl52_4 ),
inference(superposition,[],[f480,f467]) ).
fof(f807,plain,
( frontsegP(nil,sK49)
| ~ spl52_1 ),
inference(superposition,[],[f752,f467]) ).
fof(f810,plain,
( ~ ssList(nil)
| ~ spl52_1
| ~ spl52_4 ),
inference(resolution,[],[f794,f461]) ).
fof(f811,plain,
( $false
| ~ spl52_1
| ~ spl52_4
| ~ spl52_5 ),
inference(forward_subsumption_resolution,[],[f810,f486]) ).
fof(f812,plain,
( ~ spl52_1
| ~ spl52_4
| ~ spl52_5 ),
inference(avatar_contradiction_clause,[],[f811]) ).
fof(f829,plain,
( nil = sK49
| ~ ssList(sK49)
| ~ spl52_1 ),
inference(resolution,[],[f807,f347]) ).
fof(f830,plain,
( ~ ssList(sK49)
| ~ spl52_1
| spl52_3 ),
inference(forward_subsumption_resolution,[],[f829,f475]) ).
fof(f831,plain,
( $false
| ~ spl52_1
| spl52_3 ),
inference(forward_subsumption_resolution,[],[f830,f423]) ).
fof(f832,plain,
( ~ spl52_1
| spl52_3 ),
inference(avatar_contradiction_clause,[],[f831]) ).
cnf(s1,plain,
( spl52_1
| spl52_2 ),
inference(sat_conversion,[],[f471]) ).
cnf(s3,plain,
( ~ spl52_3
| spl52_4 ),
inference(sat_conversion,[],[f481]) ).
cnf(s5,plain,
( spl52_1
| ~ spl52_3 ),
inference(sat_conversion,[],[f483]) ).
cnf(s13,plain,
spl52_5,
inference(sat_conversion,[],[f513]) ).
cnf(s27,plain,
( ~ spl52_2
| spl52_3
| ~ spl52_5 ),
inference(sat_conversion,[],[f792]) ).
cnf(s28,plain,
( ~ spl52_1
| ~ spl52_4
| ~ spl52_5 ),
inference(sat_conversion,[],[f812]) ).
cnf(s31,plain,
( ~ spl52_1
| spl52_3 ),
inference(sat_conversion,[],[f832]) ).
cnf(s36,plain,
spl52_1,
inference(rat,[],[s27,s1,s5,s13]) ).
cnf(s37,plain,
spl52_3,
inference(rat,[],[s31,s36]) ).
cnf(s40,plain,
~ spl52_4,
inference(rat,[],[s28,s13,s36]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s3,s40,s37]) ).
fof(f833,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC018+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 07:26:34 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.42 Running first-order model finding
% 0.09/0.42 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
% 0.15/0.47 % (619387)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (619396)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4141283643:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (619393)% WARNING: option uhcvi not known.
% 0.15/0.47 % (619392)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2943147378_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (619393)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2226339354:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (619394)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3306847549:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (619395)dis+10_1_sil=32000:sp=arity:random_seed=16928843:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (619397)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=927928216:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (619398)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1767184240:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % (619396) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-619387-619396"...
% 0.15/0.47 % (619396)...printing done.
% 0.15/0.47 % (619396)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (619396)------------------------------
% 0.15/0.47 % (619396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (619396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (619396)CaDiCaL version: 2.1.3
% 0.15/0.47 % (619396)Termination reason: Refutation
% 0.15/0.47 % (619396)Time elapsed: 0.012 s
% 0.15/0.47 % (619396)Peak memory usage: 13 MB
% 0.15/0.47 % (619396)Instructions burned: 32 (million)
% 0.15/0.47 % (619387)Success in time 0.037 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------