%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC415+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 : n017.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 01:05:57 PM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 20 unt; 7 def)
% Number of atoms : 225 ( 50 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 265 ( 109 ~; 103 |; 32 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn 29 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X2 != X4
& tl(X3) = X4
& neq(nil,X3) )
| ? [X5] :
( ssList(X5)
& tl(X1) = X5
& X0 = X5
& neq(nil,X1) ) )
& ( ~ 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] :
( ssList(X4)
& X2 != X4
& tl(X3) = X4
& neq(nil,X3) )
| ? [X5] :
( ssList(X5)
& tl(X1) = X5
& X0 = X5
& neq(nil,X1) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f129,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f129]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X2 = X4
| tl(X3) != X4
| ~ neq(nil,X3) )
& ! [X5] :
( ~ ssList(X5)
| tl(X1) != X5
| X0 != X5
| ~ neq(nil,X1) ) )
| ( 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] :
( ~ ssList(X4)
| X2 = X4
| tl(X3) != X4
| ~ neq(nil,X3) )
& ! [X5] :
( ~ ssList(X5)
| tl(X1) != X5
| X0 != X5
| ~ neq(nil,X1) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
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(f316,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f411,plain,
! [X4] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| tl(sK50) != X4
| sK49 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
! [X5] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK48)
| sK47 != X5
| tl(sK48) != X5
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
ssList(sK50),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f415,f419]) ).
fof(f428,plain,
! [X5] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| sK49 != X5
| tl(sK50) != X5
| ~ ssList(X5) ),
inference(definition_unfolding,[],[f413,f419,f418,f419]) ).
fof(f444,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f304]) ).
fof(f456,plain,
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| sK49 != tl(sK50)
| ~ ssList(sK49) ),
inference(equality_resolution,[],[f428]) ).
fof(f458,plain,
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| sK49 = tl(sK50)
| ~ ssList(tl(sK50)) ),
inference(equality_resolution,[],[f411]) ).
fof(f586,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f444]) ).
fof(f590,definition,
( spl51_1
<=> ssList(tl(sK50)) ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
fof(f592,plain,
( ~ ssList(tl(sK50))
| spl51_1 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f594,definition,
( spl51_2
<=> sK49 = tl(sK50) ),
introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).
fof(f598,definition,
( spl51_3
<=> neq(nil,sK50) ),
introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).
fof(f600,plain,
( ~ neq(nil,sK50)
| spl51_3 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f602,definition,
( spl51_4
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl51_4])],[avatar_definition]) ).
fof(f603,plain,
( neq(sK50,nil)
| ~ spl51_4 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f605,plain,
( ~ spl51_1
| spl51_2
| ~ spl51_3
| ~ spl51_4 ),
inference(avatar_split_clause,[],[f458,f602,f598,f594,f590]) ).
fof(f608,definition,
( spl51_5
<=> ssList(sK49) ),
introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).
fof(f611,plain,
( ~ spl51_5
| ~ spl51_2
| ~ spl51_3
| ~ spl51_4 ),
inference(avatar_split_clause,[],[f456,f602,f598,f594,f608]) ).
fof(f613,plain,
spl51_4,
inference(avatar_split_clause,[],[f426,f602]) ).
fof(f614,plain,
spl51_5,
inference(avatar_split_clause,[],[f420,f608]) ).
fof(f620,definition,
( spl51_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl51_7])],[avatar_definition]) ).
fof(f621,plain,
( ssList(nil)
| ~ spl51_7 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f649,plain,
spl51_7,
inference(avatar_split_clause,[],[f306,f620]) ).
fof(f711,plain,
( ~ ssList(sK50)
| nil = sK50
| ~ ssList(nil)
| spl51_3 ),
inference(resolution,[],[f303,f600]) ).
fof(f716,plain,
( nil = sK50
| ~ ssList(nil)
| spl51_3 ),
inference(forward_subsumption_resolution,[],[f711,f417]) ).
fof(f717,plain,
( nil = sK50
| spl51_3
| ~ spl51_7 ),
inference(forward_subsumption_resolution,[],[f716,f621]) ).
fof(f743,definition,
( spl51_14
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl51_14])],[avatar_definition]) ).
fof(f745,plain,
( nil = sK50
| ~ spl51_14 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f757,plain,
( spl51_14
| spl51_3
| ~ spl51_7 ),
inference(avatar_split_clause,[],[f717,f620,f598,f743]) ).
fof(f760,plain,
( neq(nil,nil)
| ~ spl51_4
| ~ spl51_14 ),
inference(superposition,[],[f603,f745]) ).
fof(f764,plain,
( ~ ssList(nil)
| ~ spl51_4
| ~ spl51_14 ),
inference(resolution,[],[f760,f586]) ).
fof(f765,plain,
( $false
| ~ spl51_4
| ~ spl51_7
| ~ spl51_14 ),
inference(forward_subsumption_resolution,[],[f764,f621]) ).
fof(f766,plain,
( ~ spl51_4
| ~ spl51_7
| ~ spl51_14 ),
inference(avatar_contradiction_clause,[],[f765]) ).
fof(f767,plain,
( nil = sK50
| ~ ssList(sK50)
| spl51_1 ),
inference(resolution,[],[f592,f316]) ).
fof(f768,plain,
( nil = sK50
| spl51_1 ),
inference(forward_subsumption_resolution,[],[f767,f417]) ).
fof(f769,plain,
( spl51_14
| spl51_1 ),
inference(avatar_split_clause,[],[f768,f590,f743]) ).
cnf(s1,plain,
( ~ spl51_1
| spl51_2
| ~ spl51_3
| ~ spl51_4 ),
inference(sat_conversion,[],[f605]) ).
cnf(s3,plain,
( ~ spl51_2
| ~ spl51_3
| ~ spl51_4
| ~ spl51_5 ),
inference(sat_conversion,[],[f611]) ).
cnf(s5,plain,
spl51_4,
inference(sat_conversion,[],[f613]) ).
cnf(s6,plain,
spl51_5,
inference(sat_conversion,[],[f614]) ).
cnf(s16,plain,
spl51_7,
inference(sat_conversion,[],[f649]) ).
cnf(s19,plain,
( spl51_3
| ~ spl51_7
| spl51_14 ),
inference(sat_conversion,[],[f757]) ).
cnf(s20,plain,
( ~ spl51_4
| ~ spl51_7
| ~ spl51_14 ),
inference(sat_conversion,[],[f766]) ).
cnf(s21,plain,
( spl51_1
| spl51_14 ),
inference(sat_conversion,[],[f769]) ).
cnf(s26,plain,
~ spl51_14,
inference(rat,[],[s20,s16,s5]) ).
cnf(s27,plain,
spl51_1,
inference(rat,[],[s21,s26]) ).
cnf(s29,plain,
spl51_3,
inference(rat,[],[s19,s16,s26]) ).
cnf(s30,plain,
~ spl51_2,
inference(rat,[],[s3,s6,s5,s29]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s1,s5,s29,s30,s27]) ).
fof(f770,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC415+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n017.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 09:28:42 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.21/0.30 % (3428651)Will run a generic schedule for satisfiability detection.
% 0.21/0.30 % (3428661)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=476163491:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.30 % (3428657)% WARNING: option uhcvi not known.
% 0.21/0.30 % (3428657)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=895841621:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.30 % (3428659)dis+10_1_sil=32000:sp=arity:random_seed=204594888:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.30 % (3428658)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3293200038:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.30 % (3428656)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1425225600_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.30 % (3428660)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3268481041:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.30 % (3428662)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=168126487:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.30 % (3428657) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3428651-3428657"...
% 0.21/0.30 % (3428657)...printing done.
% 0.21/0.30 % (3428660) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3428651-3428660"...
% 0.21/0.30 % (3428657)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (3428657)------------------------------
% 0.21/0.31 % (3428657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3428657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3428657)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3428657)Termination reason: Refutation
% 0.21/0.31 % (3428657)Time elapsed: 0.012 s
% 0.21/0.31 % (3428657)Peak memory usage: 13 MB
% 0.21/0.31 % (3428657)Instructions burned: 18 (million)
% 0.21/0.31 % (3428651)Success in time 0.061 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------