%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC210+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 : n009.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 01:05:07 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 22 unt; 5 def)
% Number of atoms : 145 ( 19 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 142 ( 54 ~; 51 |; 20 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 16 !; 8 ?)
% 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(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax39) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ~ singletonP(X2)
| neq(X0,nil) )
& ( ~ 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)
| ~ singletonP(X2)
| neq(X0,nil) )
& ( ~ 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(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& singletonP(X2)
& ~ neq(X0,nil) )
| ( 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)
& singletonP(X2)
& ~ neq(X0,nil) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f303,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(f337,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f413,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
( ~ neq(sK50,nil)
| ~ neq(sK47,nil) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
( ~ neq(sK50,nil)
| singletonP(sK49) ),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f422,plain,
ssList(sK47),
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
ssList(sK49),
inference(definition_unfolding,[],[f422,f418]) ).
fof(f426,plain,
( ~ neq(sK50,nil)
| ~ neq(sK49,nil) ),
inference(definition_unfolding,[],[f414,f418]) ).
fof(f427,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f413,f419]) ).
fof(f533,plain,
! [X0,X1] :
( ~ neq(X0,X1)
| ssList(X1)
| X0 = X1
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f303]) ).
fof(f535,plain,
~ ssList(nil),
inference(consistent_polarity_flipping,[],[f306]) ).
fof(f620,plain,
~ ssList(sK49),
inference(consistent_polarity_flipping,[],[f423]) ).
fof(f625,plain,
( neq(sK50,nil)
| singletonP(sK49) ),
inference(consistent_polarity_flipping,[],[f415]) ).
fof(f626,plain,
( neq(sK50,nil)
| neq(sK49,nil) ),
inference(consistent_polarity_flipping,[],[f426]) ).
fof(f627,plain,
~ neq(sK50,nil),
inference(consistent_polarity_flipping,[],[f427]) ).
fof(f638,definition,
( spl51_1
<=> neq(sK49,nil) ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
fof(f640,plain,
( neq(sK49,nil)
| ~ spl51_1 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f642,definition,
( spl51_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).
fof(f647,definition,
( spl51_3
<=> singletonP(sK49) ),
introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).
fof(f649,plain,
( singletonP(sK49)
| ~ spl51_3 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f651,plain,
~ spl51_2,
inference(avatar_split_clause,[],[f627,f642]) ).
fof(f652,plain,
( spl51_1
| spl51_2 ),
inference(avatar_split_clause,[],[f626,f642,f638]) ).
fof(f653,plain,
( spl51_3
| spl51_2 ),
inference(avatar_split_clause,[],[f625,f642,f647]) ).
fof(f659,definition,
( spl51_5
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).
fof(f660,plain,
( ~ ssList(nil)
| spl51_5 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f688,plain,
~ spl51_5,
inference(avatar_split_clause,[],[f535,f659]) ).
fof(f780,definition,
( spl51_12
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl51_12])],[avatar_definition]) ).
fof(f782,plain,
( nil = sK49
| ~ spl51_12 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f792,plain,
( ssList(nil)
| nil = sK49
| ssList(sK49)
| ~ spl51_1 ),
inference(resolution,[],[f533,f640]) ).
fof(f797,plain,
( nil = sK49
| ssList(sK49)
| ~ spl51_1
| spl51_5 ),
inference(forward_subsumption_resolution,[],[f792,f660]) ).
fof(f798,plain,
( nil = sK49
| ~ spl51_1
| spl51_5 ),
inference(forward_subsumption_resolution,[],[f797,f620]) ).
fof(f799,plain,
( spl51_12
| ~ spl51_1
| spl51_5 ),
inference(avatar_split_clause,[],[f798,f659,f638,f780]) ).
fof(f822,plain,
( singletonP(nil)
| ~ spl51_3
| ~ spl51_12 ),
inference(superposition,[],[f649,f782]) ).
fof(f827,plain,
( $false
| ~ spl51_3
| ~ spl51_12 ),
inference(forward_subsumption_resolution,[],[f822,f337]) ).
fof(f828,plain,
( ~ spl51_3
| ~ spl51_12 ),
inference(avatar_contradiction_clause,[],[f827]) ).
cnf(s3,plain,
~ spl51_2,
inference(sat_conversion,[],[f651]) ).
cnf(s4,plain,
( spl51_1
| spl51_2 ),
inference(sat_conversion,[],[f652]) ).
cnf(s5,plain,
( spl51_2
| spl51_3 ),
inference(sat_conversion,[],[f653]) ).
cnf(s14,plain,
~ spl51_5,
inference(sat_conversion,[],[f688]) ).
cnf(s16,plain,
( ~ spl51_1
| spl51_5
| spl51_12 ),
inference(sat_conversion,[],[f799]) ).
cnf(s18,plain,
( ~ spl51_3
| ~ spl51_12 ),
inference(sat_conversion,[],[f828]) ).
cnf(s23,plain,
spl51_3,
inference(rat,[],[s5,s3]) ).
cnf(s24,plain,
spl51_1,
inference(rat,[],[s4,s3]) ).
cnf(s25,plain,
~ spl51_12,
inference(rat,[],[s18,s23]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s16,s14,s25,s24]) ).
fof(f829,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC210+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n009.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 08:27:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.45 % (2885656)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2885662)% WARNING: option uhcvi not known.
% 0.10/0.45 % (2885662)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2036438702:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (2885666)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1937641556:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (2885661)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1762785709_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (2885664)dis+10_1_sil=32000:sp=arity:random_seed=2550538491:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2885663)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3379688193:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (2885665)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3177040890:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (2885667)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3437832510:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2885662) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2885656-2885662"...
% 0.10/0.45 % (2885662)...printing done.
% 0.10/0.45 % (2885662)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2885662)------------------------------
% 0.10/0.45 % (2885662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2885662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2885662)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2885662)Termination reason: Refutation
% 0.10/0.45 % (2885662)Time elapsed: 0.007 s
% 0.10/0.45 % (2885662)Peak memory usage: 13 MB
% 0.10/0.45 % (2885662)Instructions burned: 18 (million)
% 0.10/0.45 % (2885656)Success in time 0.04 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------