%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX220+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 01:46:46 PM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 20 unt; 2 def)
% Number of atoms : 95 ( 19 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 95 ( 48 ~; 33 |; 7 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn 110 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
fof(f26,axiom,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(f27,axiom,
! [X0,X1,X2,X3,X4] :
( tc(X0,app(X2,X3,X4),X1)
<=> ( tc(X0,X2,arr(X4,X1))
& tc(X0,X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(f29,axiom,
! [X0,X1,X2,X3] :
( tc(X0,lam(X1),arr(X2,X3))
<=> tc(cons(X2,X0),X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(f31,axiom,
! [X0,X1,X2,X3] :
( index(X0,X2) = just(X3)
=> ( tc(X0,var(X2),X1)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
fof(f32,conjecture,
? [X0] : tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_032) ).
fof(f33,negated_conjecture,
~ ? [X0] : tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ( tc(X0,var(X2),X1)
<=> X3 = X1 )
| index(X0,X2) != just(X3) ),
inference(ennf_transformation,[],[f31]) ).
fof(f37,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
inference(ennf_transformation,[],[f33]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4] :
( ( tc(X0,app(X2,X3,X4),X1)
| ~ tc(X0,X2,arr(X4,X1))
| ~ tc(X0,X3,X4) )
& ( ( tc(X0,X2,arr(X4,X1))
& tc(X0,X3,X4) )
| ~ tc(X0,app(X2,X3,X4),X1) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4] :
( ( tc(X0,app(X2,X3,X4),X1)
| ~ tc(X0,X2,arr(X4,X1))
| ~ tc(X0,X3,X4) )
& ( ( tc(X0,X2,arr(X4,X1))
& tc(X0,X3,X4) )
| ~ tc(X0,app(X2,X3,X4),X1) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ( tc(X0,lam(X1),arr(X2,X3))
| ~ tc(cons(X2,X0),X1,X3) )
& ( tc(cons(X2,X0),X1,X3)
| ~ tc(X0,lam(X1),arr(X2,X3)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ( ( tc(X0,var(X2),X1)
| X1 != X3 )
& ( X3 = X1
| ~ tc(X0,var(X2),X1) ) )
| index(X0,X2) != just(X3) ),
inference(nnf_transformation,[],[f36]) ).
fof(f66,plain,
! [X0,X1] : just(X0) = index(cons(X0,X1),zero),
inference(cnf_transformation,[],[f25]) ).
fof(f67,plain,
! [X2,X0,X1] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[],[f26]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( tc(X0,app(X2,X3,X4),X1)
| ~ tc(X0,X2,arr(X4,X1))
| ~ tc(X0,X3,X4) ),
inference(cnf_transformation,[],[f39]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( tc(X0,lam(X1),arr(X2,X3))
| ~ tc(cons(X2,X0),X1,X3) ),
inference(cnf_transformation,[],[f40]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( tc(X0,var(X2),X1)
| X1 != X3
| index(X0,X2) != just(X3) ),
inference(cnf_transformation,[],[f41]) ).
fof(f77,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
inference(cnf_transformation,[],[f37]) ).
fof(f78,plain,
! [X2,X3,X0] :
( index(X0,X2) != just(X3)
| tc(X0,var(X2),X3) ),
inference(equality_resolution,[],[f76]) ).
fof(f84,plain,
! [X2,X0,X1] :
( just(X0) != just(X2)
| tc(cons(X0,X1),var(zero),X2) ),
inference(superposition,[],[f78,f66]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( just(X3) != index(X0,X1)
| tc(cons(X2,X0),var(suc(X1)),X3) ),
inference(superposition,[],[f78,f67]) ).
fof(f86,plain,
! [X0,X1] : tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[],[f84]) ).
fof(f87,plain,
! [X0] : ~ tc(cons(arr(a,arr(b,c)),nil),X0,arr(b,arr(a,c))),
inference(resolution,[],[f73,f77]) ).
fof(f94,plain,
! [X0] : ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),X0,arr(a,c)),
inference(resolution,[],[f87,f73]) ).
fof(f99,plain,
! [X0] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,c),
inference(resolution,[],[f94,f73]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,arr(X1,c))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2,X1) ),
inference(resolution,[],[f99,f70]) ).
fof(f112,plain,
! [X2,X3,X0,X1] :
( just(X0) != just(X1)
| tc(cons(X3,cons(X0,X2)),var(suc(zero)),X1) ),
inference(superposition,[],[f85,f66]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( index(X0,X1) != just(X2)
| tc(cons(X4,cons(X3,X0)),var(suc(suc(X1))),X2) ),
inference(superposition,[],[f85,f67]) ).
fof(f134,plain,
! [X2,X0,X1] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(equality_resolution,[],[f112]) ).
fof(f145,plain,
! [X2,X3,X0,X1,X4] :
( just(X0) != just(X2)
| tc(cons(X3,cons(X4,cons(X0,X1))),var(suc(suc(zero))),X2) ),
inference(superposition,[],[f113,f66]) ).
fof(f193,plain,
! [X2,X3,X0,X1] : tc(cons(X0,cons(X1,cons(X2,X3))),var(suc(suc(zero))),X2),
inference(equality_resolution,[],[f145]) ).
fof(f215,plain,
! [X2,X3,X0,X1,X4] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2,arr(X3,arr(X1,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,X1)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X3) ),
inference(resolution,[],[f103,f70]) ).
fof(f424,plain,
! [X0,X1] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,a) ),
inference(resolution,[],[f215,f193]) ).
fof(f428,definition,
( spl0_3
<=> ! [X1] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,a) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f429,plain,
( ! [X1] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f431,definition,
( spl0_4
<=> ! [X0] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f432,plain,
( ! [X0] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f433,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f424,f431,f428]) ).
fof(f434,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f429,f86]) ).
fof(f436,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f440,plain,
( $false
| ~ spl0_4 ),
inference(resolution,[],[f432,f134]) ).
fof(f442,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f440]) ).
cnf(s3,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f433]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f436]) ).
cnf(s5,plain,
~ spl0_4,
inference(sat_conversion,[],[f442]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5,s4]) ).
fof(f443,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX220+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:15:42 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.29 % (3928318)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (3928335)dis+10_1_sil=32000:sp=arity:random_seed=2492924965:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (3928332)% WARNING: option uhcvi not known.
% 0.20/0.29 % (3928331)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3977352325_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (3928337)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=690792715:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (3928332)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2218847403:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (3928336)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=902586242:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (3928334)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4238559834:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (3928338)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2112202677:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % Detected minimum model sizes of [3]
% 0.20/0.29 % Detected maximum model sizes of [max]
% 0.20/0.29 % TRYING [3]
% 0.20/0.29 % (3928335) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3928318-3928335"...
% 0.20/0.29 % (3928335)...printing done.
% 0.20/0.29 % (3928335)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (3928335)------------------------------
% 0.20/0.29 % (3928335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3928335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3928335)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3928335)Termination reason: Refutation
% 0.20/0.29 % (3928335)Time elapsed: 0.015 s
% 0.20/0.29 % (3928335)Peak memory usage: 13 MB
% 0.20/0.29 % (3928335)Instructions burned: 42 (million)
% 0.20/0.29 % (3928318)Success in time 0.048 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------