%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX223+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 : n020.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 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 17 unt; 0 def)
% Number of atoms : 135 ( 31 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 149 ( 69 ~; 55 |; 16 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 127 ( 125 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0,X1,X2,X3] : app(X0,X1,X2) != lam(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
fof(f23,axiom,
! [X0,X1] : lam(X0) != var(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
fof(f24,axiom,
! [X0,X1,X2] :
( X0 != lam(proj1Lam(X0))
=> ( nf(app(X0,X1,X2))
<=> ( nf(X0)
& nf(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(f26,axiom,
! [X0] :
( nf(lam(X0))
<=> nf(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(f27,axiom,
! [X0] : nf(var(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(f29,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(f30,axiom,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
fof(f31,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_031) ).
fof(f33,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_033) ).
fof(f35,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_035) ).
fof(f36,conjecture,
? [X0] :
( nf(X0)
& tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_036) ).
fof(f37,negated_conjecture,
~ ? [X0] :
( nf(X0)
& tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( nf(app(X0,X1,X2))
<=> ( nf(X0)
& nf(X1) ) )
| lam(proj1Lam(X0)) = X0 ),
inference(ennf_transformation,[],[f24]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ( tc(X0,var(X2),X1)
<=> X3 = X1 )
| index(X0,X2) != just(X3) ),
inference(ennf_transformation,[],[f35]) ).
fof(f42,plain,
! [X0] :
( ~ nf(X0)
| ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))) ),
inference(ennf_transformation,[],[f37]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( ( nf(app(X0,X1,X2))
| ~ nf(X0)
| ~ nf(X1) )
& ( ( nf(X0)
& nf(X1) )
| ~ nf(app(X0,X1,X2)) ) )
| lam(proj1Lam(X0)) = X0 ),
inference(nnf_transformation,[],[f38]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( ( nf(app(X0,X1,X2))
| ~ nf(X0)
| ~ nf(X1) )
& ( ( nf(X0)
& nf(X1) )
| ~ nf(app(X0,X1,X2)) ) )
| lam(proj1Lam(X0)) = X0 ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0] :
( ( nf(lam(X0))
| ~ nf(X0) )
& ( nf(X0)
| ~ nf(lam(X0)) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f46,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,[],[f31]) ).
fof(f47,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,[],[f46]) ).
fof(f48,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,[],[f33]) ).
fof(f49,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,[],[f41]) ).
fof(f70,plain,
! [X2,X3,X0,X1] : app(X0,X1,X2) != lam(X3),
inference(cnf_transformation,[],[f21]) ).
fof(f72,plain,
! [X0,X1] : lam(X0) != var(X1),
inference(cnf_transformation,[],[f23]) ).
fof(f75,plain,
! [X2,X0,X1] :
( nf(app(X0,X1,X2))
| ~ nf(X0)
| ~ nf(X1)
| lam(proj1Lam(X0)) = X0 ),
inference(cnf_transformation,[],[f44]) ).
fof(f78,plain,
! [X0] :
( nf(lam(X0))
| ~ nf(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f79,plain,
! [X0] : nf(var(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f81,plain,
! [X0,X1] : just(X0) = index(cons(X0,X1),zero),
inference(cnf_transformation,[],[f29]) ).
fof(f82,plain,
! [X2,X0,X1] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[],[f30]) ).
fof(f85,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,[],[f47]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( tc(X0,lam(X1),arr(X2,X3))
| ~ tc(cons(X2,X0),X1,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( tc(X0,var(X2),X1)
| X1 != X3
| index(X0,X2) != just(X3) ),
inference(cnf_transformation,[],[f49]) ).
fof(f92,plain,
! [X0] :
( ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b)))
| ~ nf(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f93,plain,
! [X2,X3,X0] :
( index(X0,X2) != just(X3)
| tc(X0,var(X2),X3) ),
inference(equality_resolution,[],[f91]) ).
fof(f100,plain,
! [X2,X0,X1] :
( just(X0) != just(X2)
| tc(cons(X0,X1),var(zero),X2) ),
inference(superposition,[],[f93,f81]) ).
fof(f101,plain,
! [X2,X3,X0,X1] :
( just(X3) != index(X0,X1)
| tc(cons(X2,X0),var(suc(X1)),X3) ),
inference(superposition,[],[f93,f82]) ).
fof(f102,plain,
! [X0,X1] : tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[],[f100]) ).
fof(f103,plain,
! [X0] :
( ~ tc(cons(arr(a,arr(a,b)),nil),X0,arr(a,b))
| ~ nf(lam(X0)) ),
inference(resolution,[],[f88,f92]) ).
fof(f112,plain,
! [X0] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,b)
| ~ nf(lam(lam(X0))) ),
inference(resolution,[],[f103,f88]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,arr(X1,b))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2,X1)
| ~ nf(lam(lam(app(X0,X2,X1)))) ),
inference(resolution,[],[f85,f112]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( just(X0) != just(X1)
| tc(cons(X3,cons(X0,X2)),var(suc(zero)),X1) ),
inference(superposition,[],[f101,f81]) ).
fof(f150,plain,
! [X2,X0,X1] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(equality_resolution,[],[f131]) ).
fof(f152,plain,
! [X2,X3,X0,X1,X4] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2,arr(X4,arr(X1,b)))
| ~ nf(lam(lam(app(app(X2,X3,X4),X0,X1))))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,X1)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X3,X4) ),
inference(resolution,[],[f120,f85]) ).
fof(f228,plain,
! [X0,X1] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,a)
| ~ nf(lam(lam(app(app(var(suc(zero)),X0,a),X1,a))))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(resolution,[],[f152,f150]) ).
fof(f238,plain,
! [X0] :
( ~ nf(lam(lam(app(app(var(suc(zero)),X0,a),var(zero),a))))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(resolution,[],[f228,f102]) ).
fof(f243,plain,
! [X0] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a)
| ~ nf(lam(app(app(var(suc(zero)),X0,a),var(zero),a))) ),
inference(resolution,[],[f238,f78]) ).
fof(f245,plain,
~ nf(lam(app(app(var(suc(zero)),var(zero),a),var(zero),a))),
inference(resolution,[],[f243,f102]) ).
fof(f248,plain,
~ nf(app(app(var(suc(zero)),var(zero),a),var(zero),a)),
inference(resolution,[],[f245,f78]) ).
fof(f253,plain,
( ~ nf(app(var(suc(zero)),var(zero),a))
| ~ nf(var(zero))
| app(var(suc(zero)),var(zero),a) = lam(proj1Lam(app(var(suc(zero)),var(zero),a))) ),
inference(resolution,[],[f248,f75]) ).
fof(f254,plain,
( ~ nf(app(var(suc(zero)),var(zero),a))
| app(var(suc(zero)),var(zero),a) = lam(proj1Lam(app(var(suc(zero)),var(zero),a))) ),
inference(forward_subsumption_resolution,[],[f253,f79]) ).
fof(f255,plain,
~ nf(app(var(suc(zero)),var(zero),a)),
inference(forward_subsumption_resolution,[],[f254,f70]) ).
fof(f259,plain,
( ~ nf(var(suc(zero)))
| ~ nf(var(zero))
| var(suc(zero)) = lam(proj1Lam(var(suc(zero)))) ),
inference(resolution,[],[f255,f75]) ).
fof(f260,plain,
( ~ nf(var(zero))
| var(suc(zero)) = lam(proj1Lam(var(suc(zero)))) ),
inference(forward_subsumption_resolution,[],[f259,f79]) ).
fof(f261,plain,
var(suc(zero)) = lam(proj1Lam(var(suc(zero)))),
inference(forward_subsumption_resolution,[],[f260,f79]) ).
fof(f262,plain,
$false,
inference(forward_subsumption_resolution,[],[f261,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX223+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 15:13:50 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.18/0.27 % (238207)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (238218)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1253044341:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.27 % (238213)% WARNING: option uhcvi not known.
% 0.18/0.27 % (238212)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3182270665_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % (238213)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2774130576:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (238214)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1777919290:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (238215)dis+10_1_sil=32000:sp=arity:random_seed=3567650671:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (238216)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2818938354:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (238217)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2097334793:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27 % Detected minimum model sizes of [3]
% 0.18/0.27 % Detected maximum model sizes of [max]
% 0.18/0.27 % TRYING [3]
% 0.18/0.27 % TRYING [4]
% 0.18/0.27 % (238215) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-238207-238215"...
% 0.18/0.27 % (238215)...printing done.
% 0.18/0.27 % (238215)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (238215)------------------------------
% 0.18/0.27 % (238215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (238215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (238215)CaDiCaL version: 2.1.3
% 0.18/0.27 % (238215)Termination reason: Refutation
% 0.18/0.27 % (238215)Time elapsed: 0.016 s
% 0.18/0.27 % (238215)Peak memory usage: 12 MB
% 0.18/0.27 % (238215)Instructions burned: 23 (million)
% 0.18/0.27 % (238207)Success in time 0.053 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------