%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 01:46:13 PM UTC 2026
% Result : Theorem 0.18s 0.90s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 10 unt; 1 def)
% Number of atoms : 62 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 59 ( 28 ~; 20 |; 5 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 61 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(a,arr(b,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_036) ).
fof(f37,negated_conjecture,
~ ? [X0] :
( nf(X0)
& tc(nil,X0,arr(a,arr(b,b))) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
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(a,arr(b,b))) ),
inference(ennf_transformation,[],[f37]) ).
fof(f45,plain,
! [X0] :
( ( nf(lam(X0))
| ~ nf(X0) )
& ( nf(X0)
| ~ nf(lam(X0)) ) ),
inference(nnf_transformation,[],[f26]) ).
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(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(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] :
( ~ nf(X0)
| ~ tc(nil,X0,arr(a,arr(b,b))) ),
inference(cnf_transformation,[],[f42]) ).
fof(f93,plain,
! [X2,X3,X0] :
( tc(X0,var(X2),X3)
| index(X0,X2) != just(X3) ),
inference(equality_resolution,[],[f91]) ).
fof(f94,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f122,plain,
! [X0,X1] : sQ0_eqProxy(just(X0),index(cons(X0,X1),zero)),
inference(equality_proxy_replacement,[],[f81,f94]) ).
fof(f126,plain,
! [X2,X3,X0] :
( ~ sQ0_eqProxy(index(X0,X2),just(X3))
| tc(X0,var(X2),X3) ),
inference(equality_proxy_replacement,[],[f93,f94]) ).
fof(f129,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f94]) ).
fof(f132,plain,
! [X0] :
( ~ nf(X0)
| ~ tc(nil,lam(X0),arr(a,arr(b,b))) ),
inference(resolution,[],[f78,f92]) ).
fof(f134,plain,
! [X0] :
( ~ nf(X0)
| ~ tc(nil,lam(lam(X0)),arr(a,arr(b,b))) ),
inference(resolution,[],[f132,f78]) ).
fof(f135,plain,
! [X0] : ~ tc(nil,lam(lam(var(X0))),arr(a,arr(b,b))),
inference(resolution,[],[f134,f79]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ sQ0_eqProxy(just(X2),index(X0,X1))
| tc(X0,var(X1),X2) ),
inference(resolution,[],[f126,f129]) ).
fof(f186,plain,
! [X0] : ~ tc(cons(a,nil),lam(var(X0)),arr(b,b)),
inference(resolution,[],[f88,f135]) ).
fof(f202,plain,
! [X0] : ~ tc(cons(b,cons(a,nil)),var(X0),b),
inference(resolution,[],[f186,f88]) ).
fof(f260,plain,
! [X0,X1] : tc(cons(X0,X1),var(zero),X0),
inference(resolution,[],[f173,f122]) ).
fof(f341,plain,
$false,
inference(resolution,[],[f260,f202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n002.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
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 15:15:07 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.90 % (435583)Detected formulas, will run a generic FOF schedule.
% 0.18/0.90 % (435594)dis-21_1_sil=8000:lcm=predicate:random_seed=2463022674:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.18/0.90 % (435594)First to succeed.
% 0.18/0.90 % (435594)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-435583"
% 0.18/0.90 % (435589)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=463705814:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/0.90 % (435592)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=891661375:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/0.90 % (435593)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1527451866:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/0.90 % (435590)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3981484539:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/0.90 % (435588)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1673354475:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/0.90 % (435591)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=844948057:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/0.90 % (435593)Also succeeded, but the first one will report.
% 0.18/0.90 % (435591)Refutation not found, incomplete strategy
% 0.18/0.90 % (435591)------------------------------
% 0.18/0.90 % (435591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/0.90 % (435591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.90 % (435591)CaDiCaL version: 2.1.3
% 0.18/0.90 % (435591)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.90 % (435591)Time elapsed: 0.038 s
% 0.18/0.90 % (435591)Peak memory usage: 89 MB
% 0.18/0.90 % (435591)Instructions burned: 59 (million)
% 0.18/0.90 % (435592)Refutation not found, incomplete strategy
% 0.18/0.90 % (435592)------------------------------
% 0.18/0.90 % (435592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/0.90 % (435592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.90 % (435592)CaDiCaL version: 2.1.3
% 0.18/0.90 % (435592)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.90 % (435592)Time elapsed: 0.045 s
% 0.18/0.90 % (435592)Peak memory usage: 88 MB
% 0.18/0.90 % (435592)Instructions burned: 76 (million)
% 0.18/0.90 % (435594)Refutation found. Thanks to Tanya!
% 0.18/0.90 % SZS status Theorem for theBenchmark
% 0.18/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.90 % (435594)------------------------------
% 0.18/0.90 % (435594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/0.90 % (435594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.90 % (435594)CaDiCaL version: 2.1.3
% 0.18/0.90 % (435594)Termination reason: Refutation
% 0.18/0.90 % (435594)Time elapsed: 0.004 s
% 0.18/0.90 % (435594)Peak memory usage: 88 MB
% 0.18/0.90 % (435594)Instructions burned: 9 (million)
% 0.18/0.90 % (435594)------------------------------
% 0.18/0.90 % (435594)------------------------------
% 0.18/0.90 % (435583)Success in time 0.278 s
% 0.18/0.90 % Vampire exiting
%------------------------------------------------------------------------------