%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 41 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 10 |; 2 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 39 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( nf(lam(X0))
<=> nf(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
fof(f27,axiom,
! [X0] : nf(var(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
fof(f29,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
fof(f36,conjecture,
? [X0] :
( nf(X0)
& tc(nil,X0,arr(a,arr(b,b))) ),
file('/export/starexec/sandbox2/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(f70,plain,
! [X0] :
( nf(lam(X0))
| ~ nf(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f72,plain,
! [X0] : nf(var(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f74,plain,
! [X0,X1] : just(X0) = index(cons(X0,X1),zero),
inference(cnf_transformation,[],[f29]) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( tc(X0,lam(X1),arr(X2,X3))
| ~ tc(cons(X2,X0),X1,X3) ),
inference(cnf_transformation,[],[f33]) ).
fof(f83,plain,
! [X2,X3,X0,X1] :
( index(X0,X2) != just(X3)
| X1 != X3
| tc(X0,var(X2),X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
! [X0] :
( ~ nf(X0)
| ~ tc(nil,X0,arr(a,arr(b,b))) ),
inference(cnf_transformation,[],[f42]) ).
fof(f86,plain,
! [X2,X3,X0] :
( tc(X0,var(X2),X3)
| index(X0,X2) != just(X3) ),
inference(equality_resolution,[],[f83]) ).
fof(f88,plain,
! [X0] :
( ~ nf(X0)
| ~ tc(nil,lam(X0),arr(a,arr(b,b))) ),
inference(resolution,[],[f70,f85]) ).
fof(f90,plain,
! [X0] :
( ~ nf(X0)
| ~ tc(nil,lam(lam(X0)),arr(a,arr(b,b))) ),
inference(resolution,[],[f88,f70]) ).
fof(f92,plain,
! [X0] : ~ tc(nil,lam(lam(var(X0))),arr(a,arr(b,b))),
inference(resolution,[],[f90,f72]) ).
fof(f116,plain,
! [X0] : ~ tc(cons(a,nil),lam(var(X0)),arr(b,b)),
inference(resolution,[],[f80,f92]) ).
fof(f130,plain,
! [X0] : ~ tc(cons(b,cons(a,nil)),var(X0),b),
inference(resolution,[],[f116,f80]) ).
fof(f148,plain,
! [X0] : index(cons(b,cons(a,nil)),X0) != just(b),
inference(resolution,[],[f130,f86]) ).
fof(f163,plain,
just(b) != just(b),
inference(superposition,[],[f148,f74]) ).
fof(f165,plain,
$false,
inference(trivial_inequality_removal,[],[f163]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n005.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
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:12:16 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.27 % (854728)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (854737)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=119052419:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (854734)% WARNING: option uhcvi not known.
% 0.20/0.27 % (854737) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-854728-854737"...
% 0.20/0.27 % (854737)...printing done.
% 0.20/0.27 % (854737)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (854737)------------------------------
% 0.20/0.27 % (854737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (854737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (854737)CaDiCaL version: 2.1.3
% 0.20/0.27 % (854737)Termination reason: Refutation
% 0.20/0.27 % (854737)Time elapsed: 0.004 s
% 0.20/0.27 % (854737)Peak memory usage: 12 MB
% 0.20/0.27 % (854737)Instructions burned: 9 (million)
% 0.20/0.27 % (854728)Success in time 0.028 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------