%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT094_1 : TPTP v9.3.1. Released v6.1.0.
% 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 09:48:07 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 8 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 59 ( 28 ~; 25 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 191 ( 49 atm; 40 fun; 94 num; 8 var)
% Number of types : 3 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
list: $tType ).
tff(func_def_0,type,
nil: list ).
tff(func_def_1,type,
cons: ( $int * list ) > list ).
tff(func_def_2,type,
head: list > $int ).
tff(func_def_3,type,
tail: list > list ).
tff(func_def_5,type,
length: list > $int ).
tff(func_def_8,type,
count: ( $int * list ) > $int ).
tff(func_def_9,type,
append: ( list * list ) > list ).
tff(func_def_12,type,
sK0: ( $int * list ) > $int ).
tff(func_def_13,type,
sK1: ( $int * list ) > list ).
tff(func_def_14,type,
sK2: ( $int * list ) > $int ).
tff(func_def_15,type,
sK3: ( $int * list ) > list ).
tff(func_def_16,type,
sK4: ( $int * list ) > $int ).
tff(func_def_17,type,
sK5: ( $int * list ) > list ).
tff(pred_def_1,type,
in: ( $int * list ) > $o ).
tff(pred_def_2,type,
inRange: ( $int * list ) > $o ).
tff(f7,axiom,
length(nil) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
tff(f8,axiom,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_1) ).
tff(f12,axiom,
! [X0: list] : ( append(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6) ).
tff(f13,axiom,
! [X0: $int,X1: list,X2: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_7) ).
tff(f15,conjecture,
~ ! [X0: list,X1: list] :
( ( $greater(length(X0),1)
& $greater(length(X1),1) )
=> $greater(length(append(X0,X1)),4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X0: list,X1: list] :
( ( $greater(length(X0),1)
& $greater(length(X1),1) )
=> $greater(length(append(X0,X1)),4) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f19,plain,
! [X0: list,X1: list] :
( ( $less(1,length(X0))
& $less(1,length(X1)) )
=> $less(4,length(append(X0,X1))) ),
inference(theory_normalization,[],[f16]) ).
tff(f37,plain,
! [X0: list,X1: list] :
( $less(4,length(append(X0,X1)))
| ~ $less(1,length(X0))
| ~ $less(1,length(X1)) ),
inference(ennf_transformation,[],[f19]) ).
tff(f38,plain,
! [X0: list,X1: list] :
( $less(4,length(append(X0,X1)))
| ~ $less(1,length(X0))
| ~ $less(1,length(X1)) ),
inference(flattening,[],[f37]) ).
tff(f64,plain,
0 = length(nil),
inference(cnf_transformation,[],[f7]) ).
tff(f65,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(cnf_transformation,[],[f8]) ).
tff(f69,plain,
! [X0: list] : ( append(nil,X0) = X0 ),
inference(cnf_transformation,[],[f12]) ).
tff(f70,plain,
! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ),
inference(cnf_transformation,[],[f13]) ).
tff(f73,plain,
! [X0: list,X1: list] :
( ~ $less(1,length(X0))
| $less(4,length(append(X0,X1)))
| ~ $less(1,length(X1)) ),
inference(cnf_transformation,[],[f38]) ).
tff(f134,plain,
! [X2: list,X0: list,X1: $int] :
( ~ $less(1,$sum(1,length(X0)))
| $less(4,length(append(cons(X1,X0),X2)))
| ~ $less(1,length(X2)) ),
inference(superposition,[],[f73,f65]) ).
tff(f135,plain,
! [X2: list,X0: list,X1: $int] :
( $less(4,length(cons(X1,append(X0,X2))))
| ~ $less(1,$sum(1,length(X0)))
| ~ $less(1,length(X2)) ),
inference(forward_demodulation,[],[f134,f70]) ).
tff(f136,plain,
! [X2: list,X0: list] :
( ~ $less(1,$sum(1,length(X0)))
| $less(4,$sum(1,length(append(X0,X2))))
| ~ $less(1,length(X2)) ),
inference(forward_demodulation,[],[f135,f65]) ).
tff(f138,plain,
! [X2: list,X0: list,X1: $int] :
( ~ $less(1,$sum(1,$sum(1,length(X0))))
| $less(4,$sum(1,length(append(cons(X1,X0),X2))))
| ~ $less(1,length(X2)) ),
inference(superposition,[],[f136,f65]) ).
tff(f139,plain,
! [X2: list,X0: list,X1: $int] :
( $less(4,$sum(1,length(cons(X1,append(X0,X2)))))
| ~ $less(1,$sum(1,$sum(1,length(X0))))
| ~ $less(1,length(X2)) ),
inference(forward_demodulation,[],[f138,f70]) ).
tff(f140,plain,
! [X2: list,X0: list] :
( ~ $less(1,$sum(1,$sum(1,length(X0))))
| $less(4,$sum(1,$sum(1,length(append(X0,X2)))))
| ~ $less(1,length(X2)) ),
inference(forward_demodulation,[],[f139,f65]) ).
tff(f150,plain,
! [X0: list] :
( ~ $less(1,$sum(1,$sum(1,0)))
| $less(4,$sum(1,$sum(1,length(append(nil,X0)))))
| ~ $less(1,length(X0)) ),
inference(superposition,[],[f140,f64]) ).
tff(f152,plain,
! [X0: list] :
( $less(4,$sum(1,$sum(1,length(append(nil,X0)))))
| ~ $less(1,length(X0)) ),
inference(evaluation,[],[f150]) ).
tff(f154,plain,
! [X0: list] :
( ~ $less(1,length(X0))
| $less(4,$sum(1,$sum(1,length(X0)))) ),
inference(forward_demodulation,[],[f152,f69]) ).
tff(f172,plain,
! [X0: list] :
( ~ $less(1,$sum(1,length(X0)))
| $less(4,$sum(1,$sum(1,$sum(1,length(X0))))) ),
inference(superposition,[],[f154,f65]) ).
tff(f187,plain,
! [X0: list] :
( ~ $less(1,$sum(1,$sum(1,length(X0))))
| $less(4,$sum(1,$sum(1,$sum(1,$sum(1,length(X0)))))) ),
inference(superposition,[],[f172,f65]) ).
tff(f213,plain,
( ~ $less(1,$sum(1,$sum(1,0)))
| $less(4,$sum(1,$sum(1,$sum(1,$sum(1,0))))) ),
inference(superposition,[],[f187,f64]) ).
tff(f215,plain,
$false,
inference(evaluation,[],[f213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT094_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n020.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 00:09:19 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.20/0.28 % (702301)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (702320)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2374159025:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (702316)% WARNING: option uhcvi not known.
% 0.20/0.28 % (702320) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-702301-702320"...
% 0.20/0.28 % (702320)...printing done.
% 0.20/0.28 % (702320)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (702320)------------------------------
% 0.20/0.28 % (702320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (702320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (702320)CaDiCaL version: 2.1.3
% 0.20/0.28 % (702320)Termination reason: Refutation
% 0.20/0.28 % (702320)Time elapsed: 0.004 s
% 0.20/0.28 % (702320)Peak memory usage: 12 MB
% 0.20/0.28 % (702320)Instructions burned: 10 (million)
% 0.20/0.28 % (702301)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------