%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT092_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 17 ( 0 atm; 3 fun; 10 num; 4 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?; 20 :)
% 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_11,type,
sK0: ( $int * list ) > $int ).
tff(func_def_12,type,
sK1: ( $int * list ) > list ).
tff(func_def_13,type,
sK2: ( $int * list ) > $int ).
tff(func_def_14,type,
sK3: ( $int * list ) > list ).
tff(func_def_15,type,
sK4: ( $int * list ) > $int ).
tff(func_def_16,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/sandbox2/benchmark/theBenchmark.p',l) ).
tff(f8,axiom,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_1) ).
tff(f12,axiom,
! [X0: list] : ( append(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_6) ).
tff(f15,conjecture,
~ ! [X0: list,X1: list] : ( length(append(X0,X1)) = length(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X0: list,X1: list] : ( length(append(X0,X1)) = length(X0) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f34,plain,
! [X0: list,X1: list] : ( length(append(X0,X1)) = length(X0) ),
inference(flattening,[],[f16]) ).
tff(f62,plain,
0 = length(nil),
inference(cnf_transformation,[],[f7]) ).
tff(f63,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(cnf_transformation,[],[f8]) ).
tff(f67,plain,
! [X0: list] : ( append(nil,X0) = X0 ),
inference(cnf_transformation,[],[f12]) ).
tff(f71,plain,
! [X0: list,X1: list] : ( length(append(X0,X1)) = length(X0) ),
inference(cnf_transformation,[],[f34]) ).
tff(f78,plain,
! [X0: list] : ( length(nil) = length(X0) ),
inference(superposition,[],[f71,f67]) ).
tff(f79,plain,
! [X0: list] : ( 0 = length(X0) ),
inference(forward_demodulation,[],[f78,f62]) ).
tff(f135,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,0) ),
inference(forward_demodulation,[],[f63,f79]) ).
tff(f136,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = 1 ),
inference(evaluation,[],[f135]) ).
tff(f137,plain,
0 = 1,
inference(forward_demodulation,[],[f136,f79]) ).
tff(f138,plain,
$false,
inference(evaluation,[],[f137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT092_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:08:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.09/0.25 % (3623415)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (3623423)dis+10_1_sil=32000:sp=arity:random_seed=2356205192:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (3623423) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3623415-3623423"...
% 0.09/0.25 % (3623423)...printing done.
% 0.09/0.25 % (3623423)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (3623423)------------------------------
% 0.09/0.25 % (3623423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (3623423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (3623423)CaDiCaL version: 2.1.3
% 0.09/0.25 % (3623423)Termination reason: Refutation
% 0.09/0.25 % (3623423)Time elapsed: 0.002 s
% 0.09/0.25 % (3623423)Peak memory usage: 12 MB
% 0.09/0.25 % (3623423)Instructions burned: 5 (million)
% 0.09/0.25 % (3623415)Success in time 0.017 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------