%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT085_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 : n011.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 09:48:06 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 19 ~; 9 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 67 ( 0 atm; 17 fun; 31 num; 19 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 : 46 ( 46 !; 0 ?; 46 :)
% 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(f1,axiom,
! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
tff(f4,axiom,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
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(f15,conjecture,
~ ! [X0: list,X1: list] :
( ( length(X0) = length(X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X0: list,X1: list] :
( ( length(X0) = length(X1) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f34,plain,
! [X0: list,X1: list] :
( ( length(X0) = length(X1) )
=> ( X0 = X1 ) ),
inference(flattening,[],[f16]) ).
tff(f37,plain,
! [X0: list,X1: list] :
( ( X0 = X1 )
| ( length(X1) != length(X0) ) ),
inference(ennf_transformation,[],[f34]) ).
tff(f38,plain,
! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1]) ).
tff(f41,plain,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
inference(cnf_transformation,[],[f4]) ).
tff(f54,plain,
0 = length(nil),
inference(cnf_transformation,[],[f7]) ).
tff(f55,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(cnf_transformation,[],[f8]) ).
tff(f63,plain,
! [X0: list,X1: list] :
( ( length(X1) != length(X0) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f37]) ).
tff(f77,plain,
! [X0: list] :
( ( 0 != length(X0) )
| ( nil = X0 ) ),
inference(superposition,[],[f63,f54]) ).
tff(f121,plain,
! [X0: list,X1: $int] :
( ( 0 != $sum(1,length(X0)) )
| ( nil = cons(X1,X0) ) ),
inference(superposition,[],[f77,f55]) ).
tff(f122,plain,
! [X2: $int,X0: list,X1: list] :
( ( length(X1) != $sum(1,length(X0)) )
| ( cons(X2,X0) = X1 ) ),
inference(superposition,[],[f63,f55]) ).
tff(f124,plain,
! [X0: list] : ( 0 != $sum(1,length(X0)) ),
inference(forward_subsumption_resolution,[],[f121,f41]) ).
tff(f155,plain,
! [X0: list] : ( 0 != $sum(1,$sum(1,length(X0))) ),
inference(superposition,[],[f124,f55]) ).
tff(f181,plain,
! [X0: list] : ( 0 != $sum(1,$sum(1,$sum(1,length(X0)))) ),
inference(superposition,[],[f155,f55]) ).
tff(f189,plain,
! [X0: list] : ( 0 != $sum(1,$sum(1,$sum(1,$sum(1,length(X0))))) ),
inference(superposition,[],[f181,f55]) ).
tff(f191,plain,
! [X0: list,X1: $int] :
( ( length(X0) != $sum(1,0) )
| ( cons(X1,nil) = X0 ) ),
inference(superposition,[],[f122,f54]) ).
tff(f193,plain,
! [X0: list,X1: $int] :
( ( 1 != length(X0) )
| ( cons(X1,nil) = X0 ) ),
inference(evaluation,[],[f191]) ).
tff(f198,plain,
! [X2: $int,X0: list,X1: $int] :
( ( 1 != $sum(1,length(X0)) )
| ( cons(X1,X0) = cons(X2,nil) ) ),
inference(superposition,[],[f193,f55]) ).
tff(f220,plain,
! [X0: $int,X1: $int] :
( ( 1 != $sum(1,0) )
| ( cons(X1,nil) = cons(X0,nil) ) ),
inference(superposition,[],[f198,f54]) ).
tff(f222,plain,
! [X0: $int,X1: $int] : ( cons(X1,nil) = cons(X0,nil) ),
inference(evaluation,[],[f220]) ).
tff(f231,plain,
! [X0: $int,X1: $int] : ( head(cons(X0,nil)) = X1 ),
inference(superposition,[],[f38,f222]) ).
tff(f352,plain,
! [X0: $int] : ( 0 != head(cons(X0,nil)) ),
inference(superposition,[],[f189,f231]) ).
tff(f380,plain,
$false,
inference(forward_subsumption_resolution,[],[f352,f231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT085_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n011.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 : Tue Sep 29 00:08:16 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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 % (3916348)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (3916354)% WARNING: option uhcvi not known.
% 0.20/0.28 % (3916354)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3214792283:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (3916354) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3916348-3916354"...
% 0.20/0.28 % (3916356)dis+10_1_sil=32000:sp=arity:random_seed=2051780686:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (3916353)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1879329935_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (3916355)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4287101274:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (3916357)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2734526529:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (3916354)...printing done.
% 0.20/0.28 % (3916354)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 % (3916354)------------------------------
% 0.20/0.28 % (3916354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3916354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3916354)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3916354)Termination reason: Refutation
% 0.20/0.28 % (3916354)Time elapsed: 0.007 s
% 0.20/0.28 % (3916354)Peak memory usage: 12 MB
% 0.20/0.28 % (3916354)Instructions burned: 16 (million)
% 0.20/0.28 % (3916348)Success in time 0.039 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------