%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT087_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 : n012.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 0.06s 0.16s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 39 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 87 ( 32 ~; 30 |; 21 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 66 ( 7 atm; 0 fun; 17 num; 42 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 : 15 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 59 !; 20 ?; 79 :)
% 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(f5,axiom,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( ( X1 = cons(X2,X3) )
& ( X0 = X2 ) )
| ? [X2: $int,X3: list] :
( ( X1 = cons(X2,X3) )
& in(X0,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_conv) ).
tff(f9,axiom,
! [X0: $int] : ( count(X0,nil) = 0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
tff(f14,axiom,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> $greater(count(X0,X1),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_8) ).
tff(f15,conjecture,
~ ! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f18,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> $less(0,count(X0,X1)) ),
inference(theory_normalization,[],[f14]) ).
tff(f31,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( ( X1 = cons(X2,X3) )
& ( X0 = X2 ) )
| ? [X4: $int,X5: list] :
( ( cons(X4,X5) = X1 )
& in(X0,X5) ) ) ),
inference(rectify,[],[f5]) ).
tff(f34,plain,
! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
inference(flattening,[],[f16]) ).
tff(f37,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ( ! [X2: $int,X3: list] :
( ( cons(X2,X3) != X1 )
| ( X0 != X2 ) )
& ! [X4: $int,X5: list] :
( ( cons(X4,X5) != X1 )
| ~ in(X0,X5) ) ) )
& ( ? [X2: $int,X3: list] :
( ( X1 = cons(X2,X3) )
& ( X0 = X2 ) )
| ? [X4: $int,X5: list] :
( ( cons(X4,X5) = X1 )
& in(X0,X5) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
tff(f38,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ( ! [X2: $int,X3: list] :
( ( cons(X2,X3) != X1 )
| ( X0 != X2 ) )
& ! [X4: $int,X5: list] :
( ( cons(X4,X5) != X1 )
| ~ in(X0,X5) ) ) )
& ( ? [X2: $int,X3: list] :
( ( X1 = cons(X2,X3) )
& ( X0 = X2 ) )
| ? [X4: $int,X5: list] :
( ( cons(X4,X5) = X1 )
& in(X0,X5) )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f37]) ).
tff(f39,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ( ! [X2: $int,X3: list] :
( ( cons(X2,X3) != X1 )
| ( X0 != X2 ) )
& ! [X4: $int,X5: list] :
( ( cons(X4,X5) != X1 )
| ~ in(X0,X5) ) ) )
& ( ? [X6: $int,X7: list] :
( ( cons(X6,X7) = X1 )
& ( X0 = X6 ) )
| ? [X8: $int,X9: list] :
( ( cons(X8,X9) = X1 )
& in(X0,X9) )
| ~ in(X0,X1) ) ),
inference(rectify,[],[f38]) ).
tff(f40,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ( ! [X2: $int,X3: list] :
( ( cons(X2,X3) != X1 )
| ( X0 != X2 ) )
& ! [X4: $int,X5: list] :
( ( cons(X4,X5) != X1 )
| ~ in(X0,X5) ) ) )
& ( ( ( cons(sK0(X0,X1),sK1(X0,X1)) = X1 )
& ( sK0(X0,X1) = X0 ) )
| ( ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 )
& in(X0,sK3(X0,X1)) )
| ~ in(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X6,sK0(X0,X1)),skolemize(X7,sK1(X0,X1)),skolemize(X8,sK2(X0,X1)),skolemize(X9,sK3(X0,X1))],[f39]) ).
tff(f45,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ $less(0,count(X0,X1)) )
& ( $less(0,count(X0,X1))
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
tff(f55,plain,
! [X2: $int,X3: list,X0: $int,X1: list] :
( in(X0,X1)
| ( cons(X2,X3) != X1 )
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f40]) ).
tff(f64,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f69,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tff(f71,plain,
! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
inference(cnf_transformation,[],[f34]) ).
tff(f72,plain,
! [X2: $int,X3: list,X0: $int] :
( in(X0,cons(X2,X3))
| ( X0 != X2 ) ),
inference(equality_resolution,[],[f55]) ).
tff(f73,plain,
! [X2: $int,X3: list] : in(X2,cons(X2,X3)),
inference(equality_resolution,[],[f72]) ).
tff(f121,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,cons(1,X1)) ),
inference(superposition,[],[f69,f71]) ).
tff(f125,plain,
! [X0: $int] :
( $less(0,0)
| ~ in(X0,cons(1,nil)) ),
inference(superposition,[],[f121,f64]) ).
tff(f126,plain,
! [X0: $int] : ~ in(X0,cons(1,nil)),
inference(evaluation,[],[f125]) ).
tff(f127,plain,
$false,
inference(resolution,[],[f126,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT087_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.11 % Computer : n012.cluster.edu
% 0.06/0.11 % Model : x86_64 x86_64
% 0.06/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.11 % Memory : 8046.5625MB
% 0.06/0.11 % OS : Linux 6.8.0-71-generic
% 0.06/0.11 % CPULimit : 300
% 0.06/0.11 % WCLimit : 300
% 0.06/0.11 % DateTime : Tue Sep 29 00:07:49 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.13 Running first-order model finding
% 0.06/0.13 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
% 0.06/0.16 % (3919969)Will run a generic schedule for satisfiability detection.
% 0.06/0.16 % (3919975)% WARNING: option uhcvi not known.
% 0.06/0.16 % (3919974)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=993965215_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.16 % (3919980)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2613573697:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.16 % (3919979)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=420019726:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.16 % (3919975)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3770954840:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.16 % (3919976)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1796194667:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.16 % (3919977)dis+10_1_sil=32000:sp=arity:random_seed=573025181:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.16 % (3919978)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2566315369:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.16 % (3919974)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.06/0.16 % (3919974)Terminated due to inappropriate strategy.
% 0.06/0.16 % (3919974)------------------------------
% 0.06/0.16 % (3919974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.16 % (3919974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.16 % (3919974)CaDiCaL version: 2.1.3
% 0.06/0.16 % (3919974)Termination reason: Inappropriate
% 0.06/0.16 % (3919974)Time elapsed: 0.0000 s
% 0.06/0.16 % (3919974)Peak memory usage: 10 MB
% 0.06/0.16 % (3919974)Instructions burned: 1 (million)
% 0.06/0.16 % (3919974)------------------------------
% 0.06/0.16 % (3919974)------------------------------
% 0.06/0.16 % (3919980) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3919969-3919980"...
% 0.06/0.16 % (3919977) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3919969-3919977"...
% 0.06/0.16 % (3919980)...printing done.
% 0.06/0.16 % (3919977)...printing done.
% 0.06/0.16 % (3919976) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3919969-3919976"...
% 0.06/0.16 % (3919980)Refutation found. Thanks to Tanya!
% 0.06/0.16 % SZS status Theorem for theBenchmark
% 0.06/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.16 % (3919980)------------------------------
% 0.06/0.16 % (3919980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.16 % (3919980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.16 % (3919980)CaDiCaL version: 2.1.3
% 0.06/0.16 % (3919980)Termination reason: Refutation
% 0.06/0.16 % (3919980)Time elapsed: 0.002 s
% 0.06/0.16 % (3919980)Peak memory usage: 12 MB
% 0.06/0.16 % (3919980)Instructions burned: 5 (million)
% 0.06/0.16 % (3919969)Success in time 0.026 s
% 0.06/0.16 % Vampire exiting
%------------------------------------------------------------------------------