%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT102_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 09:47:18 AM UTC 2026
% Result : Theorem 0.19s 1.03s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 34 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 118 ( 46 ~; 40 |; 26 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 74 ( 22 atm; 0 fun; 16 num; 36 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 : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 63 !; 10 ?; 73 :)
% 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,
sK0: ( list * $int ) > $int ).
tff(func_def_6,type,
sK1: ( list * $int ) > list ).
tff(pred_def_1,type,
inRange: ( $int * list ) > $o ).
tff(f2,axiom,
! [X1: list,X0: $int] : ( tail(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
tff(f4,axiom,
! [X1: list,X0: $int] : ( cons(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(f5,axiom,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( ( X1 = cons(X2,X3) )
& $lesseq(0,X2)
& $less(X2,X0)
& inRange(X0,X3) )
| ( X1 = nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).
tff(f6,conjecture,
~ ! [X1: $int,X0: list] :
( inRange(X1,tail(X0))
=> inRange(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f7,negated_conjecture,
~ ~ ! [X1: $int,X0: list] :
( inRange(X1,tail(X0))
=> inRange(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
! [X1: list,X0: $int] :
( ( ( X1 = nil )
| ? [X2: $int,X3: list] :
( ~ $less(X2,0)
& ( X1 = cons(X2,X3) )
& $less(X2,X0)
& inRange(X0,X3) ) )
<=> inRange(X0,X1) ),
inference(theory_normalization,[],[f5]) ).
tff(f9,plain,
! [X1: $int,X0: list] : ( tail(cons(X1,X0)) = X0 ),
inference(rectify,[],[f2]) ).
tff(f10,plain,
~ ~ ! [X1: list,X0: $int] :
( inRange(X0,tail(X1))
=> inRange(X0,X1) ),
inference(rectify,[],[f7]) ).
tff(f11,plain,
! [X1: list,X0: $int] :
( inRange(X0,tail(X1))
=> inRange(X0,X1) ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
! [X1: list,X0: $int] :
( inRange(X0,X1)
| ~ inRange(X0,tail(X1)) ),
inference(ennf_transformation,[],[f11]) ).
tff(f13,plain,
! [X1: list,X0: $int] :
( ( ( X1 = nil )
| ? [X2: $int,X3: list] :
( ~ $less(X2,0)
& ( X1 = cons(X2,X3) )
& $less(X2,X0)
& inRange(X0,X3) )
| ~ inRange(X0,X1) )
& ( inRange(X0,X1)
| ( ( nil != X1 )
& ! [X2: $int,X3: list] :
( $less(X2,0)
| ( cons(X2,X3) != X1 )
| ~ $less(X2,X0)
| ~ inRange(X0,X3) ) ) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f14,plain,
! [X1: list,X0: $int] :
( ( ( X1 = nil )
| ? [X2: $int,X3: list] :
( ~ $less(X2,0)
& ( X1 = cons(X2,X3) )
& $less(X2,X0)
& inRange(X0,X3) )
| ~ inRange(X0,X1) )
& ( inRange(X0,X1)
| ( ( nil != X1 )
& ! [X2: $int,X3: list] :
( $less(X2,0)
| ( cons(X2,X3) != X1 )
| ~ $less(X2,X0)
| ~ inRange(X0,X3) ) ) ) ),
inference(flattening,[],[f13]) ).
tff(f15,plain,
! [X0: list,X1: $int] :
( ( ( nil = X0 )
| ? [X2: $int,X3: list] :
( ~ $less(X2,0)
& ( cons(X2,X3) = X0 )
& $less(X2,X1)
& inRange(X1,X3) )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ( nil != X0 )
& ! [X4: $int,X5: list] :
( $less(X4,0)
| ( cons(X4,X5) != X0 )
| ~ $less(X4,X1)
| ~ inRange(X1,X5) ) ) ) ),
inference(rectify,[],[f14]) ).
tff(f16,plain,
! [X0: list,X1: $int] :
( ( ( nil = X0 )
| ( ~ $less(sK0(X0,X1),0)
& ( cons(sK0(X0,X1),sK1(X0,X1)) = X0 )
& $less(sK0(X0,X1),X1)
& inRange(X1,sK1(X0,X1)) )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ( nil != X0 )
& ! [X4: $int,X5: list] :
( $less(X4,0)
| ( cons(X4,X5) != X0 )
| ~ $less(X4,X1)
| ~ inRange(X1,X5) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f15]) ).
tff(f17,plain,
! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
inference(rectify,[],[f9]) ).
tff(f18,plain,
! [X0: list,X1: $int] :
( inRange(X1,X0)
| ~ inRange(X1,tail(X0)) ),
inference(rectify,[],[f12]) ).
tff(f19,plain,
! [X0: list,X1: $int] : ( nil != cons(X1,X0) ),
inference(rectify,[],[f4]) ).
tff(f22,plain,
! [X0: list,X1: $int] :
( inRange(X1,X0)
| ( nil != X0 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f24,plain,
! [X0: list,X1: $int] :
( $less(sK0(X0,X1),X1)
| ~ inRange(X1,X0)
| ( nil = X0 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f26,plain,
! [X0: list,X1: $int] :
( ~ $less(sK0(X0,X1),0)
| ~ inRange(X1,X0)
| ( nil = X0 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f28,plain,
! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f17]) ).
tff(f29,plain,
! [X0: list,X1: $int] :
( ~ inRange(X1,tail(X0))
| inRange(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f30,plain,
! [X0: list,X1: $int] : ( nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f32,plain,
! [X1: $int] : inRange(X1,nil),
inference(equality_resolution,[],[f22]) ).
tff(f34,plain,
! [X2: $int,X0: list,X1: $int] :
( inRange(X1,cons(X2,X0))
| ~ inRange(X1,X0) ),
inference(superposition,[],[f29,f28]) ).
tff(f41,plain,
! [X0: list] :
( ~ inRange(0,X0)
| ~ inRange(0,X0)
| ( nil = X0 )
| ( nil = X0 ) ),
inference(resolution,[],[f26,f24]) ).
tff(f42,plain,
! [X0: list] :
( ~ inRange(0,X0)
| ( nil = X0 ) ),
inference(duplicate_literal_removal,[],[f41]) ).
tff(f44,plain,
! [X0: $int,X1: list] :
( ( cons(X0,X1) = nil )
| ~ inRange(0,X1) ),
inference(resolution,[],[f42,f34]) ).
tff(f46,plain,
! [X1: list] : ~ inRange(0,X1),
inference(forward_subsumption_resolution,[],[f44,f30]) ).
tff(f47,plain,
$false,
inference(resolution,[],[f46,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT102_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 00:08:30 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/1.03 % (3624336)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.19/1.03 % (3624342)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3012453223:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.19/1.03 % (3624342)First to succeed.
% 0.19/1.03 % (3624342)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3624336"
% 0.19/1.03 % (3624345)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4013572519:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.19/1.03 % (3624344)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=579279886:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/1.03 % (3624343)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2295024399:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.19/1.03 % (3624347)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2639763565:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.19/1.03 % (3624341)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3946606919:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/1.03 % (3624345)Instruction limit reached!
% 0.19/1.03 % (3624345)------------------------------
% 0.19/1.03 % (3624345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.03 % (3624345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.03 % (3624345)CaDiCaL version: 2.1.3
% 0.19/1.03 % (3624345)Termination reason: Instruction limit
% 0.19/1.03 % (3624345)Termination phase: Saturation
% 0.19/1.03 % (3624345)Time elapsed: 0.004 s
% 0.19/1.03 % (3624345)Peak memory usage: 88 MB
% 0.19/1.03 % (3624345)Instructions burned: 5 (million)
% 0.19/1.03 % (3624344)Instruction limit reached!
% 0.19/1.03 % (3624344)------------------------------
% 0.19/1.03 % (3624344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.03 % (3624344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.03 % (3624344)CaDiCaL version: 2.1.3
% 0.19/1.03 % (3624344)Termination reason: Instruction limit
% 0.19/1.03 % (3624344)Termination phase: Saturation
% 0.19/1.03 % (3624344)Time elapsed: 0.006 s
% 0.19/1.03 % (3624344)Peak memory usage: 88 MB
% 0.19/1.03 % (3624344)Instructions burned: 7 (million)
% 0.19/1.03 % (3624346)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1089751900:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.19/1.03 % (3624341)Instruction limit reached!
% 0.19/1.03 % (3624341)------------------------------
% 0.19/1.03 % (3624341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.03 % (3624341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.03 % (3624341)CaDiCaL version: 2.1.3
% 0.19/1.03 % (3624341)Termination reason: Instruction limit
% 0.19/1.03 % (3624341)Time elapsed: 0.029 s
% 0.19/1.03 % (3624341)Peak memory usage: 112 MB
% 0.19/1.03 % (3624341)Instructions burned: 12 (million)
% 0.19/1.03 % (3624347)Also succeeded, but the first one will report.
% 0.19/1.03 % (3624343)Also succeeded, but the first one will report.
% 0.19/1.03 % (3624346)Also succeeded, but the first one will report.
% 0.19/1.03 % (3624342)Refutation found. Thanks to Tanya!
% 0.19/1.03 % SZS status Theorem for theBenchmark
% 0.19/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.03 % (3624342)------------------------------
% 0.19/1.03 % (3624342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.03 % (3624342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.03 % (3624342)CaDiCaL version: 2.1.3
% 0.19/1.03 % (3624342)Termination reason: Refutation
% 0.19/1.03 % (3624342)Time elapsed: 0.018 s
% 0.19/1.03 % (3624342)Peak memory usage: 112 MB
% 0.19/1.03 % (3624342)Instructions burned: 7 (million)
% 0.19/1.03 % (3624342)------------------------------
% 0.19/1.03 % (3624342)------------------------------
% 0.19/1.03 % (3624336)Success in time 0.287 s
% 0.19/1.03 % Vampire exiting
%------------------------------------------------------------------------------