%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT105_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 : n016.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 0.20s 1.21s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 124 ( 39 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 153 ( 62 ~; 51 |; 33 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 142 ( 39 atm; 20 fun; 42 num; 41 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 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 66 !; 12 ?; 78 :)
% 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_10,type,
sK0: ( list * $int ) > list ).
tff(func_def_11,type,
sK1: ( list * $int ) > $int ).
tff(pred_def_1,type,
inRange: ( $int * list ) > $o ).
tff(f1,axiom,
! [X1: list,X0: $int] : ( head(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
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] :
( ( ( X1 = nil )
| ? [X3: list,X2: $int] :
( $lesseq(0,X2)
& ( X1 = cons(X2,X3) )
& inRange(X0,X3)
& $less(X2,X0) ) )
<=> inRange(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).
tff(f6,conjecture,
~ ! [X1: $int,X0: list] :
( ( ( X0 != nil )
& inRange(X1,X0) )
=> $greatereq($difference(X1,head(X0)),2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f7,negated_conjecture,
~ ~ ! [X1: $int,X0: list] :
( ( ( X0 != nil )
& inRange(X1,X0) )
=> $greatereq($difference(X1,head(X0)),2) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
! [X0: $int,X1: list] :
( ( ( X1 = nil )
| ? [X3: list,X2: $int] :
( ~ $less(X2,0)
& ( X1 = cons(X2,X3) )
& inRange(X0,X3)
& $less(X2,X0) ) )
<=> inRange(X0,X1) ),
inference(theory_normalization,[],[f5]) ).
tff(f9,plain,
! [X1: $int,X0: list] :
( ( ( X0 != nil )
& inRange(X1,X0) )
=> ~ $less($sum(X1,$uminus(head(X0))),2) ),
inference(theory_normalization,[],[f7]) ).
tff(f22,plain,
! [X1: list,X0: $int] :
( ( ? [X2: list,X3: $int] :
( ( cons(X3,X2) = X1 )
& ~ $less(X3,0)
& inRange(X0,X2)
& $less(X3,X0) )
| ( X1 = nil ) )
<=> inRange(X0,X1) ),
inference(rectify,[],[f8]) ).
tff(f23,plain,
! [X1: list,X0: $int] :
( ( ( nil != X1 )
& inRange(X0,X1) )
=> ~ $less($sum(X0,$uminus(head(X1))),2) ),
inference(rectify,[],[f9]) ).
tff(f24,plain,
! [X0: list,X1: $int] : ( head(cons(X1,X0)) = X1 ),
inference(rectify,[],[f1]) ).
tff(f25,plain,
! [X1: list,X0: $int] :
( ~ $less($sum(X0,$uminus(head(X1))),2)
| ( nil = X1 )
| ~ inRange(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
tff(f26,plain,
! [X1: list,X0: $int] :
( ( nil = X1 )
| ~ inRange(X0,X1)
| ~ $less($sum(X0,$uminus(head(X1))),2) ),
inference(flattening,[],[f25]) ).
tff(f27,plain,
! [X0: list,X1: $int] :
( ( nil = X0 )
| ~ inRange(X1,X0)
| ~ $less($sum(X1,$uminus(head(X0))),2) ),
inference(rectify,[],[f26]) ).
tff(f28,plain,
! [X0: list,X1: $int] : ( nil != cons(X1,X0) ),
inference(rectify,[],[f4]) ).
tff(f29,plain,
! [X1: list,X0: $int] :
( ( ? [X2: list,X3: $int] :
( ( cons(X3,X2) = X1 )
& ~ $less(X3,0)
& inRange(X0,X2)
& $less(X3,X0) )
| ( X1 = nil )
| ~ inRange(X0,X1) )
& ( inRange(X0,X1)
| ( ! [X2: list,X3: $int] :
( ( cons(X3,X2) != X1 )
| $less(X3,0)
| ~ inRange(X0,X2)
| ~ $less(X3,X0) )
& ( nil != X1 ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
tff(f30,plain,
! [X1: list,X0: $int] :
( ( ? [X2: list,X3: $int] :
( ( cons(X3,X2) = X1 )
& ~ $less(X3,0)
& inRange(X0,X2)
& $less(X3,X0) )
| ( X1 = nil )
| ~ inRange(X0,X1) )
& ( inRange(X0,X1)
| ( ! [X2: list,X3: $int] :
( ( cons(X3,X2) != X1 )
| $less(X3,0)
| ~ inRange(X0,X2)
| ~ $less(X3,X0) )
& ( nil != X1 ) ) ) ),
inference(flattening,[],[f29]) ).
tff(f31,plain,
! [X0: list,X1: $int] :
( ( ? [X2: list,X3: $int] :
( ( cons(X3,X2) = X0 )
& ~ $less(X3,0)
& inRange(X1,X2)
& $less(X3,X1) )
| ( nil = X0 )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ! [X4: list,X5: $int] :
( ( cons(X5,X4) != X0 )
| $less(X5,0)
| ~ inRange(X1,X4)
| ~ $less(X5,X1) )
& ( nil != X0 ) ) ) ),
inference(rectify,[],[f30]) ).
tff(f32,plain,
! [X0: list,X1: $int] :
( ( ( ( cons(sK1(X0,X1),sK0(X0,X1)) = X0 )
& ~ $less(sK1(X0,X1),0)
& inRange(X1,sK0(X0,X1))
& $less(sK1(X0,X1),X1) )
| ( nil = X0 )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ! [X4: list,X5: $int] :
( ( cons(X5,X4) != X0 )
| $less(X5,0)
| ~ inRange(X1,X4)
| ~ $less(X5,X1) )
& ( nil != X0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f31]) ).
tff(f33,plain,
! [X0: list,X1: $int] : ( head(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f24]) ).
tff(f34,plain,
! [X0: list,X1: $int] :
( ~ $less($sum(X1,$uminus(head(X0))),2)
| ~ inRange(X1,X0)
| ( nil = X0 ) ),
inference(cnf_transformation,[],[f27]) ).
tff(f37,plain,
! [X0: list,X1: $int] : ( nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f28]) ).
tff(f38,plain,
! [X0: list,X1: $int] :
( inRange(X1,X0)
| ( nil != X0 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f39,plain,
! [X0: list,X1: $int,X4: list,X5: $int] :
( inRange(X1,X0)
| ( cons(X5,X4) != X0 )
| $less(X5,0)
| ~ inRange(X1,X4)
| ~ $less(X5,X1) ),
inference(cnf_transformation,[],[f32]) ).
tff(f44,plain,
! [X1: $int,X4: list,X5: $int] :
( inRange(X1,cons(X5,X4))
| ~ $less(X5,X1)
| $less(X5,0)
| ~ inRange(X1,X4) ),
inference(equality_resolution,[],[f39]) ).
tff(f45,plain,
! [X1: $int] : inRange(X1,nil),
inference(equality_resolution,[],[f38]) ).
tff(f64,plain,
! [X2: list,X0: $int,X1: $int] :
( ~ inRange(X1,cons(X0,X2))
| ~ $less($sum(X1,$uminus(X0)),2)
| ( nil = cons(X0,X2) ) ),
inference(superposition,[],[f34,f33]) ).
tff(f69,plain,
! [X2: list,X0: $int,X1: $int] :
( ~ $less($sum(X1,$uminus(X0)),2)
| ~ inRange(X1,cons(X0,X2)) ),
inference(forward_subsumption_resolution,[],[f64,f37]) ).
tff(f74,plain,
( ~ inRange(2,cons(1,nil))
| ~ $less($sum(2,$uminus(1)),2) ),
inference(instantiation,[],[f69]) ).
tff(f82,plain,
~ inRange(2,cons(1,nil)),
inference(evaluation,[],[f74]) ).
tff(f184,plain,
( ~ $less(1,2)
| inRange(2,cons(1,nil))
| $less(1,0)
| ~ inRange(2,nil) ),
inference(instantiation,[],[f44]) ).
tff(f190,plain,
( ~ inRange(2,nil)
| inRange(2,cons(1,nil)) ),
inference(evaluation,[],[f184]) ).
tff(f194,plain,
inRange(2,cons(1,nil)),
inference(forward_subsumption_resolution,[],[f190,f45]) ).
tff(f196,plain,
$false,
inference(forward_subsumption_resolution,[],[f194,f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT105_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n016.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 00:13:18 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running first-order theorem proving
% 0.12/0.23 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
% 0.20/1.21 % (4173081)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.20/1.21 % (4173143)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3693954652:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/1.21 % (4173143)First to succeed.
% 0.20/1.21 % (4173143)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4173081"
% 0.20/1.21 % (4173145)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2403158992:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.20/1.21 % (4173140)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2944091402:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.20/1.21 % (4173136)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3306637816:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/1.21 % (4173141)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4069877333:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.20/1.21 % (4173150)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=905281526:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.20/1.21 % (4173145)Instruction limit reached!
% 0.20/1.21 % (4173145)------------------------------
% 0.20/1.21 % (4173145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.21 % (4173145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.21 % (4173145)CaDiCaL version: 2.1.3
% 0.20/1.21 % (4173145)Termination reason: Instruction limit
% 0.20/1.21 % (4173145)Termination phase: Saturation
% 0.20/1.21 % (4173145)Time elapsed: 0.004 s
% 0.20/1.21 % (4173145)Peak memory usage: 88 MB
% 0.20/1.21 % (4173145)Instructions burned: 5 (million)
% 0.20/1.21 % (4173148)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1122496550:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.20/1.21 % (4173136)Instruction limit reached!
% 0.20/1.21 % (4173136)------------------------------
% 0.20/1.21 % (4173136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.21 % (4173136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.21 % (4173136)CaDiCaL version: 2.1.3
% 0.20/1.21 % (4173136)Termination reason: Instruction limit
% 0.20/1.21 % (4173136)Termination phase: Saturation
% 0.20/1.21 % (4173136)Time elapsed: 0.029 s
% 0.20/1.21 % (4173136)Peak memory usage: 112 MB
% 0.20/1.21 % (4173136)Instructions burned: 12 (million)
% 0.20/1.21 % (4173150)Also succeeded, but the first one will report.
% 0.20/1.21 % (4173141)Also succeeded, but the first one will report.
% 0.20/1.21 % (4173148)Instruction limit reached!
% 0.20/1.21 % (4173148)------------------------------
% 0.20/1.21 % (4173148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.21 % (4173148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.21 % (4173148)CaDiCaL version: 2.1.3
% 0.20/1.21 % (4173148)Termination reason: Instruction limit
% 0.20/1.21 % (4173148)Termination phase: Saturation
% 0.20/1.21 % (4173148)Time elapsed: 0.049 s
% 0.20/1.21 % (4173148)Peak memory usage: 112 MB
% 0.20/1.21 % (4173148)Instructions burned: 48 (million)
% 0.20/1.21 % (4173143)Refutation found. Thanks to Tanya!
% 0.20/1.21 % SZS status Theorem for theBenchmark
% 0.20/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.21 % (4173143)------------------------------
% 0.20/1.21 % (4173143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.21 % (4173143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.21 % (4173143)CaDiCaL version: 2.1.3
% 0.20/1.21 % (4173143)Termination reason: Refutation
% 0.20/1.21 % (4173143)Time elapsed: 0.003 s
% 0.20/1.21 % (4173143)Peak memory usage: 89 MB
% 0.20/1.21 % (4173143)Instructions burned: 6 (million)
% 0.20/1.21 % (4173143)------------------------------
% 0.20/1.21 % (4173143)------------------------------
% 0.20/1.21 % (4173081)Success in time 0.317 s
% 0.20/1.21 % Vampire exiting
%------------------------------------------------------------------------------