%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT094_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 : 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 09:47:17 AM UTC 2026
% Result : Theorem 2.33s 0.72s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 15 unt; 0 typ; 1 def)
% Number of atoms : 79 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 39 ~; 35 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 209 ( 53 atm; 42 fun; 102 num; 12 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 : 7 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 17 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?; 57 :)
% 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: ( list * $int ) > $int ).
tff(func_def_12,type,
sK1: ( list * $int ) > list ).
tff(func_def_13,type,
sK2: ( list * $int ) > list ).
tff(func_def_14,type,
sK3: ( list * $int ) > $int ).
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/sandbox/benchmark/theBenchmark.p',l) ).
tff(f8,axiom,
! [X1: list,X0: $int] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_1) ).
tff(f12,axiom,
! [X0: list] : ( append(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6) ).
tff(f13,axiom,
! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_7) ).
tff(f15,conjecture,
~ ! [X0: list,X1: list] :
( ( $greater(length(X0),1)
& $greater(length(X1),1) )
=> $greater(length(append(X0,X1)),4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X0: list,X1: list] :
( ( $greater(length(X0),1)
& $greater(length(X1),1) )
=> $greater(length(append(X0,X1)),4) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f17,plain,
! [X1: list,X0: list] :
( ( $less(1,length(X1))
& $less(1,length(X0)) )
=> $less(4,length(append(X0,X1))) ),
inference(theory_normalization,[],[f16]) ).
tff(f21,plain,
! [X1: $int,X0: list] : ( $sum(1,length(X0)) = length(cons(X1,X0)) ),
inference(rectify,[],[f8]) ).
tff(f22,plain,
! [X0: list,X2: list,X1: $int] : ( cons(X1,append(X2,X0)) = append(cons(X1,X2),X0) ),
inference(rectify,[],[f13]) ).
tff(f26,plain,
! [X1: list,X0: list] :
( $less(4,length(append(X0,X1)))
| ~ $less(1,length(X1))
| ~ $less(1,length(X0)) ),
inference(ennf_transformation,[],[f17]) ).
tff(f27,plain,
! [X1: list,X0: list] :
( ~ $less(1,length(X0))
| $less(4,length(append(X0,X1)))
| ~ $less(1,length(X1)) ),
inference(flattening,[],[f26]) ).
tff(f36,plain,
! [X0: list,X1: list] :
( ~ $less(1,length(X1))
| $less(4,length(append(X1,X0)))
| ~ $less(1,length(X0)) ),
inference(rectify,[],[f27]) ).
tff(f38,plain,
! [X0: list,X1: list,X2: $int] : ( cons(X2,append(X1,X0)) = append(cons(X2,X1),X0) ),
inference(rectify,[],[f22]) ).
tff(f40,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(rectify,[],[f21]) ).
tff(f46,plain,
! [X0: list] : ( append(nil,X0) = X0 ),
inference(cnf_transformation,[],[f12]) ).
tff(f58,plain,
0 = length(nil),
inference(cnf_transformation,[],[f7]) ).
tff(f59,plain,
! [X0: list,X1: list] :
( $less(4,length(append(X1,X0)))
| ~ $less(1,length(X0))
| ~ $less(1,length(X1)) ),
inference(cnf_transformation,[],[f36]) ).
tff(f62,plain,
! [X2: $int,X0: list,X1: list] : ( cons(X2,append(X1,X0)) = append(cons(X2,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tff(f64,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(cnf_transformation,[],[f40]) ).
tff(f79,definition,
( spl6_1
<=> ( 0 = length(nil) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f81,plain,
( ( 0 = length(nil) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f79]) ).
tff(f82,plain,
spl6_1,
inference(avatar_split_clause,[],[f58,f79]) ).
tff(f99,plain,
! [X2: list,X0: $int,X1: list] :
( $less(4,length(cons(X0,append(X1,X2))))
| ~ $less(1,length(X2))
| ~ $less(1,length(cons(X0,X1))) ),
inference(superposition,[],[f59,f62]) ).
tff(f100,plain,
! [X2: list,X0: $int,X1: list] :
( ~ $less(1,length(X2))
| ~ $less(1,length(cons(X0,X1)))
| $less(4,$sum(1,length(append(X1,X2)))) ),
inference(forward_demodulation,[],[f99,f64]) ).
tff(f101,plain,
! [X2: list,X1: list] :
( $less(4,$sum(1,length(append(X1,X2))))
| ~ $less(1,$sum(1,length(X1)))
| ~ $less(1,length(X2)) ),
inference(forward_demodulation,[],[f100,f64]) ).
tff(f103,plain,
! [X2: list,X0: $int,X1: list] :
( ~ $less(1,length(X2))
| $less(4,$sum(1,length(cons(X0,append(X1,X2)))))
| ~ $less(1,$sum(1,length(cons(X0,X1)))) ),
inference(superposition,[],[f101,f62]) ).
tff(f104,plain,
! [X2: list,X0: $int,X1: list] :
( $less(4,$sum(1,$sum(1,length(append(X1,X2)))))
| ~ $less(1,$sum(1,length(cons(X0,X1))))
| ~ $less(1,length(X2)) ),
inference(forward_demodulation,[],[f103,f64]) ).
tff(f106,plain,
! [X2: list,X1: list] :
( $less(4,$sum(1,$sum(1,length(append(X1,X2)))))
| ~ $less(1,$sum(1,$sum(1,length(X1))))
| ~ $less(1,length(X2)) ),
inference(forward_demodulation,[],[f104,f64]) ).
tff(f107,plain,
! [X0: list] :
( ~ $less(1,length(X0))
| ~ $less(1,$sum(1,$sum(1,length(nil))))
| $less(4,$sum(1,$sum(1,length(X0)))) ),
inference(superposition,[],[f106,f46]) ).
tff(f110,plain,
( ! [X0: list] :
( $less(4,$sum(1,$sum(1,length(X0))))
| ~ $less(1,length(X0))
| ~ $less(1,$sum(1,$sum(1,0))) )
| ~ spl6_1 ),
inference(forward_demodulation,[],[f107,f81]) ).
tff(f111,plain,
( ! [X0: list] :
( $less(4,$sum(1,$sum(1,length(X0))))
| ~ $less(1,length(X0)) )
| ~ spl6_1 ),
inference(evaluation,[],[f110]) ).
tff(f114,plain,
( ! [X0: list] :
( $less(4,$sum(1,$sum(1,$sum(1,length(X0)))))
| ~ $less(1,$sum(1,length(X0))) )
| ~ spl6_1 ),
inference(superposition,[],[f111,f64]) ).
tff(f118,plain,
( ! [X0: list] :
( $less(4,$sum(1,$sum(1,$sum(1,$sum(1,length(X0))))))
| ~ $less(1,$sum(1,$sum(1,length(X0)))) )
| ~ spl6_1 ),
inference(superposition,[],[f114,f64]) ).
tff(f122,plain,
( ~ $less(1,$sum(1,$sum(1,0)))
| $less(4,$sum(1,$sum(1,$sum(1,$sum(1,0)))))
| ~ spl6_1 ),
inference(superposition,[],[f118,f81]) ).
tff(f124,plain,
( $false
| ~ spl6_1 ),
inference(evaluation,[],[f122]) ).
tff(f125,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f124]) ).
tff(f126,plain,
$false,
inference(avatar_smt_refutation,[],[f125,f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT094_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 00:08:04 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 1.65/0.62 % (3920737)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.65/0.62 % (3920752)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3045031771:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 1.65/0.62 % (3920749)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1065329531:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 1.65/0.62 % (3920753)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1182105951:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 1.65/0.62 % (3920750)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1942143667:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 1.65/0.62 % (3920755)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1766265255:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 1.65/0.62 % (3920751)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4286407089:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 1.65/0.62 % (3920754)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3126428875:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 1.65/0.62 % (3920753)Instruction limit reached!
% 1.65/0.62 % (3920753)------------------------------
% 1.65/0.62 % (3920753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/0.62 % (3920753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.62 % (3920753)CaDiCaL version: 2.1.3
% 1.65/0.62 % (3920753)Termination reason: Instruction limit
% 1.65/0.62 % (3920753)Termination phase: Saturation
% 1.65/0.62 % (3920753)Time elapsed: 0.002 s
% 1.65/0.62 % (3920753)Peak memory usage: 88 MB
% 1.65/0.62 % (3920753)Instructions burned: 4 (million)
% 1.65/0.62 % (3920752)Instruction limit reached!
% 1.65/0.62 % (3920752)------------------------------
% 1.65/0.62 % (3920752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/0.62 % (3920752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.62 % (3920752)CaDiCaL version: 2.1.3
% 1.65/0.62 % (3920752)Termination reason: Instruction limit
% 1.65/0.62 % (3920752)Termination phase: Saturation
% 1.65/0.62 % (3920752)Time elapsed: 0.003 s
% 1.65/0.62 % (3920752)Peak memory usage: 88 MB
% 1.65/0.62 % (3920752)Instructions burned: 8 (million)
% 1.65/0.62 % (3920749)Instruction limit reached!
% 1.65/0.62 % (3920749)------------------------------
% 1.65/0.62 % (3920749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/0.62 % (3920749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.62 % (3920749)CaDiCaL version: 2.1.3
% 1.65/0.62 % (3920749)Termination reason: Instruction limit
% 1.65/0.62 % (3920749)Termination phase: Saturation
% 1.65/0.62 % (3920749)Time elapsed: 0.018 s
% 1.65/0.62 % (3920749)Peak memory usage: 114 MB
% 1.65/0.62 % (3920749)Instructions burned: 12 (million)
% 1.65/0.62 % (3920754)First to succeed.
% 1.65/0.62 % (3920754)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3920737"
% 1.65/0.62 % (3920750)Also succeeded, but the first one will report.
% 1.65/0.62 % (3920755)Also succeeded, but the first one will report.
% 1.65/0.62 % (3920751)Instruction limit reached!
% 1.65/0.62 % (3920751)------------------------------
% 1.65/0.62 % (3920751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/0.62 % (3920751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.62 % (3920751)CaDiCaL version: 2.1.3
% 1.65/0.62 % (3920751)Termination reason: Instruction limit
% 1.65/0.62 % (3920751)Termination phase: Saturation
% 1.65/0.62 % (3920751)Time elapsed: 0.083 s
% 1.65/0.62 % (3920751)Peak memory usage: 116 MB
% 1.65/0.62 % (3920751)Instructions burned: 204 (million)
% 1.65/0.62 % (3920763)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3766163333:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.65/0.62 % (3920764)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=130128257:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 1.65/0.62 % (3920763)Also succeeded, but the first one will report.
% 1.65/0.62 % (3920764)Instruction limit reached!
% 1.65/0.62 % (3920764)------------------------------
% 2.33/0.72 % (3920764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.72 % (3920764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.72 % (3920764)CaDiCaL version: 2.1.3
% 2.33/0.72 % (3920764)Termination reason: Instruction limit
% 2.33/0.72 % (3920764)Termination phase: Saturation
% 2.33/0.72 % (3920764)Time elapsed: 0.013 s
% 2.33/0.72 % (3920764)Peak memory usage: 88 MB
% 2.33/0.72 % (3920764)Instructions burned: 31 (million)
% 2.33/0.72 % (3920765)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=526924686:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 2.33/0.72 % (3920765)Instruction limit reached!
% 2.33/0.72 % (3920765)------------------------------
% 2.33/0.72 % (3920765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.72 % (3920765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.72 % (3920765)CaDiCaL version: 2.1.3
% 2.33/0.72 % (3920765)Termination reason: Instruction limit
% 2.33/0.72 % (3920765)Termination phase: Saturation
% 2.33/0.72 % (3920765)Time elapsed: 0.006 s
% 2.33/0.72 % (3920765)Peak memory usage: 90 MB
% 2.33/0.72 % (3920765)Instructions burned: 16 (million)
% 2.33/0.72 % (3920754)Refutation found. Thanks to Tanya!
% 2.33/0.72 % SZS status Theorem for theBenchmark
% 2.33/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.33/0.72 % (3920754)------------------------------
% 2.33/0.72 % (3920754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.72 % (3920754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.72 % (3920754)CaDiCaL version: 2.1.3
% 2.33/0.72 % (3920754)Termination reason: Refutation
% 2.33/0.72 % (3920754)Time elapsed: 0.021 s
% 2.33/0.72 % (3920754)Peak memory usage: 116 MB
% 2.33/0.72 % (3920754)Instructions burned: 13 (million)
% 2.33/0.72 % (3920754)------------------------------
% 2.33/0.72 % (3920754)------------------------------
% 2.33/0.72 % (3920737)Success in time 0.297 s
% 2.33/0.72 % Vampire exiting
%------------------------------------------------------------------------------