%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT089_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 : n015.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 09:47:16 AM UTC 2026
% Result : Theorem 3.69s 1.23s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 6 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 66 ( 11 atm; 8 fun; 22 num; 25 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 : 16 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?; 40 :)
% 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 ) > $int ).
tff(func_def_14,type,
sK3: ( list * $int ) > list ).
tff(func_def_15,type,
sK4: ( list * $int ) > $int ).
tff(func_def_16,type,
sK5: ( list * $int ) > 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(f9,axiom,
! [X0: $int] : ( count(X0,nil) = 0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(f10,axiom,
! [X0: $int,X2: list,X3: $int,X1: $int] :
( ( X0 != X1 )
=> ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_3) ).
tff(f15,conjecture,
~ ! [X0: $int,X1: list] : $greatereq(count(X0,X1),length(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X0: $int,X1: list] : $greatereq(count(X0,X1),length(X1)),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f19,plain,
! [X0: $int,X1: list] : ~ $less(count(X0,X1),length(X1)),
inference(theory_normalization,[],[f16]) ).
tff(f34,plain,
! [X1: $int,X0: list] : ( $sum(1,length(X0)) = length(cons(X1,X0)) ),
inference(rectify,[],[f8]) ).
tff(f37,plain,
! [X3: $int,X1: list,X0: $int] :
( ( X0 != X3 )
=> ( count(X0,X1) = count(X0,cons(X3,X1)) ) ),
inference(rectify,[],[f10]) ).
tff(f40,plain,
! [X0: $int,X3: $int,X1: list] :
( ( X0 = X3 )
| ( count(X0,X1) = count(X0,cons(X3,X1)) ) ),
inference(ennf_transformation,[],[f37]) ).
tff(f47,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(rectify,[],[f34]) ).
tff(f55,plain,
! [X0: $int,X1: $int,X2: list] :
( ( X0 = X1 )
| ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
inference(rectify,[],[f40]) ).
tff(f64,plain,
0 = length(nil),
inference(cnf_transformation,[],[f7]) ).
tff(f65,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f67,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(cnf_transformation,[],[f47]) ).
tff(f71,plain,
! [X0: $int,X1: list] : ~ $less(count(X0,X1),length(X1)),
inference(cnf_transformation,[],[f19]) ).
tff(f80,plain,
! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f55]) ).
tff(f151,plain,
! [X2: $int,X0: $int,X1: list] :
( ~ $less(count(X0,X1),length(cons(X2,X1)))
| ( X0 = X2 ) ),
inference(superposition,[],[f71,f80]) ).
tff(f160,plain,
! [X2: $int,X0: $int,X1: list] :
( ~ $less(count(X0,X1),$sum(1,length(X1)))
| ( X0 = X2 ) ),
inference(forward_demodulation,[],[f151,f67]) ).
tff(f190,plain,
( ( 0 = 1 )
| ~ $less(count(1,nil),$sum(1,length(nil))) ),
inference(instantiation,[],[f160]) ).
tff(f194,plain,
~ $less(count(1,nil),$sum(1,length(nil))),
inference(evaluation,[],[f190]) ).
tff(f195,plain,
~ $less(count(1,nil),$sum(1,0)),
inference(forward_demodulation,[],[f194,f64]) ).
tff(f196,plain,
~ $less(count(1,nil),1),
inference(evaluation,[],[f195]) ).
tff(f197,plain,
~ $less(0,1),
inference(forward_demodulation,[],[f196,f65]) ).
tff(f198,plain,
$false,
inference(evaluation,[],[f197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT089_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 00:11:32 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.69/1.23 % (3169562)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.69/1.23 % (3169653)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=579947409:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.69/1.23 % (3169653)Instruction limit reached!
% 3.69/1.23 % (3169653)------------------------------
% 3.69/1.23 % (3169653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.23 % (3169653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.23 % (3169653)CaDiCaL version: 2.1.3
% 3.69/1.23 % (3169653)Termination reason: Instruction limit
% 3.69/1.23 % (3169653)Termination phase: Saturation
% 3.69/1.23 % (3169653)Time elapsed: 0.003 s
% 3.69/1.23 % (3169653)Peak memory usage: 89 MB
% 3.69/1.23 % (3169653)Instructions burned: 7 (million)
% 3.69/1.23 % (3169655)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=129257222:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.69/1.23 % (3169652)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2485099675:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.69/1.23 % (3169649)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2078926441:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.69/1.23 % (3169650)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=383450052:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.69/1.23 % (3169656)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3657378693:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.69/1.23 % (3169651)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3890426896:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.69/1.23 % (3169652)First to succeed.
% 3.69/1.23 % (3169652)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3169562"
% 3.69/1.23 % (3169649)Instruction limit reached!
% 3.69/1.23 % (3169649)------------------------------
% 3.69/1.23 % (3169649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.23 % (3169649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.23 % (3169649)CaDiCaL version: 2.1.3
% 3.69/1.23 % (3169649)Termination reason: Instruction limit
% 3.69/1.23 % (3169649)Termination phase: Saturation
% 3.69/1.23 % (3169649)Time elapsed: 0.031 s
% 3.69/1.23 % (3169649)Peak memory usage: 114 MB
% 3.69/1.23 % (3169649)Instructions burned: 12 (million)
% 3.69/1.23 % (3169655)Also succeeded, but the first one will report.
% 3.69/1.23 % (3169650)Also succeeded, but the first one will report.
% 3.69/1.23 % (3169656)Also succeeded, but the first one will report.
% 3.69/1.23 % (3169679)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3906759528:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.69/1.23 % (3169679)Instruction limit reached!
% 3.69/1.23 % (3169679)------------------------------
% 3.69/1.23 % (3169679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.23 % (3169679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.23 % (3169679)CaDiCaL version: 2.1.3
% 3.69/1.23 % (3169679)Termination reason: Instruction limit
% 3.69/1.23 % (3169679)Termination phase: Saturation
% 3.69/1.23 % (3169679)Time elapsed: 0.006 s
% 3.69/1.23 % (3169679)Peak memory usage: 88 MB
% 3.69/1.23 % (3169679)Instructions burned: 17 (million)
% 3.69/1.23 % (3169651)Instruction limit reached!
% 3.69/1.23 % (3169651)------------------------------
% 3.69/1.23 % (3169651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.23 % (3169651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.23 % (3169651)CaDiCaL version: 2.1.3
% 3.69/1.23 % (3169651)Termination reason: Instruction limit
% 3.69/1.23 % (3169651)Termination phase: Saturation
% 3.69/1.23 % (3169651)Time elapsed: 0.154 s
% 3.69/1.23 % (3169651)Peak memory usage: 117 MB
% 3.69/1.23 % (3169651)Instructions burned: 206 (million)
% 3.69/1.23 % (3169700)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=4151910152:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.69/1.23 % (3169711)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1873838041:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.69/1.23 % (3169711)Instruction limit reached!
% 3.69/1.23 % (3169711)------------------------------
% 3.69/1.23 % (3169711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.23 % (3169711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.23 % (3169711)CaDiCaL version: 2.1.3
% 3.69/1.23 % (3169711)Termination reason: Instruction limit
% 3.69/1.23 % (3169711)Termination phase: Saturation
% 3.69/1.23 % (3169711)Time elapsed: 0.007 s
% 3.69/1.23 % (3169711)Peak memory usage: 90 MB
% 3.69/1.23 % (3169711)Instructions burned: 19 (million)
% 3.69/1.23 % (3169700)Instruction limit reached!
% 3.69/1.23 % (3169700)------------------------------
% 3.69/1.23 % (3169700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.23 % (3169700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.23 % (3169700)CaDiCaL version: 2.1.3
% 3.69/1.23 % (3169700)Termination reason: Instruction limit
% 3.69/1.23 % (3169700)Termination phase: Saturation
% 3.69/1.23 % (3169700)Time elapsed: 0.023 s
% 3.69/1.23 % (3169700)Peak memory usage: 89 MB
% 3.69/1.23 % (3169700)Instructions burned: 29 (million)
% 3.69/1.23 % (3169652)Refutation found. Thanks to Tanya!
% 3.69/1.23 % SZS status Theorem for theBenchmark
% 3.69/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.23 % (3169652)------------------------------
% 3.69/1.23 % (3169652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.23 % (3169652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.23 % (3169652)CaDiCaL version: 2.1.3
% 3.69/1.23 % (3169652)Termination reason: Refutation
% 3.69/1.23 % (3169652)Time elapsed: 0.005 s
% 3.69/1.23 % (3169652)Peak memory usage: 89 MB
% 3.69/1.23 % (3169652)Instructions burned: 5 (million)
% 3.69/1.23 % (3169652)------------------------------
% 3.69/1.23 % (3169652)------------------------------
% 3.69/1.23 % (3169562)Success in time 0.438 s
% 3.69/1.23 % Vampire exiting
%------------------------------------------------------------------------------