%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT088_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 : n008.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 0.17s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 58 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 101 ( 39 ~; 34 |; 21 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 76 ( 7 atm; 0 fun; 10 num; 59 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 : 14 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 108 ( 88 !; 20 ?; 108 :)
% 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_10,type,
sK0: ( $int * list ) > $int ).
tff(func_def_11,type,
sK1: ( $int * list ) > list ).
tff(func_def_12,type,
sK2: ( $int * list ) > $int ).
tff(func_def_13,type,
sK3: ( $int * list ) > list ).
tff(func_def_14,type,
sK4: ( $int * list ) > list ).
tff(func_def_15,type,
sK5: ( $int * list ) > $int ).
tff(pred_def_1,type,
in: ( $int * list ) > $o ).
tff(pred_def_2,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,
! [X1: list,X0: $int] :
( ( ? [X2: $int,X3: list] :
( ( X1 = cons(X2,X3) )
& in(X0,X3) )
| ? [X3: list,X2: $int] :
( ( X1 = cons(X2,X3) )
& ( X0 = X2 ) ) )
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_conv) ).
tff(f9,axiom,
! [X0: $int] : ( count(X0,nil) = 0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(f14,axiom,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> $greater(count(X0,X1),0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_8) ).
tff(f15,conjecture,
~ ! [X0: $int,X1: list] :
( ( X1 != nil )
=> ( count(X0,X1) = count(X0,tail(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X0: $int,X1: list] :
( ( X1 != nil )
=> ( count(X0,X1) = count(X0,tail(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f18,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
<=> in(X0,X1) ),
inference(theory_normalization,[],[f14]) ).
tff(f20,plain,
! [X1: $int,X0: list] :
( ( ? [X2: $int,X3: list] :
( in(X1,X3)
& ( cons(X2,X3) = X0 ) )
| ? [X4: list,X5: $int] :
( ( cons(X5,X4) = X0 )
& ( X1 = X5 ) ) )
<=> in(X1,X0) ),
inference(rectify,[],[f5]) ).
tff(f25,plain,
! [X0: $int,X1: list] :
( ( X1 != nil )
=> ( count(X0,X1) = count(X0,tail(X1)) ) ),
inference(flattening,[],[f16]) ).
tff(f26,plain,
! [X1: $int,X0: list] : ( nil != cons(X1,X0) ),
inference(rectify,[],[f4]) ).
tff(f27,plain,
! [X1: $int,X0: list] : ( tail(cons(X1,X0)) = X0 ),
inference(rectify,[],[f2]) ).
tff(f31,plain,
! [X1: list,X0: $int] :
( ( nil = X1 )
| ( count(X0,X1) = count(X0,tail(X1)) ) ),
inference(ennf_transformation,[],[f25]) ).
tff(f38,plain,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
inference(rectify,[],[f26]) ).
tff(f39,plain,
! [X0: list,X1: $int] :
( ( nil = X0 )
| ( count(X1,tail(X0)) = count(X1,X0) ) ),
inference(rectify,[],[f31]) ).
tff(f40,plain,
! [X1: $int,X0: list] :
( ( ? [X2: $int,X3: list] :
( in(X1,X3)
& ( cons(X2,X3) = X0 ) )
| ? [X4: list,X5: $int] :
( ( cons(X5,X4) = X0 )
& ( X1 = X5 ) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( ! [X2: $int,X3: list] :
( ~ in(X1,X3)
| ( cons(X2,X3) != X0 ) )
& ! [X4: list,X5: $int] :
( ( cons(X5,X4) != X0 )
| ( X1 != X5 ) ) ) ) ),
inference(nnf_transformation,[],[f20]) ).
tff(f41,plain,
! [X1: $int,X0: list] :
( ( ? [X2: $int,X3: list] :
( in(X1,X3)
& ( cons(X2,X3) = X0 ) )
| ? [X4: list,X5: $int] :
( ( cons(X5,X4) = X0 )
& ( X1 = X5 ) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( ! [X2: $int,X3: list] :
( ~ in(X1,X3)
| ( cons(X2,X3) != X0 ) )
& ! [X4: list,X5: $int] :
( ( cons(X5,X4) != X0 )
| ( X1 != X5 ) ) ) ) ),
inference(flattening,[],[f40]) ).
tff(f42,plain,
! [X0: $int,X1: list] :
( ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ? [X4: list,X5: $int] :
( ( cons(X5,X4) = X1 )
& ( X0 = X5 ) )
| ~ in(X0,X1) )
& ( in(X0,X1)
| ( ! [X6: $int,X7: list] :
( ~ in(X0,X7)
| ( cons(X6,X7) != X1 ) )
& ! [X8: list,X9: $int] :
( ( cons(X9,X8) != X1 )
| ( X0 != X9 ) ) ) ) ),
inference(rectify,[],[f41]) ).
tff(f43,plain,
! [X0: $int,X1: list] :
( ( ( in(X0,sK3(X0,X1))
& ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) )
| ( ( cons(sK5(X0,X1),sK4(X0,X1)) = X1 )
& ( sK5(X0,X1) = X0 ) )
| ~ in(X0,X1) )
& ( in(X0,X1)
| ( ! [X6: $int,X7: list] :
( ~ in(X0,X7)
| ( cons(X6,X7) != X1 ) )
& ! [X8: list,X9: $int] :
( ( cons(X9,X8) != X1 )
| ( X0 != X9 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X5,sK5(X0,X1))],[f42]) ).
tff(f44,plain,
! [X0: $int,X1: list] :
( ( $less(0,count(X0,X1))
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ $less(0,count(X0,X1)) ) ),
inference(nnf_transformation,[],[f18]) ).
tff(f45,plain,
! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
inference(rectify,[],[f27]) ).
tff(f57,plain,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
inference(cnf_transformation,[],[f38]) ).
tff(f59,plain,
! [X0: list,X1: $int] :
( ( count(X1,tail(X0)) = count(X1,X0) )
| ( nil = X0 ) ),
inference(cnf_transformation,[],[f39]) ).
tff(f60,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f62,plain,
! [X0: $int,X1: list,X8: list,X9: $int] :
( in(X0,X1)
| ( cons(X9,X8) != X1 )
| ( X0 != X9 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f69,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tff(f71,plain,
! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f45]) ).
tff(f76,plain,
! [X0: $int,X8: list,X9: $int] :
( in(X0,cons(X9,X8))
| ( X0 != X9 ) ),
inference(equality_resolution,[],[f62]) ).
tff(f77,plain,
! [X8: list,X9: $int] : in(X9,cons(X9,X8)),
inference(equality_resolution,[],[f76]) ).
tff(f84,plain,
! [X2: $int,X0: list,X1: $int] :
( ( count(X1,X0) = count(X1,cons(X2,X0)) )
| ( nil = cons(X2,X0) ) ),
inference(superposition,[],[f59,f71]) ).
tff(f85,plain,
! [X2: $int,X0: list,X1: $int] : ( count(X1,X0) = count(X1,cons(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f84,f57]) ).
tff(f92,plain,
! [X2: $int,X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,cons(X2,X1)) ),
inference(superposition,[],[f69,f85]) ).
tff(f105,plain,
! [X0: $int,X1: $int] :
( $less(0,0)
| ~ in(X0,cons(X1,nil)) ),
inference(superposition,[],[f92,f60]) ).
tff(f107,plain,
! [X0: $int,X1: $int] : ~ in(X0,cons(X1,nil)),
inference(evaluation,[],[f105]) ).
tff(f117,plain,
$false,
inference(resolution,[],[f107,f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT088_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n008.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 00:08:54 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running first-order theorem proving
% 0.11/0.21 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
% 0.17/1.31 % (2783864)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.17/1.31 % (2783990)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3115017040:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.17/1.31 % (2783990)Instruction limit reached!
% 0.17/1.31 % (2783990)------------------------------
% 0.17/1.31 % (2783990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.31 % (2783990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.31 % (2783990)CaDiCaL version: 2.1.3
% 0.17/1.31 % (2783990)Termination reason: Instruction limit
% 0.17/1.31 % (2783990)Termination phase: Saturation
% 0.17/1.31 % (2783990)Time elapsed: 0.003 s
% 0.17/1.31 % (2783990)Peak memory usage: 89 MB
% 0.17/1.31 % (2783990)Instructions burned: 7 (million)
% 0.17/1.31 % (2783988)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2703223114:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.17/1.31 % (2783991)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3903591396:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.17/1.31 % (2783989)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=141772122:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.17/1.31 % (2783987)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=236654751:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.17/1.31 % (2783986)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1107289671:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.17/1.31 % (2783989)Instruction limit reached!
% 0.17/1.31 % (2783989)------------------------------
% 0.17/1.31 % (2783989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.31 % (2783989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.31 % (2783989)CaDiCaL version: 2.1.3
% 0.17/1.31 % (2783989)Termination reason: Instruction limit
% 0.17/1.31 % (2783989)Termination phase: Saturation
% 0.17/1.31 % (2783989)Time elapsed: 0.005 s
% 0.17/1.31 % (2783989)Peak memory usage: 88 MB
% 0.17/1.31 % (2783989)Instructions burned: 7 (million)
% 0.17/1.31 % (2783992)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1843619675:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.17/1.31 % (2783986)Refutation not found, incomplete strategy
% 0.17/1.31 % (2783986)------------------------------
% 0.17/1.31 % (2783986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.31 % (2783986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.31 % (2783986)CaDiCaL version: 2.1.3
% 0.17/1.31 % (2783986)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.31 % (2783986)Time elapsed: 0.028 s
% 0.17/1.31 % (2783986)Peak memory usage: 112 MB
% 0.17/1.31 % (2783986)Instructions burned: 6 (million)
% 0.17/1.31 % (2783987)First to succeed.
% 0.17/1.31 % (2783987)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2783864"
% 0.17/1.31 % (2783991)Also succeeded, but the first one will report.
% 0.17/1.31 % (2783988)Also succeeded, but the first one will report.
% 0.17/1.31 % (2783992)Also succeeded, but the first one will report.
% 0.17/1.31 % (2783994)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=4094734521:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.17/1.31 % (2783994)Also succeeded, but the first one will report.
% 0.17/1.31 % (2784000)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=2922202555:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.17/1.31 % (2784000)Also succeeded, but the first one will report.
% 0.17/1.31 % (2783986)------------------------------
% 0.17/1.31 % (2783986)------------------------------
% 0.17/1.31 % (2783987)Refutation found. Thanks to Tanya!
% 0.17/1.31 % SZS status Theorem for theBenchmark
% 0.17/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.31 % (2783987)------------------------------
% 0.17/1.31 % (2783987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.31 % (2783987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.31 % (2783987)CaDiCaL version: 2.1.3
% 0.17/1.31 % (2783987)Termination reason: Refutation
% 0.17/1.31 % (2783987)Time elapsed: 0.032 s
% 0.17/1.31 % (2783987)Peak memory usage: 115 MB
% 0.17/1.31 % (2783987)Instructions burned: 10 (million)
% 0.17/1.31 % (2783987)------------------------------
% 0.17/1.31 % (2783987)------------------------------
% 0.17/1.31 % (2783864)Success in time 0.451 s
% 0.17/1.31 % Vampire exiting
%------------------------------------------------------------------------------