%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT084_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 : n018.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 3.00s 1.19s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 4 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 37 ( 6 atm; 9 fun; 12 num; 10 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 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 13 !; 3 ?; 16 :)
% 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: ( $int * list ) > list ).
tff(func_def_16,type,
sK5: ( $int * list ) > $int ).
tff(func_def_17,type,
sK6: list ).
tff(pred_def_1,type,
in: ( $int * list ) > $o ).
tff(pred_def_2,type,
inRange: ( $int * list ) > $o ).
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(f15,conjecture,
~ ? [X0: list] : ( length(X0) = length(cons(1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ? [X0: list] : ( length(X0) = length(cons(1,X0)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f19,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f24,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f31,plain,
? [X0: list] : ( length(X0) = length(cons(1,X0)) ),
inference(flattening,[],[f16]) ).
tff(f46,plain,
! [X0: list,X1: $int] : ( $sum(1,length(X0)) = length(cons(X1,X0)) ),
inference(rectify,[],[f8]) ).
tff(f54,plain,
length(sK6) = length(cons(1,sK6)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f31]) ).
tff(f66,plain,
! [X0: list,X1: $int] : ( $sum(1,length(X0)) = length(cons(X1,X0)) ),
inference(cnf_transformation,[],[f46]) ).
tff(f79,plain,
length(sK6) = length(cons(1,sK6)),
inference(cnf_transformation,[],[f54]) ).
tff(f395,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f28,f24]) ).
tff(f509,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f395,f19]) ).
tff(f782,plain,
$sum(1,length(sK6)) = length(sK6),
inference(superposition,[],[f66,f79]) ).
tff(f841,plain,
$less(length(sK6),length(sK6)),
inference(superposition,[],[f509,f782]) ).
tff(f886,plain,
$false,
inference(forward_subsumption_resolution,[],[f841,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT084_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 00:10:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.00/1.19 % (3914062)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.00/1.19 % (3914069)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2857132613:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.00/1.19 % (3914069)First to succeed.
% 3.00/1.19 % (3914069)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3914062"
% 3.00/1.19 % (3914072)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1544024923:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.00/1.19 % (3914068)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1117727001:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.00/1.19 % (3914071)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=758985346:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.00/1.19 % (3914073)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4257035948:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.00/1.19 % (3914070)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2044410523:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.00/1.19 % (3914067)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4254674204:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.00/1.19 % (3914071)Instruction limit reached!
% 3.00/1.19 % (3914071)------------------------------
% 3.00/1.19 % (3914071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.19 % (3914071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.19 % (3914071)CaDiCaL version: 2.1.3
% 3.00/1.19 % (3914071)Termination reason: Instruction limit
% 3.00/1.19 % (3914071)Termination phase: Saturation
% 3.00/1.19 % (3914071)Time elapsed: 0.004 s
% 3.00/1.19 % (3914071)Peak memory usage: 88 MB
% 3.00/1.19 % (3914071)Instructions burned: 5 (million)
% 3.00/1.19 % (3914070)Instruction limit reached!
% 3.00/1.19 % (3914070)------------------------------
% 3.00/1.19 % (3914070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.19 % (3914070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.19 % (3914070)CaDiCaL version: 2.1.3
% 3.00/1.19 % (3914070)Termination reason: Instruction limit
% 3.00/1.19 % (3914070)Termination phase: Saturation
% 3.00/1.19 % (3914070)Time elapsed: 0.006 s
% 3.00/1.19 % (3914070)Peak memory usage: 88 MB
% 3.00/1.19 % (3914070)Instructions burned: 7 (million)
% 3.00/1.19 % (3914067)Instruction limit reached!
% 3.00/1.19 % (3914067)------------------------------
% 3.00/1.19 % (3914067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.19 % (3914067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.19 % (3914067)CaDiCaL version: 2.1.3
% 3.00/1.19 % (3914067)Termination reason: Instruction limit
% 3.00/1.19 % (3914067)Termination phase: Saturation
% 3.00/1.19 % (3914067)Time elapsed: 0.031 s
% 3.00/1.19 % (3914067)Peak memory usage: 115 MB
% 3.00/1.19 % (3914067)Instructions burned: 12 (million)
% 3.00/1.19 % (3914072)Also succeeded, but the first one will report.
% 3.00/1.19 % (3914068)Also succeeded, but the first one will report.
% 3.00/1.19 % (3914073)Also succeeded, but the first one will report.
% 3.00/1.19 % (3914069)Refutation found. Thanks to Tanya!
% 3.00/1.19 % SZS status Theorem for theBenchmark
% 3.00/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.00/1.19 % (3914069)------------------------------
% 3.00/1.19 % (3914069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.19 % (3914069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.19 % (3914069)CaDiCaL version: 2.1.3
% 3.00/1.19 % (3914069)Termination reason: Refutation
% 3.00/1.19 % (3914069)Time elapsed: 0.030 s
% 3.00/1.19 % (3914069)Peak memory usage: 113 MB
% 3.00/1.19 % (3914069)Instructions burned: 36 (million)
% 3.00/1.19 % (3914069)------------------------------
% 3.00/1.19 % (3914069)------------------------------
% 3.00/1.19 % (3914062)Success in time 0.339 s
% 3.00/1.19 % Vampire exiting
%------------------------------------------------------------------------------