%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT093_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 : n002.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 2.80s 1.16s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 34 ( 0 atm; 18 fun; 14 num; 2 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 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 ) > list ).
tff(func_def_14,type,
sK3: ( list * $int ) > $int ).
tff(func_def_15,type,
sK4: ( $int * list ) > list ).
tff(func_def_16,type,
sK5: ( $int * list ) > $int ).
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(f12,axiom,
! [X0: list] : ( append(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6) ).
tff(f15,conjecture,
~ ! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f19,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f35,plain,
! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) ),
inference(flattening,[],[f16]) ).
tff(f60,plain,
! [X0: list] : ( append(nil,X0) = X0 ),
inference(cnf_transformation,[],[f12]) ).
tff(f61,plain,
0 = length(nil),
inference(cnf_transformation,[],[f7]) ).
tff(f65,plain,
! [X0: list,X1: list] : ( length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1) ),
inference(cnf_transformation,[],[f35]) ).
tff(f92,plain,
! [X0: list] : ( length(X0) = $sum($sum(length(nil),length(X0)),1) ),
inference(superposition,[],[f65,f60]) ).
tff(f94,plain,
! [X0: list] : ( length(X0) = $sum(1,$sum(length(nil),length(X0))) ),
inference(forward_demodulation,[],[f92,f19]) ).
tff(f95,plain,
! [X0: list] : ( length(X0) = $sum(1,$sum(0,length(X0))) ),
inference(forward_demodulation,[],[f94,f61]) ).
tff(f96,plain,
! [X0: list] : ( length(X0) = $sum(1,length(X0)) ),
inference(evaluation,[],[f95]) ).
tff(f123,plain,
0 = $sum(1,0),
inference(superposition,[],[f96,f61]) ).
tff(f125,plain,
$false,
inference(evaluation,[],[f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT093_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 : n002.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 00:10:52 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 2.80/1.16 % (912575)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.80/1.16 % (912583)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2967798796:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.80/1.16 % (912583)First to succeed.
% 2.80/1.16 % (912583)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-912575"
% 2.80/1.16 % (912585)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=865857364:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.80/1.16 % (912580)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=995711575:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.80/1.16 % (912584)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=498229471:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.80/1.16 % (912581)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2471081546:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.80/1.16 % (912586)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2341380889:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.80/1.16 % (912582)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3390256960:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.80/1.16 % (912584)Instruction limit reached!
% 2.80/1.16 % (912584)------------------------------
% 2.80/1.16 % (912584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (912584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (912584)CaDiCaL version: 2.1.3
% 2.80/1.16 % (912584)Termination reason: Instruction limit
% 2.80/1.16 % (912584)Termination phase: Saturation
% 2.80/1.16 % (912584)Time elapsed: 0.004 s
% 2.80/1.16 % (912584)Peak memory usage: 88 MB
% 2.80/1.16 % (912584)Instructions burned: 5 (million)
% 2.80/1.16 % (912582)Also succeeded, but the first one will report.
% 2.80/1.16 % (912580)Instruction limit reached!
% 2.80/1.16 % (912580)------------------------------
% 2.80/1.16 % (912580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (912580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (912580)CaDiCaL version: 2.1.3
% 2.80/1.16 % (912580)Termination reason: Instruction limit
% 2.80/1.16 % (912580)Termination phase: Saturation
% 2.80/1.16 % (912580)Time elapsed: 0.032 s
% 2.80/1.16 % (912580)Peak memory usage: 114 MB
% 2.80/1.16 % (912580)Instructions burned: 13 (million)
% 2.80/1.16 % (912581)Also succeeded, but the first one will report.
% 2.80/1.16 % (912585)Also succeeded, but the first one will report.
% 2.80/1.16 % (912586)Also succeeded, but the first one will report.
% 2.80/1.16 % (912583)Refutation found. Thanks to Tanya!
% 2.80/1.16 % SZS status Theorem for theBenchmark
% 2.80/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.16 % (912583)------------------------------
% 2.80/1.16 % (912583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (912583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (912583)CaDiCaL version: 2.1.3
% 2.80/1.16 % (912583)Termination reason: Refutation
% 2.80/1.16 % (912583)Time elapsed: 0.003 s
% 2.80/1.16 % (912583)Peak memory usage: 89 MB
% 2.80/1.16 % (912583)Instructions burned: 4 (million)
% 2.80/1.16 % (912583)------------------------------
% 2.80/1.16 % (912583)------------------------------
% 2.80/1.16 % (912575)Success in time 0.31 s
% 2.80/1.16 % Vampire exiting
%------------------------------------------------------------------------------