%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI189_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:32:39 AM UTC 2026
% Result : Theorem 3.71s 1.28s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 28 ( 0 atm; 5 fun; 15 num; 8 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 0 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_3,type,
2: $int > $int ).
tff(func_def_7,type,
-1: $int > $int ).
tff(func_def_9,type,
10: $int > $int ).
tff(func_def_10,type,
-2: $int > $int ).
tff(pred_def_1,type,
p: $int > $o ).
tff(f1,conjecture,
( ! [X0: $int] : p($product(2,X0))
=> p(10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : p($product(2,X0))
=> p(10) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
( ! [X0: $int] : p($product(2,X0))
& ~ p(10) ),
inference(ennf_transformation,[],[f2]) ).
tff(f4,plain,
~ p(10),
inference(cnf_transformation,[],[f3]) ).
tff(f5,plain,
! [X0: $int] : p($product(2,X0)),
inference(cnf_transformation,[],[f3]) ).
tff(f6,plain,
! [X0: $int] : p(2(X0)),
inference(alasca_normalization,[],[f5]) ).
tff(f7,plain,
! [X0: $int] : ( 2(X0) != 10(1) ),
inference(constrained_resolution,[],[f6,f4]) ).
tff(f8,plain,
! [X0: $int] : ( 0 != $sum(X0,-5) ),
inference(alasca_normalization,[],[f7]) ).
tff(f9,plain,
! [X0: $int] : ( 0 != X0 ),
inference(arithmetic_subterm_generalization,[],[f8]) ).
tff(f10,plain,
$false,
inference(equality_resolution,[],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI189_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 20:44:00 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.71/1.28 % (3439655)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.71/1.28 % (3439684)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1342003136:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.71/1.28 % (3439686)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4259071886:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.71/1.28 % (3439683)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2754527091:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.71/1.28 % (3439682)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3441911629:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.71/1.28 % (3439685)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3315914505:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.71/1.28 % (3439688)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=735272225:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.71/1.28 % (3439687)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2396617976:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.71/1.28 % (3439686)Instruction limit reached!
% 3.71/1.28 % (3439686)------------------------------
% 3.71/1.28 % (3439686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439686)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439686)Termination reason: Instruction limit
% 3.71/1.28 % (3439686)Termination phase: Saturation
% 3.71/1.28 % (3439686)Time elapsed: 0.004 s
% 3.71/1.28 % (3439686)Peak memory usage: 89 MB
% 3.71/1.28 % (3439686)Instructions burned: 5 (million)
% 3.71/1.28 % (3439685)Instruction limit reached!
% 3.71/1.28 % (3439685)------------------------------
% 3.71/1.28 % (3439685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439685)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439685)Termination reason: Instruction limit
% 3.71/1.28 % (3439685)Termination phase: Saturation
% 3.71/1.28 % (3439685)Time elapsed: 0.005 s
% 3.71/1.28 % (3439685)Peak memory usage: 88 MB
% 3.71/1.28 % (3439685)Instructions burned: 7 (million)
% 3.71/1.28 % (3439683)Refutation not found, incomplete strategy
% 3.71/1.28 % (3439683)------------------------------
% 3.71/1.28 % (3439683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439683)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439683)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.28 % (3439683)Time elapsed: 0.028 s
% 3.71/1.28 % (3439683)Peak memory usage: 114 MB
% 3.71/1.28 % (3439683)Instructions burned: 5 (million)
% 3.71/1.28 % (3439687)Refutation not found, incomplete strategy
% 3.71/1.28 % (3439687)------------------------------
% 3.71/1.28 % (3439687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439687)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439687)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.28 % (3439687)Time elapsed: 0.028 s
% 3.71/1.28 % (3439687)Peak memory usage: 114 MB
% 3.71/1.28 % (3439687)Instructions burned: 6 (million)
% 3.71/1.28 % (3439682)Refutation not found, incomplete strategy
% 3.71/1.28 % (3439682)------------------------------
% 3.71/1.28 % (3439682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439682)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439682)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.28 % (3439682)Time elapsed: 0.029 s
% 3.71/1.28 % (3439682)Peak memory usage: 115 MB
% 3.71/1.28 % (3439682)Instructions burned: 6 (million)
% 3.71/1.28 % (3439684)Instruction limit reached!
% 3.71/1.28 % (3439684)------------------------------
% 3.71/1.28 % (3439684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439684)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439684)Termination reason: Instruction limit
% 3.71/1.28 % (3439684)Termination phase: Saturation
% 3.71/1.28 % (3439684)Time elapsed: 0.084 s
% 3.71/1.28 % (3439684)Peak memory usage: 114 MB
% 3.71/1.28 % (3439684)Instructions burned: 201 (million)
% 3.71/1.28 % (3439688)Instruction limit reached!
% 3.71/1.28 % (3439688)------------------------------
% 3.71/1.28 % (3439688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439688)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439688)Termination reason: Instruction limit
% 3.71/1.28 % (3439688)Termination phase: Saturation
% 3.71/1.28 % (3439688)Time elapsed: 0.044 s
% 3.71/1.28 % (3439688)Peak memory usage: 115 MB
% 3.71/1.28 % (3439688)Instructions burned: 34 (million)
% 3.71/1.28 % (3439698)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=4248358133:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.71/1.28 % (3439698)First to succeed.
% 3.71/1.28 % (3439698)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3439655"
% 3.71/1.28 % (3439696)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1031244214:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.71/1.28 % (3439697)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=3221723754:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.71/1.28 % (3439696)Refutation not found, incomplete strategy
% 3.71/1.28 % (3439696)------------------------------
% 3.71/1.28 % (3439696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439696)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439696)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.28 % (3439696)Time elapsed: 0.001 s
% 3.71/1.28 % (3439696)Peak memory usage: 88 MB
% 3.71/1.28 % (3439697)Instruction limit reached!
% 3.71/1.28 % (3439697)------------------------------
% 3.71/1.28 % (3439697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439697)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439697)Termination reason: Instruction limit
% 3.71/1.28 % (3439697)Termination phase: Saturation
% 3.71/1.28 % (3439697)Time elapsed: 0.016 s
% 3.71/1.28 % (3439697)Peak memory usage: 88 MB
% 3.71/1.28 % (3439697)Instructions burned: 30 (million)
% 3.71/1.28 % (3439699)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=83186576:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.71/1.28 % (3439699)Instruction limit reached!
% 3.71/1.28 % (3439699)------------------------------
% 3.71/1.28 % (3439699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439699)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439699)Termination reason: Instruction limit
% 3.71/1.28 % (3439699)Termination phase: Saturation
% 3.71/1.28 % (3439699)Time elapsed: 0.016 s
% 3.71/1.28 % (3439699)Peak memory usage: 89 MB
% 3.71/1.28 % (3439699)Instructions burned: 25 (million)
% 3.71/1.28 % (3439682)------------------------------
% 3.71/1.28 % (3439682)------------------------------
% 3.71/1.28 % (3439687)------------------------------
% 3.71/1.28 % (3439687)------------------------------
% 3.71/1.28 % (3439683)------------------------------
% 3.71/1.28 % (3439683)------------------------------
% 3.71/1.28 % (3439703)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=1954106887:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 3.71/1.28 % (3439703)Refutation not found, incomplete strategy
% 3.71/1.28 % (3439703)------------------------------
% 3.71/1.28 % (3439703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439703)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439703)Termination reason: Refutation not found, incomplete strategy
% 3.71/1.28 % (3439703)Time elapsed: 0.001 s
% 3.71/1.28 % (3439703)Peak memory usage: 88 MB
% 3.71/1.28 % (3439698)Refutation found. Thanks to Tanya!
% 3.71/1.28 % SZS status Theorem for theBenchmark
% 3.71/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.28 % (3439698)------------------------------
% 3.71/1.28 % (3439698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.28 % (3439698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.28 % (3439698)CaDiCaL version: 2.1.3
% 3.71/1.28 % (3439698)Termination reason: Refutation
% 3.71/1.28 % (3439698)Time elapsed: 0.001 s
% 3.71/1.28 % (3439698)Peak memory usage: 90 MB
% 3.71/1.28 % (3439698)Instructions burned: 1 (million)
% 3.71/1.28 % (3439698)------------------------------
% 3.71/1.28 % (3439698)------------------------------
% 3.71/1.28 % (3439655)Success in time 0.444 s
% 3.71/1.28 % Vampire exiting
%------------------------------------------------------------------------------