%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE144+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 11:40:27 AM UTC 2026
% Result : Theorem 14.50s 3.12s
% Output : Refutation 15.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 104 ( 75 unt; 0 def)
% Number of atoms : 135 ( 90 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 31 ~; 27 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 168 ( 167 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f11,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).
fof(f12,axiom,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold2) ).
fof(f13,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X2),X1),X2)
=> leq(multiplication(star(X0),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction1) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f17,axiom,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isolation) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f19,conjecture,
! [X0] : strong_iteration(star(X0)) = strong_iteration(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] : strong_iteration(star(X0)) = strong_iteration(one),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] : strong_iteration(star(X0)) != strong_iteration(one),
inference(ennf_transformation,[],[f20]) ).
fof(f23,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X1),X2)
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f25,plain,
strong_iteration(one) != strong_iteration(star(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f27,plain,
strong_iteration(one) != strong_iteration(star(sK0)),
inference(cnf_transformation,[],[f25]) ).
fof(f28,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f31,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X2),X1),X2)
| leq(multiplication(star(X0),X1),X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f37,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f38,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f39,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f42,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f45,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[],[f28,f39]) ).
fof(f53,plain,
! [X0,X1] : addition(star(X0),X1) = addition(one,addition(multiplication(X0,star(X0)),X1)),
inference(superposition,[],[f38,f30]) ).
fof(f54,plain,
! [X0,X1] : addition(strong_iteration(X0),X1) = addition(one,addition(multiplication(X0,strong_iteration(X0)),X1)),
inference(superposition,[],[f38,f47]) ).
fof(f61,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f39,f38]) ).
fof(f69,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),
inference(superposition,[],[f30,f42]) ).
fof(f94,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f40,f31]) ).
fof(f110,plain,
! [X2,X0,X1] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(superposition,[],[f94,f42]) ).
fof(f121,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f41,f32]) ).
fof(f132,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f38,f41]) ).
fof(f151,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f38,f37]) ).
fof(f166,plain,
! [X0] : strong_iteration(X0) = addition(one,strong_iteration(X0)),
inference(superposition,[],[f151,f47]) ).
fof(f188,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(superposition,[],[f36,f31]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(X0,multiplication(X1,X2)))
| leq(X2,multiplication(strong_iteration(X1),X0)) ),
inference(superposition,[],[f36,f39]) ).
fof(f257,plain,
! [X0] : addition(one,multiplication(X0,star(X0))) = addition(star(X0),multiplication(X0,star(X0))),
inference(superposition,[],[f53,f37]) ).
fof(f274,plain,
! [X0] : addition(one,multiplication(X0,star(X0))) = multiplication(addition(one,X0),star(X0)),
inference(forward_demodulation,[],[f257,f94]) ).
fof(f278,plain,
! [X0] : star(X0) = multiplication(addition(one,X0),star(X0)),
inference(forward_demodulation,[],[f274,f30]) ).
fof(f310,plain,
! [X0] : addition(one,multiplication(X0,strong_iteration(X0))) = addition(strong_iteration(X0),multiplication(X0,strong_iteration(X0))),
inference(superposition,[],[f54,f37]) ).
fof(f327,plain,
! [X0] : addition(one,multiplication(X0,strong_iteration(X0))) = multiplication(addition(one,X0),strong_iteration(X0)),
inference(forward_demodulation,[],[f310,f94]) ).
fof(f331,plain,
! [X0] : strong_iteration(X0) = multiplication(addition(one,X0),strong_iteration(X0)),
inference(forward_demodulation,[],[f327,f47]) ).
fof(f480,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(superposition,[],[f35,f37]) ).
fof(f597,plain,
! [X0] : multiplication(addition(one,X0),addition(one,strong_iteration(X0))) = addition(addition(one,X0),strong_iteration(X0)),
inference(superposition,[],[f121,f331]) ).
fof(f601,plain,
! [X0] : multiplication(addition(one,X0),addition(one,strong_iteration(X0))) = addition(strong_iteration(X0),addition(one,X0)),
inference(forward_demodulation,[],[f597,f39]) ).
fof(f610,plain,
! [X0] : multiplication(addition(one,X0),addition(one,strong_iteration(X0))) = addition(X0,addition(strong_iteration(X0),one)),
inference(forward_demodulation,[],[f601,f61]) ).
fof(f617,plain,
! [X0] : multiplication(addition(one,X0),addition(one,strong_iteration(X0))) = addition(X0,addition(one,strong_iteration(X0))),
inference(forward_demodulation,[],[f610,f39]) ).
fof(f620,plain,
! [X0] : multiplication(addition(one,X0),strong_iteration(X0)) = addition(X0,strong_iteration(X0)),
inference(forward_demodulation,[],[f617,f166]) ).
fof(f621,plain,
! [X0] : strong_iteration(X0) = addition(X0,strong_iteration(X0)),
inference(forward_demodulation,[],[f620,f331]) ).
fof(f845,plain,
! [X0,X1] :
( leq(X0,multiplication(strong_iteration(one),X1))
| addition(X0,X1) != addition(X0,addition(X0,X1)) ),
inference(resolution,[],[f188,f46]) ).
fof(f885,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
inference(forward_subsumption_resolution,[],[f845,f151]) ).
fof(f886,plain,
! [X0,X1] : multiplication(strong_iteration(one),X1) = addition(X0,multiplication(strong_iteration(one),X1)),
inference(resolution,[],[f885,f45]) ).
fof(f888,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(superposition,[],[f885,f32]) ).
fof(f1215,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,addition(X3,X2)),multiplication(X1,X2)) = addition(multiplication(X0,X3),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f132,f40]) ).
fof(f1739,plain,
! [X0] : star(strong_iteration(X0)) = multiplication(strong_iteration(X0),star(strong_iteration(X0))),
inference(superposition,[],[f278,f166]) ).
fof(f2382,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| addition(multiplication(star(X0),multiplication(X0,X1)),X1) = X1 ),
inference(resolution,[],[f480,f45]) ).
fof(f2392,plain,
! [X0,X1] :
( addition(X1,multiplication(star(X0),multiplication(X0,X1))) = X1
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[],[f2382,f39]) ).
fof(f2394,plain,
! [X0,X1] :
( multiplication(addition(one,multiplication(star(X0),X0)),X1) = X1
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[],[f2392,f110]) ).
fof(f2395,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| multiplication(star(X0),X1) = X1 ),
inference(forward_demodulation,[],[f2394,f29]) ).
fof(f2396,plain,
! [X0,X1] :
( multiplication(star(X0),X1) = X1
| addition(multiplication(X0,X1),X1) != X1 ),
inference(resolution,[],[f2395,f46]) ).
fof(f2410,plain,
! [X0,X1] :
( addition(X1,multiplication(X0,X1)) != X1
| multiplication(star(X0),X1) = X1 ),
inference(forward_demodulation,[],[f2396,f39]) ).
fof(f2412,plain,
! [X0,X1] :
( multiplication(addition(one,X0),X1) != X1
| multiplication(star(X0),X1) = X1 ),
inference(forward_demodulation,[],[f2410,f94]) ).
fof(f2414,plain,
! [X0] :
( multiplication(one,X0) != X0
| multiplication(star(one),X0) = X0 ),
inference(superposition,[],[f2412,f37]) ).
fof(f2466,plain,
! [X0] : multiplication(star(one),X0) = X0,
inference(forward_subsumption_resolution,[],[f2414,f31]) ).
fof(f2500,plain,
one = star(one),
inference(superposition,[],[f32,f2466]) ).
fof(f2550,plain,
strong_iteration(one) = addition(one,multiplication(strong_iteration(one),zero)),
inference(superposition,[],[f33,f2500]) ).
fof(f2579,plain,
strong_iteration(one) = multiplication(strong_iteration(one),zero),
inference(forward_demodulation,[],[f2550,f886]) ).
fof(f2699,plain,
! [X0] : strong_iteration(one) = addition(X0,strong_iteration(one)),
inference(resolution,[],[f888,f45]) ).
fof(f2701,plain,
! [X0] : strong_iteration(one) = multiplication(star(X0),strong_iteration(one)),
inference(resolution,[],[f888,f2395]) ).
fof(f2707,plain,
addition(one,strong_iteration(one)) = star(strong_iteration(one)),
inference(superposition,[],[f29,f2701]) ).
fof(f2738,plain,
strong_iteration(one) = star(strong_iteration(one)),
inference(forward_demodulation,[],[f2707,f621]) ).
fof(f2771,plain,
! [X0] : strong_iteration(one) = addition(strong_iteration(one),X0),
inference(superposition,[],[f39,f2699]) ).
fof(f2847,plain,
! [X2,X0,X1] : addition(multiplication(strong_iteration(one),addition(X0,X1)),multiplication(X2,X1)) = addition(multiplication(strong_iteration(one),X0),multiplication(strong_iteration(one),X1)),
inference(superposition,[],[f1215,f2771]) ).
fof(f2871,plain,
! [X2,X0,X1] : multiplication(strong_iteration(one),X1) = addition(multiplication(strong_iteration(one),addition(X0,X1)),multiplication(X2,X1)),
inference(forward_demodulation,[],[f2847,f886]) ).
fof(f3185,plain,
! [X0,X1] : addition(multiplication(strong_iteration(one),addition(zero,X0)),multiplication(X1,X0)) = addition(strong_iteration(one),multiplication(addition(strong_iteration(one),X1),X0)),
inference(superposition,[],[f1215,f2579]) ).
fof(f3188,plain,
! [X0,X1] : strong_iteration(one) = addition(multiplication(strong_iteration(one),addition(zero,X0)),multiplication(X1,X0)),
inference(forward_demodulation,[],[f3185,f2771]) ).
fof(f3207,plain,
! [X0] : strong_iteration(one) = multiplication(strong_iteration(one),X0),
inference(forward_demodulation,[],[f3188,f2871]) ).
fof(f3265,plain,
! [X0] :
( ~ leq(strong_iteration(one),X0)
| multiplication(star(strong_iteration(one)),X0) = X0 ),
inference(superposition,[],[f2395,f3207]) ).
fof(f3286,plain,
! [X0] :
( multiplication(strong_iteration(one),X0) = X0
| ~ leq(strong_iteration(one),X0) ),
inference(forward_demodulation,[],[f3265,f2738]) ).
fof(f3310,plain,
! [X0] :
( ~ leq(strong_iteration(one),X0)
| strong_iteration(one) = X0 ),
inference(forward_demodulation,[],[f3286,f3207]) ).
fof(f6061,plain,
! [X0,X1] :
( ~ leq(multiplication(X1,star(multiplication(X0,X1))),star(multiplication(X0,X1)))
| leq(multiplication(X1,star(multiplication(X0,X1))),multiplication(strong_iteration(X0),one)) ),
inference(superposition,[],[f193,f69]) ).
fof(f6098,plain,
! [X0,X1] :
( ~ leq(multiplication(X1,star(multiplication(X0,X1))),star(multiplication(X0,X1)))
| leq(multiplication(X1,star(multiplication(X0,X1))),strong_iteration(X0)) ),
inference(forward_demodulation,[],[f6061,f32]) ).
fof(f6213,plain,
! [X0] :
( ~ leq(multiplication(strong_iteration(one),star(strong_iteration(one))),star(strong_iteration(one)))
| leq(multiplication(strong_iteration(one),star(strong_iteration(one))),strong_iteration(star(X0))) ),
inference(superposition,[],[f6098,f2701]) ).
fof(f6226,plain,
! [X0] :
( ~ leq(multiplication(strong_iteration(one),strong_iteration(one)),strong_iteration(one))
| leq(multiplication(strong_iteration(one),star(strong_iteration(one))),strong_iteration(star(X0))) ),
inference(forward_demodulation,[],[f6213,f2738]) ).
fof(f6251,plain,
! [X0] : leq(multiplication(strong_iteration(one),star(strong_iteration(one))),strong_iteration(star(X0))),
inference(forward_subsumption_resolution,[],[f6226,f888]) ).
fof(f6274,plain,
! [X0] : leq(star(strong_iteration(one)),strong_iteration(star(X0))),
inference(forward_demodulation,[],[f6251,f1739]) ).
fof(f6281,plain,
! [X0] : leq(strong_iteration(one),strong_iteration(star(X0))),
inference(forward_demodulation,[],[f6274,f2738]) ).
fof(f6288,plain,
$false,
inference(unit_resulting_resolution,[],[f3310,f27,f6281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE144+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.40 % Computer : n020.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sun Sep 27 13:13:19 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 14.50/3.12 % (3371770)Detected formulas, will run a generic FOF schedule.
% 14.50/3.12 % (3371776)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1234772519:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 14.50/3.12 % (3371781)dis-21_1_sil=8000:lcm=predicate:random_seed=3690215271:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 14.50/3.12 % (3371781)Refutation not found, incomplete strategy
% 14.50/3.12 % (3371781)------------------------------
% 14.50/3.12 % (3371781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371781)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371781)Termination reason: Refutation not found, incomplete strategy
% 14.50/3.12 % (3371781)Time elapsed: 0.002 s
% 14.50/3.12 % (3371781)Peak memory usage: 88 MB
% 14.50/3.12 % (3371781)Instructions burned: 1 (million)
% 14.50/3.12 % (3371775)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3230983850:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 14.50/3.12 % (3371779)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2145339962:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 14.50/3.12 % (3371778)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3939904663:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 14.50/3.12 % (3371780)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1340508074:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 14.50/3.12 % (3371777)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3516109252:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 14.50/3.12 % (3371778)Refutation not found, incomplete strategy
% 14.50/3.12 % (3371778)------------------------------
% 14.50/3.12 % (3371778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371778)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371778)Termination reason: Refutation not found, incomplete strategy
% 14.50/3.12 % (3371778)Time elapsed: 0.002 s
% 14.50/3.12 % (3371778)Peak memory usage: 88 MB
% 14.50/3.12 % (3371779)Instruction limit reached!
% 14.50/3.12 % (3371779)------------------------------
% 14.50/3.12 % (3371779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371779)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371779)Termination reason: Instruction limit
% 14.50/3.12 % (3371779)Termination phase: Saturation
% 14.50/3.12 % (3371779)Time elapsed: 0.114 s
% 14.50/3.12 % (3371779)Peak memory usage: 89 MB
% 14.50/3.12 % (3371779)Instructions burned: 120 (million)
% 14.50/3.12 % (3371780)Instruction limit reached!
% 14.50/3.12 % (3371780)------------------------------
% 14.50/3.12 % (3371780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371780)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371780)Termination reason: Instruction limit
% 14.50/3.12 % (3371780)Termination phase: Saturation
% 14.50/3.12 % (3371780)Time elapsed: 0.130 s
% 14.50/3.12 % (3371780)Peak memory usage: 89 MB
% 14.50/3.12 % (3371780)Instructions burned: 140 (million)
% 14.50/3.12 % (3371781)------------------------------
% 14.50/3.12 % (3371781)------------------------------
% 14.50/3.12 % (3371778)------------------------------
% 14.50/3.12 % (3371778)------------------------------
% 14.50/3.12 % (3371791)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1158441297:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 14.50/3.12 % (3371790)lrs+10_1_sil=8000:sp=occurrence:random_seed=2993023749:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 14.50/3.12 % (3371792)lrs+1011_1_sil=32000:sp=occurrence:random_seed=771266481:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 14.50/3.12 % (3371791)Refutation not found, incomplete strategy
% 14.50/3.12 % (3371791)------------------------------
% 14.50/3.12 % (3371791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371791)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371791)Termination reason: Refutation not found, incomplete strategy
% 14.50/3.12 % (3371791)Time elapsed: 0.007 s
% 14.50/3.12 % (3371791)Peak memory usage: 88 MB
% 14.50/3.12 % (3371791)Instructions burned: 4 (million)
% 14.50/3.12 % (3371793)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3922386365:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 14.50/3.12 % (3371790)Instruction limit reached!
% 14.50/3.12 % (3371790)------------------------------
% 14.50/3.12 % (3371790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371790)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371790)Termination reason: Instruction limit
% 14.50/3.12 % (3371790)Termination phase: Saturation
% 14.50/3.12 % (3371790)Time elapsed: 0.287 s
% 14.50/3.12 % (3371790)Peak memory usage: 91 MB
% 14.50/3.12 % (3371790)Instructions burned: 285 (million)
% 14.50/3.12 % (3371792)Instruction limit reached!
% 14.50/3.12 % (3371792)------------------------------
% 14.50/3.12 % (3371792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371792)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371792)Termination reason: Instruction limit
% 14.50/3.12 % (3371792)Termination phase: Saturation
% 14.50/3.12 % (3371792)Time elapsed: 0.329 s
% 14.50/3.12 % (3371792)Peak memory usage: 91 MB
% 14.50/3.12 % (3371792)Instructions burned: 325 (million)
% 14.50/3.12 % (3371793)Instruction limit reached!
% 14.50/3.12 % (3371793)------------------------------
% 14.50/3.12 % (3371793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371793)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371793)Termination reason: Instruction limit
% 14.50/3.12 % (3371793)Termination phase: Saturation
% 14.50/3.12 % (3371793)Time elapsed: 0.130 s
% 14.50/3.12 % (3371793)Peak memory usage: 91 MB
% 14.50/3.12 % (3371793)Instructions burned: 250 (million)
% 14.50/3.12 % (3371791)------------------------------
% 14.50/3.12 % (3371791)------------------------------
% 14.50/3.12 % (3371798)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2680514594:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2990 on theBenchmark for (2990ds/294Mi)
% 14.50/3.12 % (3371798)Refutation not found, incomplete strategy
% 14.50/3.12 % (3371798)------------------------------
% 14.50/3.12 % (3371798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371798)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371798)Termination reason: Refutation not found, incomplete strategy
% 14.50/3.12 % (3371798)Time elapsed: 0.003 s
% 14.50/3.12 % (3371798)Peak memory usage: 88 MB
% 14.50/3.12 % (3371798)Instructions burned: 1 (million)
% 14.50/3.12 % (3371800)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4267890912:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 14.50/3.12 % (3371800)Refutation not found, incomplete strategy
% 14.50/3.12 % (3371800)------------------------------
% 14.50/3.12 % (3371800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371800)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371800)Termination reason: Refutation not found, incomplete strategy
% 14.50/3.12 % (3371800)Time elapsed: 0.002 s
% 14.50/3.12 % (3371800)Peak memory usage: 88 MB
% 14.50/3.12 % (3371800)Instructions burned: 1 (million)
% 14.50/3.12 % (3371777)Refutation not found, incomplete strategy
% 14.50/3.12 % (3371777)------------------------------
% 14.50/3.12 % (3371777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371777)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371777)Termination reason: Refutation not found, incomplete strategy
% 14.50/3.12 % (3371777)Time elapsed: 0.983 s
% 14.50/3.12 % (3371777)Peak memory usage: 128 MB
% 14.50/3.12 % (3371777)Instructions burned: 888 (million)
% 14.50/3.12 % (3371799)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3447306494:i=2350_2989 on theBenchmark for (2989ds/2350Mi)
% 14.50/3.12 % (3371801)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2360454593:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 14.50/3.12 % (3371801)Refutation not found, incomplete strategy
% 14.50/3.12 % (3371801)------------------------------
% 14.50/3.12 % (3371801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371801)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371801)Termination reason: Refutation not found, incomplete strategy
% 14.50/3.12 % (3371801)Time elapsed: 0.002 s
% 14.50/3.12 % (3371801)Peak memory usage: 87 MB
% 14.50/3.12 % (3371800)------------------------------
% 14.50/3.12 % (3371800)------------------------------
% 14.50/3.12 % (3371798)------------------------------
% 14.50/3.12 % (3371798)------------------------------
% 14.50/3.12 % (3371776)First to succeed.
% 14.50/3.12 % (3371776)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3371770"
% 14.50/3.12 % (3371777)------------------------------
% 14.50/3.12 % (3371777)------------------------------
% 14.50/3.12 % (3371806)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2233743084:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2985 on theBenchmark for (2985ds/114Mi)
% 14.50/3.12 % (3371806)Refutation not found, incomplete strategy
% 14.50/3.12 % (3371806)------------------------------
% 14.50/3.12 % (3371806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371806)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371806)Termination reason: Refutation not found, incomplete strategy
% 14.50/3.12 % (3371806)Time elapsed: 0.002 s
% 14.50/3.12 % (3371806)Peak memory usage: 88 MB
% 14.50/3.12 % (3371801)------------------------------
% 14.50/3.12 % (3371801)------------------------------
% 14.50/3.12 % (3371808)lrs+10_1_sil=8000:sp=occurrence:random_seed=2069768597:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2984 on theBenchmark for (2984ds/907Mi)
% 14.50/3.12 % (3371810)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2542106056:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 14.50/3.12 % (3371810)Refutation not found, incomplete strategy
% 14.50/3.12 % (3371810)------------------------------
% 14.50/3.12 % (3371810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.50/3.12 % (3371810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.50/3.12 % (3371810)CaDiCaL version: 2.1.3
% 14.50/3.12 % (3371810)Termination reason: Refutation not found, incomplete strategy
% 14.50/3.12 % (3371810)Time elapsed: 0.002 s
% 14.50/3.12 % (3371810)Peak memory usage: 88 MB
% 14.50/3.12 % (3371806)------------------------------
% 14.50/3.12 % (3371806)------------------------------
% 14.50/3.12 % (3371776)Refutation found. Thanks to Tanya!
% 14.50/3.12 % SZS status Theorem for theBenchmark
% 14.50/3.12 % SZS output start Proof for theBenchmark
% See solution above
% 15.36/3.43 % (3371776)------------------------------
% 15.36/3.43 % (3371776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/3.43 % (3371776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/3.43 % (3371776)CaDiCaL version: 2.1.3
% 15.36/3.43 % (3371776)Termination reason: Refutation
% 15.36/3.43 % (3371776)Time elapsed: 1.457 s
% 15.36/3.43 % (3371776)Peak memory usage: 138 MB
% 15.36/3.43 % (3371776)Instructions burned: 1845 (million)
% 15.36/3.43 % (3371776)------------------------------
% 15.36/3.43 % (3371776)------------------------------
% 15.36/3.43 % (3371770)Success in time 2.048 s
% 15.36/3.43 % Vampire exiting
%------------------------------------------------------------------------------