%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE042+2 : 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 : n013.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 11:40:11 AM UTC 2026
% Result : Theorem 11.48s 2.35s
% Output : Refutation 12.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of formulae : 117 ( 87 unt; 8 def)
% Number of atoms : 149 ( 76 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 61 ( 29 ~; 24 |; 3 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 99 !; 2 ?)
% 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',additive_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',right_distributivity) ).
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',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
fof(f15,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X1)
=> leq(multiplication(star(X0),X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X0)
=> leq(multiplication(X2,star(X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_right) ).
fof(f17,conjecture,
! [X0,X1] :
( leq(multiplication(star(multiplication(X0,X1)),X0),multiplication(X0,star(multiplication(X1,X0))))
& leq(multiplication(X0,star(multiplication(X1,X0))),multiplication(star(multiplication(X0,X1)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( leq(multiplication(star(multiplication(X0,X1)),X0),multiplication(X0,star(multiplication(X1,X0))))
& leq(multiplication(X0,star(multiplication(X1,X0))),multiplication(star(multiplication(X0,X1)),X0)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f21,plain,
? [X0,X1] :
( ~ leq(multiplication(star(multiplication(X0,X1)),X0),multiplication(X0,star(multiplication(X1,X0))))
| ~ leq(multiplication(X0,star(multiplication(X1,X0))),multiplication(star(multiplication(X0,X1)),X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f23,plain,
( ~ leq(multiplication(star(multiplication(sK0,sK1)),sK0),multiplication(sK0,star(multiplication(sK1,sK0))))
| ~ leq(multiplication(sK0,star(multiplication(sK1,sK0))),multiplication(star(multiplication(sK0,sK1)),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
fof(f24,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f25,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f28,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f29,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f38,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f41,plain,
( ~ leq(multiplication(star(multiplication(sK0,sK1)),sK0),multiplication(sK0,star(multiplication(sK1,sK0))))
| ~ leq(multiplication(sK0,star(multiplication(sK1,sK0))),multiplication(star(multiplication(sK0,sK1)),sK0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,definition,
sF2 = multiplication(sK0,sK1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f43,plain,
multiplication(sK0,sK1) = sF2,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF3 = star(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f45,plain,
star(sF2) = sF3,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF4 = multiplication(sF3,sK0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f47,plain,
multiplication(sF3,sK0) = sF4,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF5 = multiplication(sK1,sK0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f49,plain,
multiplication(sK1,sK0) = sF5,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF6 = star(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f51,plain,
star(sF5) = sF6,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF7 = multiplication(sK0,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f53,plain,
multiplication(sK0,sF6) = sF7,
inference(reorient_equations,[],[f52]) ).
fof(f54,plain,
( ~ leq(sF4,sF7)
| ~ leq(sF7,sF4) ),
inference(definition_folding,[],[f41,f47,f45,f43,f53,f51,f49,f53,f51,f49,f47,f45,f43]) ).
fof(f56,definition,
( spl8_1
<=> leq(sF7,sF4) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f58,plain,
( ~ leq(sF7,sF4)
| spl8_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl8_2
<=> leq(sF4,sF7) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f62,plain,
( ~ leq(sF4,sF7)
| spl8_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f54,f60,f56]) ).
fof(f66,plain,
! [X0] : multiplication(sK0,multiplication(sK1,X0)) = multiplication(sF2,X0),
inference(superposition,[],[f28,f43]) ).
fof(f68,plain,
! [X0] : multiplication(sF3,multiplication(sK0,X0)) = multiplication(sF4,X0),
inference(superposition,[],[f28,f47]) ).
fof(f72,plain,
! [X0] : multiplication(sK0,addition(sF6,X0)) = addition(sF7,multiplication(sK0,X0)),
inference(superposition,[],[f31,f53]) ).
fof(f101,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(resolution,[],[f35,f37]) ).
fof(f102,plain,
! [X0] : star(X0) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(forward_demodulation,[],[f101,f25]) ).
fof(f103,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(resolution,[],[f38,f35]) ).
fof(f106,plain,
! [X0] : star(X0) = addition(one,addition(multiplication(star(X0),X0),star(X0))),
inference(forward_demodulation,[],[f103,f25]) ).
fof(f110,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(star(X0),X0))),
inference(superposition,[],[f106,f24]) ).
fof(f119,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f32,f30]) ).
fof(f123,plain,
! [X0] : multiplication(addition(sF3,X0),sK0) = addition(sF4,multiplication(X0,sK0)),
inference(superposition,[],[f32,f47]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ leq(addition(X0,multiplication(X1,X2)),X2)
| leq(multiplication(star(X1),X0),X2) ),
inference(superposition,[],[f39,f24]) ).
fof(f153,plain,
multiplication(sF2,sK0) = multiplication(sK0,sF5),
inference(superposition,[],[f66,f49]) ).
fof(f169,plain,
! [X0] : multiplication(sK0,multiplication(sF5,X0)) = multiplication(multiplication(sF2,sK0),X0),
inference(superposition,[],[f28,f153]) ).
fof(f170,plain,
! [X0] : multiplication(sK0,multiplication(sF5,X0)) = multiplication(sF2,multiplication(sK0,X0)),
inference(forward_demodulation,[],[f169,f28]) ).
fof(f197,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f36,f27]) ).
fof(f201,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f197]) ).
fof(f208,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(superposition,[],[f102,f24]) ).
fof(f213,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f25,f27]) ).
fof(f240,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f213,f102]) ).
fof(f253,plain,
sF3 = addition(one,sF3),
inference(superposition,[],[f240,f45]) ).
fof(f254,plain,
sF6 = addition(one,sF6),
inference(superposition,[],[f240,f51]) ).
fof(f260,plain,
! [X0] : addition(sF3,X0) = addition(one,addition(sF3,X0)),
inference(superposition,[],[f25,f253]) ).
fof(f264,plain,
! [X0] : addition(sF6,X0) = addition(one,addition(sF6,X0)),
inference(superposition,[],[f25,f254]) ).
fof(f270,plain,
! [X0] : multiplication(sF3,X0) = addition(X0,multiplication(sF3,X0)),
inference(superposition,[],[f119,f253]) ).
fof(f322,plain,
! [X2,X0,X1] :
( ~ leq(addition(X0,multiplication(X1,X2)),X1)
| leq(multiplication(X0,star(X2)),X1) ),
inference(superposition,[],[f40,f24]) ).
fof(f346,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f31,f29]) ).
fof(f367,plain,
! [X0] : multiplication(X0,sF6) = addition(X0,multiplication(X0,sF6)),
inference(superposition,[],[f346,f254]) ).
fof(f596,plain,
multiplication(sF4,sF5) = multiplication(sF3,multiplication(sF2,sK0)),
inference(superposition,[],[f68,f153]) ).
fof(f597,plain,
multiplication(sF4,sF6) = multiplication(sF3,sF7),
inference(superposition,[],[f68,f53]) ).
fof(f1711,plain,
multiplication(sF3,sF7) = addition(sF4,multiplication(sF3,sF7)),
inference(superposition,[],[f367,f597]) ).
fof(f2009,plain,
sF6 = addition(one,addition(sF6,multiplication(sF5,sF6))),
inference(superposition,[],[f208,f51]) ).
fof(f2031,plain,
sF6 = addition(sF6,multiplication(sF5,sF6)),
inference(forward_demodulation,[],[f2009,f264]) ).
fof(f2294,plain,
sF3 = addition(one,addition(sF3,multiplication(sF3,sF2))),
inference(superposition,[],[f110,f45]) ).
fof(f2317,plain,
sF3 = addition(sF3,multiplication(sF3,sF2)),
inference(forward_demodulation,[],[f2294,f260]) ).
fof(f5644,plain,
multiplication(sF3,sK0) = addition(sF4,multiplication(multiplication(sF3,sF2),sK0)),
inference(superposition,[],[f123,f2317]) ).
fof(f5669,plain,
multiplication(sF3,sK0) = addition(sF4,multiplication(sF3,multiplication(sF2,sK0))),
inference(forward_demodulation,[],[f5644,f28]) ).
fof(f5682,plain,
multiplication(sF3,sK0) = addition(sF4,multiplication(sF4,sF5)),
inference(forward_demodulation,[],[f5669,f596]) ).
fof(f5685,plain,
sF4 = addition(sF4,multiplication(sF4,sF5)),
inference(forward_demodulation,[],[f5682,f47]) ).
fof(f7230,plain,
( ~ leq(sF4,sF4)
| leq(multiplication(sF4,star(sF5)),sF4) ),
inference(superposition,[],[f322,f5685]) ).
fof(f7260,plain,
leq(multiplication(sF4,star(sF5)),sF4),
inference(forward_subsumption_resolution,[],[f7230,f201]) ).
fof(f7272,plain,
leq(multiplication(sF4,sF6),sF4),
inference(forward_demodulation,[],[f7260,f51]) ).
fof(f7274,plain,
leq(multiplication(sF3,sF7),sF4),
inference(forward_demodulation,[],[f7272,f597]) ).
fof(f7276,plain,
sF4 = addition(multiplication(sF3,sF7),sF4),
inference(resolution,[],[f7274,f35]) ).
fof(f7280,plain,
sF4 = addition(sF4,multiplication(sF3,sF7)),
inference(superposition,[],[f24,f7276]) ).
fof(f7330,plain,
sF4 = multiplication(sF3,sF7),
inference(forward_demodulation,[],[f7280,f1711]) ).
fof(f7338,plain,
sF4 = addition(sF7,sF4),
inference(superposition,[],[f270,f7330]) ).
fof(f7364,plain,
( sF4 != sF4
| leq(sF7,sF4) ),
inference(superposition,[],[f36,f7338]) ).
fof(f7382,plain,
leq(sF7,sF4),
inference(trivial_inequality_removal,[],[f7364]) ).
fof(f7388,plain,
( $false
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f7382,f58]) ).
fof(f7389,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f7388]) ).
fof(f7414,plain,
multiplication(sK0,sF6) = addition(sF7,multiplication(sK0,multiplication(sF5,sF6))),
inference(superposition,[],[f72,f2031]) ).
fof(f7446,plain,
multiplication(sK0,sF6) = addition(sF7,multiplication(sF2,multiplication(sK0,sF6))),
inference(forward_demodulation,[],[f7414,f170]) ).
fof(f7451,plain,
sF7 = addition(sF7,multiplication(sF2,sF7)),
inference(forward_demodulation,[],[f7446,f53]) ).
fof(f7453,plain,
( ~ leq(sF7,sF7)
| leq(multiplication(star(sF2),sF7),sF7) ),
inference(superposition,[],[f152,f7451]) ).
fof(f7486,plain,
leq(multiplication(star(sF2),sF7),sF7),
inference(forward_subsumption_resolution,[],[f7453,f201]) ).
fof(f7490,plain,
leq(multiplication(sF3,sF7),sF7),
inference(forward_demodulation,[],[f7486,f45]) ).
fof(f7491,plain,
leq(sF4,sF7),
inference(forward_demodulation,[],[f7490,f7330]) ).
fof(f7492,plain,
( $false
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f7491,f62]) ).
fof(f7493,plain,
spl8_2,
inference(avatar_contradiction_clause,[],[f7492]) ).
cnf(s1,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s32,plain,
spl8_1,
inference(sat_conversion,[],[f7389]) ).
cnf(s35,plain,
spl8_2,
inference(sat_conversion,[],[f7493]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s1,s35,s32]) ).
fof(f7494,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE042+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n013.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 13:04:37 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 10.34/2.13 % (208998)Detected formulas, will run a generic FOF schedule.
% 10.34/2.13 % (209008)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3317012921:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.34/2.13 % (209009)dis-21_1_sil=8000:lcm=predicate:random_seed=1730372152: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)
% 10.34/2.13 % (209003)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=1479859441:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.34/2.13 % (209004)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=2766786914:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.34/2.13 % (209006)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2634245928:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.34/2.13 % (209005)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=312037890:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.34/2.13 % (209007)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2830903827:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.34/2.13 % (209006)Refutation not found, incomplete strategy
% 10.34/2.13 % (209006)------------------------------
% 10.34/2.13 % (209006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.13 % (209006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.13 % (209006)CaDiCaL version: 2.1.3
% 10.34/2.13 % (209006)Termination reason: Refutation not found, incomplete strategy
% 10.34/2.13 % (209006)Time elapsed: 0.001 s
% 10.34/2.13 % (209006)Peak memory usage: 88 MB
% 10.34/2.13 % (209009)Refutation not found, incomplete strategy
% 10.34/2.13 % (209009)------------------------------
% 10.34/2.13 % (209009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.13 % (209009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.13 % (209009)CaDiCaL version: 2.1.3
% 10.34/2.13 % (209009)Termination reason: Refutation not found, incomplete strategy
% 10.34/2.13 % (209009)Time elapsed: 0.002 s
% 10.34/2.13 % (209009)Peak memory usage: 88 MB
% 10.34/2.13 % (209009)Instructions burned: 1 (million)
% 10.34/2.13 % (209007)Instruction limit reached!
% 10.34/2.13 % (209007)------------------------------
% 10.34/2.13 % (209007)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.13 % (209007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.13 % (209007)CaDiCaL version: 2.1.3
% 10.34/2.13 % (209007)Termination reason: Instruction limit
% 10.34/2.13 % (209007)Termination phase: Saturation
% 10.34/2.13 % (209007)Time elapsed: 0.067 s
% 10.34/2.13 % (209007)Peak memory usage: 88 MB
% 10.34/2.13 % (209007)Instructions burned: 120 (million)
% 10.34/2.13 % (209008)Instruction limit reached!
% 10.34/2.13 % (209008)------------------------------
% 10.34/2.13 % (209008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.13 % (209008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.13 % (209008)CaDiCaL version: 2.1.3
% 10.34/2.13 % (209008)Termination reason: Instruction limit
% 10.34/2.13 % (209008)Termination phase: Saturation
% 10.34/2.13 % (209008)Time elapsed: 0.085 s
% 10.34/2.13 % (209008)Peak memory usage: 90 MB
% 10.34/2.13 % (209008)Instructions burned: 141 (million)
% 10.34/2.13 % (209017)lrs+10_1_sil=8000:sp=occurrence:random_seed=1301123203:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.34/2.13 % (209018)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3676687275:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.34/2.13 % (209009)------------------------------
% 10.34/2.13 % (209009)------------------------------
% 10.34/2.13 % (209006)------------------------------
% 10.34/2.13 % (209006)------------------------------
% 10.34/2.13 % (209018)Instruction limit reached!
% 10.34/2.13 % (209018)------------------------------
% 10.34/2.13 % (209018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.34/2.13 % (209018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.34/2.13 % (209018)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209018)Termination reason: Instruction limit
% 11.48/2.35 % (209018)Termination phase: Saturation
% 11.48/2.35 % (209018)Time elapsed: 0.094 s
% 11.48/2.35 % (209018)Peak memory usage: 90 MB
% 11.48/2.35 % (209018)Instructions burned: 158 (million)
% 11.48/2.35 % (209021)lrs+1011_1_sil=32000:sp=occurrence:random_seed=967007159:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 11.48/2.35 % (209022)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=3789849833:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 11.48/2.35 % (209017)Instruction limit reached!
% 11.48/2.35 % (209017)------------------------------
% 11.48/2.35 % (209017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209017)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209017)Termination reason: Instruction limit
% 11.48/2.35 % (209017)Termination phase: Saturation
% 11.48/2.35 % (209017)Time elapsed: 0.181 s
% 11.48/2.35 % (209017)Peak memory usage: 91 MB
% 11.48/2.35 % (209017)Instructions burned: 285 (million)
% 11.48/2.35 % (209021)Instruction limit reached!
% 11.48/2.35 % (209021)------------------------------
% 11.48/2.35 % (209021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209021)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209021)Termination reason: Instruction limit
% 11.48/2.35 % (209021)Termination phase: Saturation
% 11.48/2.35 % (209021)Time elapsed: 0.114 s
% 11.48/2.35 % (209021)Peak memory usage: 93 MB
% 11.48/2.35 % (209021)Instructions burned: 326 (million)
% 11.48/2.35 % (209023)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=329887518:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 11.48/2.35 % (209023)Refutation not found, incomplete strategy
% 11.48/2.35 % (209023)------------------------------
% 11.48/2.35 % (209023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209023)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209023)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.35 % (209023)Time elapsed: 0.002 s
% 11.48/2.35 % (209023)Peak memory usage: 88 MB
% 11.48/2.35 % (209023)Instructions burned: 1 (million)
% 11.48/2.35 % (209026)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2421018763:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 11.48/2.35 % (209027)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1682064170:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 11.48/2.35 % (209027)Refutation not found, incomplete strategy
% 11.48/2.35 % (209027)------------------------------
% 11.48/2.35 % (209027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209027)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209027)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.35 % (209027)Time elapsed: 0.001 s
% 11.48/2.35 % (209027)Peak memory usage: 89 MB
% 11.48/2.35 % (209027)Instructions burned: 1 (million)
% 11.48/2.35 % (209022)Instruction limit reached!
% 11.48/2.35 % (209022)------------------------------
% 11.48/2.35 % (209022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209022)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209022)Termination reason: Instruction limit
% 11.48/2.35 % (209022)Termination phase: Saturation
% 11.48/2.35 % (209022)Time elapsed: 0.160 s
% 11.48/2.35 % (209022)Peak memory usage: 91 MB
% 11.48/2.35 % (209022)Instructions burned: 249 (million)
% 11.48/2.35 % (209005)Refutation not found, incomplete strategy
% 11.48/2.35 % (209005)------------------------------
% 11.48/2.35 % (209005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209005)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209005)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.35 % (209005)Time elapsed: 0.607 s
% 11.48/2.35 % (209005)Peak memory usage: 127 MB
% 11.48/2.35 % (209005)Instructions burned: 905 (million)
% 11.48/2.35 % (209027)------------------------------
% 11.48/2.35 % (209027)------------------------------
% 11.48/2.35 % (209031)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1475428568:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 11.48/2.35 % (209031)Refutation not found, incomplete strategy
% 11.48/2.35 % (209031)------------------------------
% 11.48/2.35 % (209031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209031)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209031)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.35 % (209031)Time elapsed: 0.001 s
% 11.48/2.35 % (209031)Peak memory usage: 88 MB
% 11.48/2.35 % (209023)------------------------------
% 11.48/2.35 % (209023)------------------------------
% 11.48/2.35 % (209033)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4172530819:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 11.48/2.35 % (209033)Refutation not found, incomplete strategy
% 11.48/2.35 % (209033)------------------------------
% 11.48/2.35 % (209033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209033)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209033)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.35 % (209033)Time elapsed: 0.001 s
% 11.48/2.35 % (209033)Peak memory usage: 89 MB
% 11.48/2.35 % (209033)Instructions burned: 2 (million)
% 11.48/2.35 % (209034)lrs+10_1_sil=8000:sp=occurrence:random_seed=99463719:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 11.48/2.35 % (209005)------------------------------
% 11.48/2.35 % (209005)------------------------------
% 11.48/2.35 % (209033)------------------------------
% 11.48/2.35 % (209033)------------------------------
% 11.48/2.35 % (209031)------------------------------
% 11.48/2.35 % (209031)------------------------------
% 11.48/2.35 % (209037)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=271526334:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 11.48/2.35 % (209037)Refutation not found, incomplete strategy
% 11.48/2.35 % (209037)------------------------------
% 11.48/2.35 % (209037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209037)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209037)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.35 % (209037)Time elapsed: 0.001 s
% 11.48/2.35 % (209037)Peak memory usage: 88 MB
% 11.48/2.35 % (209038)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3752063853:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 11.48/2.35 % (209039)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3889607240:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 11.48/2.35 % (209039)Refutation not found, incomplete strategy
% 11.48/2.35 % (209039)------------------------------
% 11.48/2.35 % (209039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209039)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209039)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.35 % (209039)Time elapsed: 0.002 s
% 11.48/2.35 % (209039)Peak memory usage: 89 MB
% 11.48/2.35 % (209039)Instructions burned: 1 (million)
% 11.48/2.35 % (209037)------------------------------
% 11.48/2.35 % (209037)------------------------------
% 11.48/2.35 % (209039)------------------------------
% 11.48/2.35 % (209039)------------------------------
% 11.48/2.35 % (209003)First to succeed.
% 11.48/2.35 % (209003)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-208998"
% 11.48/2.35 % (209043)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=667624235:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 11.48/2.35 % (209043)Refutation not found, incomplete strategy
% 11.48/2.35 % (209043)------------------------------
% 11.48/2.35 % (209043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209043)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209043)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.35 % (209043)Time elapsed: 0.001 s
% 11.48/2.35 % (209043)Peak memory usage: 88 MB
% 11.48/2.35 % (209043)Instructions burned: 1 (million)
% 11.48/2.35 % (209034)Instruction limit reached!
% 11.48/2.35 % (209034)------------------------------
% 11.48/2.35 % (209034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.35 % (209034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.35 % (209034)CaDiCaL version: 2.1.3
% 11.48/2.35 % (209034)Termination reason: Instruction limit
% 11.48/2.35 % (209034)Termination phase: Saturation
% 11.48/2.35 % (209034)Time elapsed: 0.542 s
% 11.48/2.35 % (209034)Peak memory usage: 96 MB
% 11.48/2.35 % (209034)Instructions burned: 907 (million)
% 11.48/2.35 % (209044)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=868443710:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 11.48/2.35 % (209046)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2051352858:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/125Mi)
% 11.48/2.35 % (209003)Refutation found. Thanks to Tanya!
% 11.48/2.35 % SZS status Theorem for theBenchmark
% 11.48/2.35 % SZS output start Proof for theBenchmark
% See solution above
% 12.65/2.54 % (209003)------------------------------
% 12.65/2.54 % (209003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.54 % (209003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.54 % (209003)CaDiCaL version: 2.1.3
% 12.65/2.54 % (209003)Termination reason: Refutation
% 12.65/2.54 % (209003)Time elapsed: 1.338 s
% 12.65/2.54 % (209003)Peak memory usage: 142 MB
% 12.65/2.54 % (209003)Instructions burned: 2151 (million)
% 12.65/2.54 % (209003)------------------------------
% 12.65/2.54 % (209003)------------------------------
% 12.65/2.54 % (208998)Success in time 1.737 s
% 12.65/2.54 % Vampire exiting
%------------------------------------------------------------------------------