%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE040+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 : n004.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 11:40:10 AM UTC 2026
% Result : Theorem 6.89s 1.99s
% Output : Refutation 8.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 79 ( 54 unt; 2 def)
% Number of atoms : 106 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 24 ~; 20 |; 3 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 111 !; 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',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(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(f17,conjecture,
! [X0] :
( leq(multiplication(star(X0),star(X0)),star(X0))
& leq(star(X0),multiplication(star(X0),star(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] :
( leq(multiplication(star(X0),star(X0)),star(X0))
& leq(star(X0),multiplication(star(X0),star(X0))) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0] :
( ~ leq(multiplication(star(X0),star(X0)),star(X0))
| ~ leq(star(X0),multiplication(star(X0),star(X0))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f21,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f22,plain,
( ~ leq(multiplication(star(sK0),star(sK0)),star(sK0))
| ~ leq(star(sK0),multiplication(star(sK0),star(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f24,plain,
( ~ leq(multiplication(star(sK0),star(sK0)),star(sK0))
| ~ leq(star(sK0),multiplication(star(sK0),star(sK0))) ),
inference(cnf_transformation,[],[f22]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f40,definition,
( spl1_1
<=> leq(star(sK0),multiplication(star(sK0),star(sK0))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f41,plain,
( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| spl1_1 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,definition,
( spl1_2
<=> leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f44,plain,
( ~ leq(multiplication(star(sK0),star(sK0)),star(sK0))
| spl1_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f24,f43,f40]) ).
fof(f46,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f33,f38]) ).
fof(f55,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f32,f37]) ).
fof(f80,plain,
! [X2,X0,X1] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(superposition,[],[f55,f31]) ).
fof(f126,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(resolution,[],[f28,f29]) ).
fof(f131,plain,
! [X0] : star(X0) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(forward_demodulation,[],[f126,f36]) ).
fof(f134,plain,
! [X2,X0,X1] : addition(X1,addition(multiplication(X0,X1),X2)) = addition(multiplication(addition(one,X0),X1),X2),
inference(superposition,[],[f35,f55]) ).
fof(f144,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f36,f35]) ).
fof(f164,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(star(multiplication(X0,X1)),addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))))),
inference(superposition,[],[f131,f31]) ).
fof(f166,plain,
! [X0,X1] : addition(star(X0),X1) = addition(star(X0),addition(addition(one,multiplication(X0,star(X0))),X1)),
inference(superposition,[],[f35,f131]) ).
fof(f168,plain,
! [X0,X1] : addition(star(X0),X1) = addition(star(X0),addition(one,addition(multiplication(X0,star(X0)),X1))),
inference(forward_demodulation,[],[f166,f35]) ).
fof(f170,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(one,addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),star(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f164,f144]) ).
fof(f172,plain,
! [X0,X1] : addition(star(X0),X1) = addition(one,addition(addition(multiplication(X0,star(X0)),X1),star(X0))),
inference(forward_demodulation,[],[f168,f144]) ).
fof(f174,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(one,addition(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))))),
inference(forward_demodulation,[],[f170,f36]) ).
fof(f176,plain,
! [X0,X1] : addition(star(X0),X1) = addition(one,addition(star(X0),addition(multiplication(X0,star(X0)),X1))),
inference(forward_demodulation,[],[f172,f36]) ).
fof(f178,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(one,multiplication(addition(one,multiplication(X0,X1)),star(multiplication(X0,X1)))),
inference(forward_demodulation,[],[f174,f80]) ).
fof(f179,plain,
! [X0,X1] : addition(star(X0),X1) = addition(one,addition(multiplication(addition(one,X0),star(X0)),X1)),
inference(forward_demodulation,[],[f176,f134]) ).
fof(f201,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f35,f34]) ).
fof(f202,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f30,f34]) ).
fof(f206,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f202]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ leq(addition(X0,multiplication(X1,X2)),X2)
| leq(multiplication(star(X1),X0),X2) ),
inference(superposition,[],[f26,f36]) ).
fof(f361,plain,
! [X0,X1] :
( ~ leq(multiplication(addition(one,X0),X1),X1)
| leq(multiplication(star(X0),X1),X1) ),
inference(superposition,[],[f252,f55]) ).
fof(f637,plain,
! [X0] : star(X0) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(superposition,[],[f178,f37]) ).
fof(f645,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(one,star(multiplication(X0,X1))),
inference(superposition,[],[f201,f178]) ).
fof(f1020,plain,
! [X0] : addition(one,multiplication(addition(one,X0),star(X0))) = addition(star(X0),multiplication(addition(one,X0),star(X0))),
inference(superposition,[],[f179,f34]) ).
fof(f1066,plain,
! [X0] : addition(one,multiplication(addition(one,X0),star(X0))) = multiplication(addition(one,addition(one,X0)),star(X0)),
inference(forward_demodulation,[],[f1020,f55]) ).
fof(f1084,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[],[f1066,f201]) ).
fof(f1094,plain,
! [X0] : star(X0) = multiplication(addition(one,X0),star(X0)),
inference(forward_demodulation,[],[f1084,f637]) ).
fof(f1115,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(superposition,[],[f361,f1094]) ).
fof(f1149,plain,
! [X0] : leq(multiplication(star(X0),star(X0)),star(X0)),
inference(forward_subsumption_resolution,[],[f1115,f206]) ).
fof(f1168,plain,
! [X0] : star(X0) = addition(multiplication(star(X0),star(X0)),star(X0)),
inference(resolution,[],[f1149,f29]) ).
fof(f1169,plain,
! [X0] : star(X0) = addition(star(X0),multiplication(star(X0),star(X0))),
inference(forward_demodulation,[],[f1168,f36]) ).
fof(f1170,plain,
! [X0] : star(X0) = multiplication(star(X0),addition(one,star(X0))),
inference(forward_demodulation,[],[f1169,f46]) ).
fof(f1366,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f645,f37]) ).
fof(f1389,plain,
! [X0] : star(X0) = multiplication(star(X0),star(X0)),
inference(superposition,[],[f1170,f1366]) ).
fof(f1407,plain,
( ~ leq(star(sK0),star(sK0))
| spl1_1 ),
inference(superposition,[],[f41,f1389]) ).
fof(f1448,plain,
( $false
| spl1_1 ),
inference(forward_subsumption_resolution,[],[f1407,f206]) ).
fof(f1449,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f1448]) ).
fof(f1457,plain,
( $false
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f44,f1149]) ).
fof(f1458,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f1457]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f45]) ).
cnf(s2,plain,
spl1_1,
inference(sat_conversion,[],[f1449]) ).
cnf(s3,plain,
spl1_2,
inference(sat_conversion,[],[f1458]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f1459,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE040+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:05:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 6.89/1.99 % (3500810)Detected formulas, will run a generic FOF schedule.
% 6.89/1.99 % (3500818)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3225901361:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.89/1.99 % (3500818)Refutation not found, incomplete strategy
% 6.89/1.99 % (3500818)------------------------------
% 6.89/1.99 % (3500818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500818)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500818)Termination reason: Refutation not found, incomplete strategy
% 6.89/1.99 % (3500818)Time elapsed: 0.001 s
% 6.89/1.99 % (3500818)Peak memory usage: 88 MB
% 6.89/1.99 % (3500820)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1647203882:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.89/1.99 % (3500819)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=457596137:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.89/1.99 % (3500821)dis-21_1_sil=8000:lcm=predicate:random_seed=3824276034: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)
% 6.89/1.99 % (3500815)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=1329854318:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.89/1.99 % (3500816)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=2143722230:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.89/1.99 % (3500817)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=3334853971:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.89/1.99 % (3500821)Refutation not found, incomplete strategy
% 6.89/1.99 % (3500821)------------------------------
% 6.89/1.99 % (3500821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500821)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500821)Termination reason: Refutation not found, incomplete strategy
% 6.89/1.99 % (3500821)Time elapsed: 0.002 s
% 6.89/1.99 % (3500821)Peak memory usage: 88 MB
% 6.89/1.99 % (3500821)Instructions burned: 1 (million)
% 6.89/1.99 % (3500819)Instruction limit reached!
% 6.89/1.99 % (3500819)------------------------------
% 6.89/1.99 % (3500819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500819)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500819)Termination reason: Instruction limit
% 6.89/1.99 % (3500819)Termination phase: Saturation
% 6.89/1.99 % (3500819)Time elapsed: 0.067 s
% 6.89/1.99 % (3500819)Peak memory usage: 88 MB
% 6.89/1.99 % (3500819)Instructions burned: 120 (million)
% 6.89/1.99 % (3500820)Instruction limit reached!
% 6.89/1.99 % (3500820)------------------------------
% 6.89/1.99 % (3500820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500820)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500820)Termination reason: Instruction limit
% 6.89/1.99 % (3500820)Termination phase: Saturation
% 6.89/1.99 % (3500820)Time elapsed: 0.091 s
% 6.89/1.99 % (3500820)Peak memory usage: 90 MB
% 6.89/1.99 % (3500820)Instructions burned: 139 (million)
% 6.89/1.99 % (3500818)------------------------------
% 6.89/1.99 % (3500818)------------------------------
% 6.89/1.99 % (3500831)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2991675635:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.89/1.99 % (3500829)lrs+10_1_sil=8000:sp=occurrence:random_seed=3221806375:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.89/1.99 % (3500830)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2665956826:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.89/1.99 % (3500821)------------------------------
% 6.89/1.99 % (3500821)------------------------------
% 6.89/1.99 % (3500830)Instruction limit reached!
% 6.89/1.99 % (3500830)------------------------------
% 6.89/1.99 % (3500830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500830)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500830)Termination reason: Instruction limit
% 6.89/1.99 % (3500830)Termination phase: Saturation
% 6.89/1.99 % (3500830)Time elapsed: 0.080 s
% 6.89/1.99 % (3500830)Peak memory usage: 90 MB
% 6.89/1.99 % (3500830)Instructions burned: 158 (million)
% 6.89/1.99 % (3500831)Instruction limit reached!
% 6.89/1.99 % (3500831)------------------------------
% 6.89/1.99 % (3500831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500831)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500831)Termination reason: Instruction limit
% 6.89/1.99 % (3500831)Termination phase: Saturation
% 6.89/1.99 % (3500831)Time elapsed: 0.112 s
% 6.89/1.99 % (3500831)Peak memory usage: 93 MB
% 6.89/1.99 % (3500831)Instructions burned: 328 (million)
% 6.89/1.99 % (3500829)Instruction limit reached!
% 6.89/1.99 % (3500829)------------------------------
% 6.89/1.99 % (3500829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500829)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500829)Termination reason: Instruction limit
% 6.89/1.99 % (3500829)Termination phase: Saturation
% 6.89/1.99 % (3500829)Time elapsed: 0.180 s
% 6.89/1.99 % (3500829)Peak memory usage: 91 MB
% 6.89/1.99 % (3500829)Instructions burned: 285 (million)
% 6.89/1.99 % (3500837)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2826761590:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.89/1.99 % (3500835)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=3929758611:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.89/1.99 % (3500836)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=377357908:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.89/1.99 % (3500836)Refutation not found, incomplete strategy
% 6.89/1.99 % (3500836)------------------------------
% 6.89/1.99 % (3500836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500836)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500836)Termination reason: Refutation not found, incomplete strategy
% 6.89/1.99 % (3500836)Time elapsed: 0.002 s
% 6.89/1.99 % (3500836)Peak memory usage: 88 MB
% 6.89/1.99 % (3500836)Instructions burned: 1 (million)
% 6.89/1.99 % (3500838)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4173781633:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.89/1.99 % (3500838)Refutation not found, incomplete strategy
% 6.89/1.99 % (3500838)------------------------------
% 6.89/1.99 % (3500838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500838)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500838)Termination reason: Refutation not found, incomplete strategy
% 6.89/1.99 % (3500838)Time elapsed: 0.002 s
% 6.89/1.99 % (3500838)Peak memory usage: 88 MB
% 6.89/1.99 % (3500838)Instructions burned: 1 (million)
% 6.89/1.99 % (3500835)Instruction limit reached!
% 6.89/1.99 % (3500835)------------------------------
% 6.89/1.99 % (3500835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500835)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500835)Termination reason: Instruction limit
% 6.89/1.99 % (3500835)Termination phase: Saturation
% 6.89/1.99 % (3500835)Time elapsed: 0.157 s
% 6.89/1.99 % (3500835)Peak memory usage: 91 MB
% 6.89/1.99 % (3500835)Instructions burned: 249 (million)
% 6.89/1.99 % (3500817)Refutation not found, incomplete strategy
% 6.89/1.99 % (3500817)------------------------------
% 6.89/1.99 % (3500817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500817)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500817)Termination reason: Refutation not found, incomplete strategy
% 6.89/1.99 % (3500817)Time elapsed: 0.593 s
% 6.89/1.99 % (3500817)Peak memory usage: 127 MB
% 6.89/1.99 % (3500817)Instructions burned: 889 (million)
% 6.89/1.99 % (3500836)------------------------------
% 6.89/1.99 % (3500836)------------------------------
% 6.89/1.99 % (3500843)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3534500468:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.89/1.99 % (3500843)Refutation not found, incomplete strategy
% 6.89/1.99 % (3500843)------------------------------
% 6.89/1.99 % (3500843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500843)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500843)Termination reason: Refutation not found, incomplete strategy
% 6.89/1.99 % (3500843)Time elapsed: 0.001 s
% 6.89/1.99 % (3500843)Peak memory usage: 88 MB
% 6.89/1.99 % (3500816)First to succeed.
% 6.89/1.99 % (3500816)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3500810"
% 6.89/1.99 % (3500838)------------------------------
% 6.89/1.99 % (3500838)------------------------------
% 6.89/1.99 % (3500815)Also succeeded, but the first one will report.
% 6.89/1.99 % (3500844)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3413869513:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 6.89/1.99 % (3500844)Refutation not found, incomplete strategy
% 6.89/1.99 % (3500844)------------------------------
% 6.89/1.99 % (3500844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500844)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500844)Termination reason: Refutation not found, incomplete strategy
% 6.89/1.99 % (3500844)Time elapsed: 0.001 s
% 6.89/1.99 % (3500844)Peak memory usage: 88 MB
% 6.89/1.99 % (3500817)------------------------------
% 6.89/1.99 % (3500817)------------------------------
% 6.89/1.99 % (3500846)lrs+10_1_sil=8000:sp=occurrence:random_seed=1846706959:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 6.89/1.99 % (3500843)------------------------------
% 6.89/1.99 % (3500843)------------------------------
% 6.89/1.99 % (3500837)Also succeeded, but the first one will report.
% 6.89/1.99 % (3500848)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3969159707:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 6.89/1.99 % (3500848)Refutation not found, incomplete strategy
% 6.89/1.99 % (3500848)------------------------------
% 6.89/1.99 % (3500848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.99 % (3500848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.99 % (3500848)CaDiCaL version: 2.1.3
% 6.89/1.99 % (3500848)Termination reason: Refutation not found, incomplete strategy
% 6.89/1.99 % (3500848)Time elapsed: 0.001 s
% 6.89/1.99 % (3500848)Peak memory usage: 88 MB
% 6.89/1.99 % (3500816)Refutation found. Thanks to Tanya!
% 6.89/1.99 % SZS status Theorem for theBenchmark
% 6.89/1.99 % SZS output start Proof for theBenchmark
% See solution above
% 8.68/2.10 % (3500816)------------------------------
% 8.68/2.10 % (3500816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.10 % (3500816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.10 % (3500816)CaDiCaL version: 2.1.3
% 8.68/2.10 % (3500816)Termination reason: Refutation
% 8.68/2.10 % (3500816)Time elapsed: 0.748 s
% 8.68/2.10 % (3500816)Peak memory usage: 130 MB
% 8.68/2.10 % (3500816)Instructions burned: 1138 (million)
% 8.68/2.10 % (3500816)------------------------------
% 8.68/2.10 % (3500816)------------------------------
% 8.68/2.10 % (3500810)Success in time 1.161 s
% 8.68/2.10 % Vampire exiting
%------------------------------------------------------------------------------