%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE092+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 : n010.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 11:40:18 AM UTC 2026
% Result : Theorem 9.35s 2.10s
% Output : Refutation 10.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 114 ( 114 unt; 3 def)
% Number of atoms : 114 ( 113 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 107 ( 106 !; 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
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(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f14,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain3) ).
fof(f21,conjecture,
! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0] : coantidomain(X0) != domain(coantidomain(X0)),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
coantidomain(sK0) != domain(coantidomain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f23]) ).
fof(f25,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f37,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f14]) ).
fof(f38,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f42,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
coantidomain(sK0) != domain(coantidomain(sK0)),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
coantidomain(sK0) != antidomain(antidomain(coantidomain(sK0))),
inference(definition_unfolding,[],[f44,f39]) ).
fof(f46,definition,
sF1 = coantidomain(sK0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f47,plain,
coantidomain(sK0) = sF1,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF2 = antidomain(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f49,plain,
antidomain(sF1) = sF2,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF3 = antidomain(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f51,plain,
antidomain(sF2) = sF3,
inference(reorient_equations,[],[f50]) ).
fof(f52,plain,
sF1 != sF3,
inference(definition_folding,[],[f45,f51,f49,f47,f47]) ).
fof(f59,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(superposition,[],[f38,f25]) ).
fof(f64,plain,
one = addition(coantidomain(sF1),sF1),
inference(superposition,[],[f42,f47]) ).
fof(f79,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f25,f27]) ).
fof(f81,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(zero,multiplication(X1,coantidomain(X0))),
inference(superposition,[],[f33,f40]) ).
fof(f83,plain,
! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[],[f33,f31]) ).
fof(f85,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(superposition,[],[f33,f36]) ).
fof(f94,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,antidomain(X1)),X1),
inference(forward_demodulation,[],[f85,f27]) ).
fof(f97,plain,
! [X0,X1] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(forward_demodulation,[],[f81,f79]) ).
fof(f122,plain,
! [X0] : multiplication(one,X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(superposition,[],[f94,f38]) ).
fof(f127,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f122,f31]) ).
fof(f136,plain,
one = addition(sF2,antidomain(sF2)),
inference(superposition,[],[f59,f49]) ).
fof(f142,plain,
one = addition(sF2,sF3),
inference(forward_demodulation,[],[f136,f51]) ).
fof(f149,plain,
zero = antidomain(one),
inference(superposition,[],[f36,f30]) ).
fof(f165,plain,
one = addition(antidomain(zero),zero),
inference(superposition,[],[f38,f149]) ).
fof(f166,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f165,f27]) ).
fof(f251,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(X0,addition(X1,coantidomain(X0))),
inference(superposition,[],[f32,f40]) ).
fof(f257,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[],[f32,f36]) ).
fof(f278,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0)),
inference(forward_demodulation,[],[f257,f27]) ).
fof(f280,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(X0,addition(X1,coantidomain(X0))),
inference(forward_demodulation,[],[f251,f27]) ).
fof(f292,plain,
! [X2,X0,X1] : multiplication(antidomain(multiplication(X1,X2)),multiplication(X0,X2)) = multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f278,f33]) ).
fof(f293,plain,
! [X2,X0,X1] : multiplication(antidomain(multiplication(X0,X2)),multiplication(X0,X1)) = multiplication(antidomain(multiplication(X0,X2)),multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f278,f32]) ).
fof(f295,plain,
! [X0] : multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)) = multiplication(antidomain(antidomain(antidomain(X0))),one),
inference(superposition,[],[f278,f59]) ).
fof(f306,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)),
inference(forward_demodulation,[],[f295,f30]) ).
fof(f312,plain,
! [X0] : antidomain(X0) = antidomain(antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f306,f127]) ).
fof(f336,plain,
! [X0] : multiplication(X0,one) = multiplication(X0,coantidomain(coantidomain(X0))),
inference(superposition,[],[f280,f42]) ).
fof(f349,plain,
! [X0] : multiplication(X0,coantidomain(coantidomain(X0))) = X0,
inference(forward_demodulation,[],[f336,f30]) ).
fof(f403,plain,
! [X0,X1] : multiplication(antidomain(multiplication(coantidomain(X0),X1)),multiplication(coantidomain(coantidomain(X0)),X1)) = multiplication(antidomain(multiplication(coantidomain(X0),X1)),multiplication(one,X1)),
inference(superposition,[],[f292,f42]) ).
fof(f419,plain,
! [X0,X1] : multiplication(antidomain(multiplication(coantidomain(X0),X1)),multiplication(coantidomain(coantidomain(X0)),X1)) = multiplication(antidomain(multiplication(coantidomain(X0),X1)),X1),
inference(forward_demodulation,[],[f403,f31]) ).
fof(f448,plain,
! [X0] : multiplication(coantidomain(X0),coantidomain(coantidomain(coantidomain(X0)))) = multiplication(one,coantidomain(coantidomain(coantidomain(X0)))),
inference(superposition,[],[f97,f42]) ).
fof(f470,plain,
! [X0] : coantidomain(coantidomain(coantidomain(X0))) = multiplication(coantidomain(X0),coantidomain(coantidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f448,f31]) ).
fof(f480,plain,
! [X0] : coantidomain(X0) = coantidomain(coantidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f470,f349]) ).
fof(f490,plain,
sF1 = coantidomain(coantidomain(sF1)),
inference(superposition,[],[f480,f47]) ).
fof(f541,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f26,f28]) ).
fof(f744,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),multiplication(X0,antidomain(antidomain(X1)))),
inference(superposition,[],[f94,f37]) ).
fof(f753,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f744,f36]) ).
fof(f801,plain,
! [X0] : zero = multiplication(antidomain(zero),multiplication(X0,antidomain(antidomain(coantidomain(X0))))),
inference(superposition,[],[f753,f40]) ).
fof(f868,plain,
! [X0] : zero = multiplication(one,multiplication(X0,antidomain(antidomain(coantidomain(X0))))),
inference(forward_demodulation,[],[f801,f166]) ).
fof(f876,plain,
! [X0] : zero = multiplication(X0,antidomain(antidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f868,f31]) ).
fof(f958,plain,
zero = multiplication(coantidomain(sF1),antidomain(antidomain(sF1))),
inference(superposition,[],[f876,f490]) ).
fof(f992,plain,
zero = multiplication(coantidomain(sF1),antidomain(sF2)),
inference(forward_demodulation,[],[f958,f49]) ).
fof(f1000,plain,
zero = multiplication(coantidomain(sF1),sF3),
inference(forward_demodulation,[],[f992,f51]) ).
fof(f1166,plain,
one = addition(sF2,one),
inference(superposition,[],[f541,f142]) ).
fof(f1546,plain,
multiplication(antidomain(sF1),coantidomain(sF1)) = multiplication(antidomain(sF1),one),
inference(superposition,[],[f278,f64]) ).
fof(f1552,plain,
antidomain(sF1) = multiplication(antidomain(sF1),coantidomain(sF1)),
inference(forward_demodulation,[],[f1546,f30]) ).
fof(f1556,plain,
sF2 = multiplication(sF2,coantidomain(sF1)),
inference(forward_demodulation,[],[f1552,f49]) ).
fof(f1946,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,antidomain(X1))),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(X1))),multiplication(X0,one)),
inference(superposition,[],[f293,f38]) ).
fof(f2001,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,antidomain(X1))),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(X1))),X0),
inference(forward_demodulation,[],[f1946,f30]) ).
fof(f2034,plain,
! [X0] : multiplication(antidomain(zero),X0) = multiplication(antidomain(zero),multiplication(X0,antidomain(antidomain(antidomain(coantidomain(X0)))))),
inference(superposition,[],[f2001,f876]) ).
fof(f2101,plain,
! [X0] : multiplication(antidomain(zero),X0) = multiplication(antidomain(zero),multiplication(X0,antidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f2034,f312]) ).
fof(f2113,plain,
! [X0] : multiplication(one,X0) = multiplication(one,multiplication(X0,antidomain(coantidomain(X0)))),
inference(forward_demodulation,[],[f2101,f166]) ).
fof(f2117,plain,
! [X0] : multiplication(one,X0) = multiplication(X0,antidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f2113,f31]) ).
fof(f2119,plain,
! [X0] : multiplication(X0,antidomain(coantidomain(X0))) = X0,
inference(forward_demodulation,[],[f2117,f31]) ).
fof(f2123,plain,
coantidomain(sF1) = multiplication(coantidomain(sF1),antidomain(sF1)),
inference(superposition,[],[f2119,f490]) ).
fof(f2162,plain,
coantidomain(sF1) = multiplication(coantidomain(sF1),sF2),
inference(forward_demodulation,[],[f2123,f49]) ).
fof(f2273,plain,
multiplication(addition(sF2,one),coantidomain(sF1)) = addition(sF2,coantidomain(sF1)),
inference(superposition,[],[f83,f1556]) ).
fof(f2281,plain,
multiplication(one,coantidomain(sF1)) = addition(sF2,coantidomain(sF1)),
inference(forward_demodulation,[],[f2273,f1166]) ).
fof(f2287,plain,
coantidomain(sF1) = addition(sF2,coantidomain(sF1)),
inference(forward_demodulation,[],[f2281,f31]) ).
fof(f2614,plain,
multiplication(antidomain(zero),multiplication(coantidomain(coantidomain(sF1)),sF3)) = multiplication(antidomain(zero),sF3),
inference(superposition,[],[f419,f1000]) ).
fof(f2644,plain,
multiplication(one,sF3) = multiplication(one,multiplication(coantidomain(coantidomain(sF1)),sF3)),
inference(forward_demodulation,[],[f2614,f166]) ).
fof(f2653,plain,
multiplication(one,sF3) = multiplication(coantidomain(coantidomain(sF1)),sF3),
inference(forward_demodulation,[],[f2644,f31]) ).
fof(f2656,plain,
multiplication(one,sF3) = multiplication(sF1,sF3),
inference(forward_demodulation,[],[f2653,f490]) ).
fof(f2657,plain,
sF3 = multiplication(sF1,sF3),
inference(forward_demodulation,[],[f2656,f31]) ).
fof(f4540,plain,
multiplication(sF1,coantidomain(sF1)) = multiplication(sF1,sF2),
inference(superposition,[],[f280,f2287]) ).
fof(f4553,plain,
zero = multiplication(sF1,sF2),
inference(forward_demodulation,[],[f4540,f40]) ).
fof(f4559,plain,
! [X0] : addition(multiplication(X0,sF2),zero) = multiplication(addition(X0,sF1),sF2),
inference(superposition,[],[f33,f4553]) ).
fof(f4587,plain,
! [X0] : multiplication(X0,sF2) = multiplication(addition(X0,sF1),sF2),
inference(forward_demodulation,[],[f4559,f27]) ).
fof(f5168,plain,
multiplication(one,sF2) = multiplication(coantidomain(sF1),sF2),
inference(superposition,[],[f4587,f64]) ).
fof(f5203,plain,
coantidomain(sF1) = multiplication(one,sF2),
inference(forward_demodulation,[],[f5168,f2162]) ).
fof(f5213,plain,
sF2 = coantidomain(sF1),
inference(forward_demodulation,[],[f5203,f31]) ).
fof(f5247,plain,
sF1 = multiplication(sF1,antidomain(sF2)),
inference(superposition,[],[f2119,f5213]) ).
fof(f5248,plain,
sF1 = multiplication(sF1,sF3),
inference(forward_demodulation,[],[f5247,f51]) ).
fof(f5250,plain,
sF1 = sF3,
inference(forward_demodulation,[],[f5248,f2657]) ).
fof(f5252,plain,
$false,
inference(forward_subsumption_resolution,[],[f5250,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE092+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n010.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 13:10:03 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.46 Running first-order theorem proving
% 0.11/0.46 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
% 9.35/2.10 % (952619)Detected formulas, will run a generic FOF schedule.
% 9.35/2.10 % (952631)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=2697599886:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.35/2.10 % (952636)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1572670927:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.35/2.10 % (952634)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2635411724:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.35/2.10 % (952633)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=4170415488:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.35/2.10 % (952634)Refutation not found, incomplete strategy
% 9.35/2.10 % (952634)------------------------------
% 9.35/2.10 % (952634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952634)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952634)Termination reason: Refutation not found, incomplete strategy
% 9.35/2.10 % (952634)Time elapsed: 0.002 s
% 9.35/2.10 % (952634)Peak memory usage: 88 MB
% 9.35/2.10 % (952632)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=1810644219:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.35/2.10 % (952637)dis-21_1_sil=8000:lcm=predicate:random_seed=3976797324: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)
% 9.35/2.10 % (952635)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2102346133:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.35/2.10 % (952637)Refutation not found, incomplete strategy
% 9.35/2.10 % (952637)------------------------------
% 9.35/2.10 % (952637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952637)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952637)Termination reason: Refutation not found, incomplete strategy
% 9.35/2.10 % (952637)Time elapsed: 0.002 s
% 9.35/2.10 % (952637)Peak memory usage: 88 MB
% 9.35/2.10 % (952637)Instructions burned: 1 (million)
% 9.35/2.10 % (952636)Instruction limit reached!
% 9.35/2.10 % (952636)------------------------------
% 9.35/2.10 % (952636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952636)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952636)Termination reason: Instruction limit
% 9.35/2.10 % (952636)Termination phase: Saturation
% 9.35/2.10 % (952636)Time elapsed: 0.131 s
% 9.35/2.10 % (952636)Peak memory usage: 89 MB
% 9.35/2.10 % (952636)Instructions burned: 140 (million)
% 9.35/2.10 % (952635)Instruction limit reached!
% 9.35/2.10 % (952635)------------------------------
% 9.35/2.10 % (952635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952635)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952635)Termination reason: Instruction limit
% 9.35/2.10 % (952635)Termination phase: Saturation
% 9.35/2.10 % (952635)Time elapsed: 0.113 s
% 9.35/2.10 % (952635)Peak memory usage: 89 MB
% 9.35/2.10 % (952635)Instructions burned: 119 (million)
% 9.35/2.10 % (952649)lrs+10_1_sil=8000:sp=occurrence:random_seed=2053065229:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 9.35/2.10 % (952650)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4016283241:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 9.35/2.10 % (952650)Refutation not found, incomplete strategy
% 9.35/2.10 % (952650)------------------------------
% 9.35/2.10 % (952650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952650)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952650)Termination reason: Refutation not found, incomplete strategy
% 9.35/2.10 % (952650)Time elapsed: 0.002 s
% 9.35/2.10 % (952650)Peak memory usage: 88 MB
% 9.35/2.10 % (952650)Instructions burned: 1 (million)
% 9.35/2.10 % (952634)------------------------------
% 9.35/2.10 % (952634)------------------------------
% 9.35/2.10 % (952637)------------------------------
% 9.35/2.10 % (952637)------------------------------
% 9.35/2.10 % (952649)Instruction limit reached!
% 9.35/2.10 % (952649)------------------------------
% 9.35/2.10 % (952649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952649)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952649)Termination reason: Instruction limit
% 9.35/2.10 % (952649)Termination phase: Saturation
% 9.35/2.10 % (952649)Time elapsed: 0.172 s
% 9.35/2.10 % (952649)Peak memory usage: 91 MB
% 9.35/2.10 % (952649)Instructions burned: 285 (million)
% 9.35/2.10 % (952655)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3746811055:i=325:sd=1:ss=axioms:sgt=32_2994 on theBenchmark for (2994ds/325Mi)
% 9.35/2.10 % (952657)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2559909541:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 9.35/2.10 % (952657)Refutation not found, incomplete strategy
% 9.35/2.10 % (952657)------------------------------
% 9.35/2.10 % (952657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952657)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952657)Termination reason: Refutation not found, incomplete strategy
% 9.35/2.10 % (952657)Time elapsed: 0.001 s
% 9.35/2.10 % (952657)Peak memory usage: 88 MB
% 9.35/2.10 % (952657)Instructions burned: 1 (million)
% 9.35/2.10 % (952656)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=1175086644:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 9.35/2.10 % (952650)------------------------------
% 9.35/2.10 % (952650)------------------------------
% 9.35/2.10 % (952657)------------------------------
% 9.35/2.10 % (952657)------------------------------
% 9.35/2.10 % (952656)Instruction limit reached!
% 9.35/2.10 % (952656)------------------------------
% 9.35/2.10 % (952656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952656)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952656)Termination reason: Instruction limit
% 9.35/2.10 % (952656)Termination phase: Saturation
% 9.35/2.10 % (952656)Time elapsed: 0.149 s
% 9.35/2.10 % (952656)Peak memory usage: 92 MB
% 9.35/2.10 % (952656)Instructions burned: 249 (million)
% 9.35/2.10 % (952655)Instruction limit reached!
% 9.35/2.10 % (952655)------------------------------
% 9.35/2.10 % (952655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952655)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952655)Termination reason: Instruction limit
% 9.35/2.10 % (952655)Termination phase: Saturation
% 9.35/2.10 % (952655)Time elapsed: 0.202 s
% 9.35/2.10 % (952655)Peak memory usage: 92 MB
% 9.35/2.10 % (952655)Instructions burned: 325 (million)
% 9.35/2.10 % (952661)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3969474788:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 9.35/2.10 % (952633)Refutation not found, incomplete strategy
% 9.35/2.10 % (952633)------------------------------
% 9.35/2.10 % (952633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952633)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952633)Termination reason: Refutation not found, incomplete strategy
% 9.35/2.10 % (952633)Time elapsed: 0.739 s
% 9.35/2.10 % (952633)Peak memory usage: 128 MB
% 9.35/2.10 % (952633)Instructions burned: 888 (million)
% 9.35/2.10 % (952662)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2582304689:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 9.35/2.10 % (952662)Refutation not found, incomplete strategy
% 9.35/2.10 % (952662)------------------------------
% 9.35/2.10 % (952662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952662)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952662)Termination reason: Refutation not found, incomplete strategy
% 9.35/2.10 % (952662)Time elapsed: 0.002 s
% 9.35/2.10 % (952662)Peak memory usage: 88 MB
% 9.35/2.10 % (952662)Instructions burned: 1 (million)
% 9.35/2.10 % (952663)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1762249005:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 9.35/2.10 % (952663)Refutation not found, incomplete strategy
% 9.35/2.10 % (952663)------------------------------
% 9.35/2.10 % (952663)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952663)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952663)Termination reason: Refutation not found, incomplete strategy
% 9.35/2.10 % (952663)Time elapsed: 0.001 s
% 9.35/2.10 % (952663)Peak memory usage: 87 MB
% 9.35/2.10 % (952665)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=163986050:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 9.35/2.10 % (952665)Refutation not found, incomplete strategy
% 9.35/2.10 % (952665)------------------------------
% 9.35/2.10 % (952665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.10 % (952665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.10 % (952665)CaDiCaL version: 2.1.3
% 9.35/2.10 % (952665)Termination reason: Refutation not found, incomplete strategy
% 9.35/2.10 % (952665)Time elapsed: 0.001 s
% 9.35/2.10 % (952665)Peak memory usage: 88 MB
% 9.35/2.10 % (952633)------------------------------
% 9.35/2.10 % (952633)------------------------------
% 9.35/2.10 % (952631)First to succeed.
% 9.35/2.10 % (952631)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-952619"
% 9.35/2.10 % (952632)Also succeeded, but the first one will report.
% 9.35/2.10 % (952662)------------------------------
% 9.35/2.10 % (952662)------------------------------
% 9.35/2.10 % (952663)------------------------------
% 9.35/2.10 % (952663)------------------------------
% 9.35/2.10 % (952665)------------------------------
% 9.35/2.10 % (952665)------------------------------
% 9.35/2.10 % (952737)lrs+10_1_sil=8000:sp=occurrence:random_seed=1879788640:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 9.35/2.10 % (952631)Refutation found. Thanks to Tanya!
% 9.35/2.10 % SZS status Theorem for theBenchmark
% 9.35/2.10 % SZS output start Proof for theBenchmark
% See solution above
% 10.12/2.30 % (952631)------------------------------
% 10.12/2.30 % (952631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.30 % (952631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.30 % (952631)CaDiCaL version: 2.1.3
% 10.12/2.30 % (952631)Termination reason: Refutation
% 10.12/2.30 % (952631)Time elapsed: 1.011 s
% 10.12/2.30 % (952631)Peak memory usage: 136 MB
% 10.12/2.30 % (952631)Instructions burned: 1649 (million)
% 10.12/2.30 % (952631)------------------------------
% 10.12/2.30 % (952631)------------------------------
% 10.12/2.30 % (952619)Success in time 1.356 s
% 10.12/2.30 % Vampire exiting
%------------------------------------------------------------------------------