%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE129+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 11:40:24 AM UTC 2026
% Result : Theorem 3.50s 1.45s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 16 unt; 1 def)
% Number of atoms : 36 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 6 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).
fof(f29,conjecture,
! [X0] :
( ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero )
=> divergence(X0) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero )
=> divergence(X0) = zero ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
? [X0] :
( zero != divergence(X0)
& ! [X1] :
( domain(X1) = zero
| forward_diamond(X0,domain(X1)) != addition(domain(X1),forward_diamond(X0,domain(X1))) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f32,plain,
( zero != divergence(sK0)
& ! [X1] :
( domain(X1) = zero
| forward_diamond(sK0,domain(X1)) != addition(domain(X1),forward_diamond(sK0,domain(X1))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f31]) ).
fof(f33,plain,
! [X1] :
( zero = domain(X1)
| forward_diamond(sK0,domain(X1)) != addition(domain(X1),forward_diamond(sK0,domain(X1))) ),
inference(cnf_transformation,[],[f32]) ).
fof(f34,plain,
zero != divergence(sK0),
inference(cnf_transformation,[],[f32]) ).
fof(f37,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f44,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f45,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f45,f44,f44]) ).
fof(f48,plain,
! [X1] :
( antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))) != addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))))
| zero = antidomain(antidomain(X1)) ),
inference(definition_unfolding,[],[f33,f44,f47,f44,f44,f47,f44]) ).
fof(f49,plain,
! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
inference(definition_unfolding,[],[f46,f47]) ).
fof(f50,definition,
~ sP1(zero),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
fof(f51,plain,
sP1(divergence(sK0)),
inference(inequality_splitting,[],[f34,f50]) ).
fof(f58,plain,
! [X0] :
( antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))) != addition(divergence(X0),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))))
| zero = divergence(X0) ),
inference(superposition,[],[f48,f49]) ).
fof(f61,plain,
( divergence(sK0) != addition(divergence(sK0),divergence(sK0))
| zero = divergence(sK0) ),
inference(superposition,[],[f58,f49]) ).
fof(f62,plain,
zero = divergence(sK0),
inference(forward_subsumption_resolution,[],[f61,f37]) ).
fof(f63,plain,
sP1(zero),
inference(superposition,[],[f51,f62]) ).
fof(f67,plain,
$false,
inference(forward_subsumption_resolution,[],[f63,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE129+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n017.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 13:07:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.50/1.45 % (2539591)Detected formulas, will run a generic FOF schedule.
% 3.50/1.45 % (2539602)dis-21_1_sil=8000:lcm=predicate:random_seed=2399817861: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)
% 3.50/1.45 % (2539602)Refutation not found, incomplete strategy
% 3.50/1.45 % (2539602)------------------------------
% 3.50/1.45 % (2539602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.45 % (2539602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.45 % (2539602)CaDiCaL version: 2.1.3
% 3.50/1.45 % (2539602)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.45 % (2539602)Time elapsed: 0.001 s
% 3.50/1.45 % (2539602)Peak memory usage: 88 MB
% 3.50/1.45 % (2539602)Instructions burned: 2 (million)
% 3.50/1.45 % (2539600)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3998767416:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.50/1.45 % (2539596)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=747727587:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.50/1.45 % (2539599)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=288396438:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.50/1.45 % (2539597)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=3811425033:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.50/1.45 % (2539598)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=2767764133:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.50/1.45 % (2539599)First to succeed.
% 3.50/1.45 % (2539600)Also succeeded, but the first one will report.
% 3.50/1.45 % (2539599)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2539591"
% 3.50/1.45 % (2539601)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3073759798:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.50/1.45 % (2539601)Also succeeded, but the first one will report.
% 3.50/1.45 % (2539602)------------------------------
% 3.50/1.45 % (2539602)------------------------------
% 3.50/1.45 % (2539610)lrs+10_1_sil=8000:sp=occurrence:random_seed=1641199140:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.50/1.45 % (2539610)Also succeeded, but the first one will report.
% 3.50/1.45 % (2539599)Refutation found. Thanks to Tanya!
% 3.50/1.45 % SZS status Theorem for theBenchmark
% 3.50/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.45 % (2539599)------------------------------
% 3.50/1.45 % (2539599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.45 % (2539599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.45 % (2539599)CaDiCaL version: 2.1.3
% 3.50/1.45 % (2539599)Termination reason: Refutation
% 3.50/1.45 % (2539599)Time elapsed: 0.003 s
% 3.50/1.45 % (2539599)Peak memory usage: 89 MB
% 3.50/1.45 % (2539599)Instructions burned: 2 (million)
% 3.50/1.45 % (2539599)------------------------------
% 3.50/1.45 % (2539599)------------------------------
% 3.50/1.45 % (2539591)Success in time 0.415 s
% 3.50/1.45 % Vampire exiting
%------------------------------------------------------------------------------