%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE131+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 11:40:56 AM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 41 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 40 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',domain_difference) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+7.ax',divergence1) ).
fof(f29,conjecture,
! [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> divergence(X0) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> divergence(X0) = zero ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
? [X0] :
( zero != divergence(X0)
& ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) ),
inference(ennf_transformation,[],[f30]) ).
fof(f33,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f44,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f46,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f47,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f53,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[],[f22]) ).
fof(f54,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f58,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f60,plain,
! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))),
inference(cnf_transformation,[],[f32]) ).
fof(f61,plain,
zero != divergence(sK0),
inference(cnf_transformation,[],[f32]) ).
fof(f65,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(antidomain(antidomain(X0)),antidomain(X1)),
inference(definition_unfolding,[],[f53,f47]) ).
fof(f66,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f54,f47,f47]) ).
fof(f68,plain,
! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
inference(definition_unfolding,[],[f58,f66]) ).
fof(f70,plain,
! [X1] : antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1)))))))))))))) = addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))),
inference(definition_unfolding,[],[f60,f66,f65,f47,f66,f47,f47,f66,f65,f47,f66,f47]) ).
fof(f72,plain,
zero = antidomain(one),
inference(superposition,[],[f38,f44]) ).
fof(f80,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f35,f33]) ).
fof(f82,plain,
one = addition(antidomain(zero),zero),
inference(superposition,[],[f46,f72]) ).
fof(f87,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f82,f35]) ).
fof(f161,plain,
! [X0] : antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(X0))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0))))))))))))) = addition(divergence(X0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(X0))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))))))))))),
inference(superposition,[],[f70,f68]) ).
fof(f527,plain,
antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(sK0))),antidomain(divergence(sK0)))))))) = addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(sK0))),antidomain(divergence(sK0))))))))),
inference(superposition,[],[f161,f68]) ).
fof(f529,plain,
antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero))))) = addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero)))))),
inference(forward_demodulation,[],[f527,f44]) ).
fof(f530,plain,
antidomain(antidomain(multiplication(star(sK0),antidomain(one)))) = addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(one))))),
inference(forward_demodulation,[],[f529,f87]) ).
fof(f531,plain,
antidomain(antidomain(multiplication(star(sK0),zero))) = addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),zero)))),
inference(forward_demodulation,[],[f530,f72]) ).
fof(f532,plain,
antidomain(antidomain(zero)) = addition(divergence(sK0),antidomain(antidomain(zero))),
inference(forward_demodulation,[],[f531,f42]) ).
fof(f533,plain,
antidomain(one) = addition(divergence(sK0),antidomain(one)),
inference(forward_demodulation,[],[f532,f87]) ).
fof(f534,plain,
antidomain(one) = addition(antidomain(one),divergence(sK0)),
inference(forward_demodulation,[],[f533,f33]) ).
fof(f535,plain,
zero = addition(zero,divergence(sK0)),
inference(forward_demodulation,[],[f534,f72]) ).
fof(f536,plain,
zero = divergence(sK0),
inference(forward_demodulation,[],[f535,f80]) ).
fof(f537,plain,
$false,
inference(forward_subsumption_resolution,[],[f536,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE131+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:11:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.46 % (2967666)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (2967675)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=427311334:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (2967672)% WARNING: option uhcvi not known.
% 0.11/0.46 % (2967671)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1187380631_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (2967672)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=297640202:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (2967673)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=387640802:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (2967674)dis+10_1_sil=32000:sp=arity:random_seed=2650248572:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (2967677)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4147976910:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (2967676)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=409682450:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (2967675) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2967666-2967675"...
% 0.11/0.46 % (2967675)...printing done.
% 0.11/0.46 % (2967675)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (2967675)------------------------------
% 0.11/0.46 % (2967675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (2967675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (2967675)CaDiCaL version: 2.1.3
% 0.11/0.46 % (2967675)Termination reason: Refutation
% 0.11/0.46 % (2967675)Time elapsed: 0.010 s
% 0.11/0.46 % (2967675)Peak memory usage: 12 MB
% 0.11/0.46 % (2967675)Instructions burned: 28 (million)
% 0.11/0.46 % (2967666)Success in time 0.039 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------