%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE129+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 : n009.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 0.33s 0.60s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 5 |; 1 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 21 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
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(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero )
=> divergence(X0) = zero ),
file('/export/starexec/sandbox2/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(f32,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(f36,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f47,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
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(sK0,domain(X1)) != addition(domain(X1),forward_diamond(sK0,domain(X1)))
| zero = domain(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f61,plain,
zero != divergence(sK0),
inference(cnf_transformation,[],[f32]) ).
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(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,[],[f60,f66,f47,f47,f66,f47,f47]) ).
fof(f160,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,[],[f70,f68]) ).
fof(f167,plain,
( divergence(sK0) != addition(divergence(sK0),divergence(sK0))
| zero = divergence(sK0) ),
inference(superposition,[],[f160,f68]) ).
fof(f168,plain,
zero = divergence(sK0),
inference(forward_subsumption_resolution,[],[f167,f36]) ).
fof(f169,plain,
$false,
inference(forward_subsumption_resolution,[],[f168,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE129+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.22/0.48 % Computer : n009.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sun Sep 27 13:11:45 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.27/0.54 Running first-order model finding
% 0.27/0.55 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
% 0.33/0.60 % (2027401)Will run a generic schedule for satisfiability detection.
% 0.33/0.60 % (2027410)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2230242970:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/0.60 % (2027410) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2027401-2027410"...
% 0.33/0.60 % (2027410)...printing done.
% 0.33/0.60 % (2027410)Refutation found. Thanks to Tanya!
% 0.33/0.60 % SZS status Theorem for theBenchmark
% 0.33/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.61 % (2027410)------------------------------
% 0.33/0.61 % (2027410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.61 % (2027410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.61 % (2027410)CaDiCaL version: 2.1.3
% 0.33/0.61 % (2027410)Termination reason: Refutation
% 0.33/0.61 % (2027410)Time elapsed: 0.005 s
% 0.33/0.61 % (2027410)Peak memory usage: 12 MB
% 0.33/0.61 % (2027410)Instructions burned: 7 (million)
% 0.33/0.61 % (2027401)Success in time 0.043 s
% 0.33/0.61 % Vampire exiting
%------------------------------------------------------------------------------