%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE133+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 45 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 6 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 70 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',domain_difference) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
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))))
& ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) )
=> ! [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) ),
file('/export/starexec/sandbox/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))))
& ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) )
=> ! [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
? [X0] :
( ? [X3] : forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) != addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))))
& ! [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))))
& ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f33,plain,
? [X0] :
( ? [X3] : forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) != addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))))
& ! [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))))
& ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f43,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f45,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f47,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f48,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f54,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f61,plain,
! [X2] : forward_diamond(sK0,domain(X2)) = forward_diamond(sK0,forward_diamond(sK0,domain(X2))),
inference(cnf_transformation,[],[f33]) ).
fof(f62,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,[],[f33]) ).
fof(f63,plain,
forward_diamond(star(sK0),domain_difference(domain(sK1),forward_diamond(sK0,domain(sK1)))) != addition(forward_diamond(sK0,domain(sK1)),forward_diamond(star(sK0),domain_difference(domain(sK1),forward_diamond(sK0,domain(sK1))))),
inference(cnf_transformation,[],[f33]) ).
fof(f67,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(antidomain(antidomain(X0)),antidomain(X1)),
inference(definition_unfolding,[],[f54,f48]) ).
fof(f68,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f55,f48,f48]) ).
fof(f72,plain,
antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(sK1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))))))))) != addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(sK1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))))))))))),
inference(definition_unfolding,[],[f63,f68,f67,f48,f68,f48,f68,f48,f68,f67,f48,f68,f48]) ).
fof(f73,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,[],[f62,f68,f67,f48,f68,f48,f48,f68,f67,f48,f68,f48]) ).
fof(f74,plain,
! [X2] : antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X2))))))) = antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X2)))))))))))),
inference(definition_unfolding,[],[f61,f68,f48,f68,f68,f48]) ).
fof(f80,plain,
! [X0] : antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0)))))))))))))) = addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))))))))))),
inference(superposition,[],[f73,f74]) ).
fof(f81,plain,
! [X0] : antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero))))) = addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero)))))),
inference(forward_demodulation,[],[f80,f45]) ).
fof(f82,plain,
! [X0] : antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero))))) = addition(antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero))))),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0)))))))),
inference(forward_demodulation,[],[f81,f34]) ).
fof(f88,plain,
zero = antidomain(one),
inference(superposition,[],[f39,f45]) ).
fof(f97,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f36,f34]) ).
fof(f106,plain,
one = addition(antidomain(zero),zero),
inference(superposition,[],[f47,f88]) ).
fof(f111,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f106,f36]) ).
fof(f143,plain,
! [X0,X1] : addition(antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero))))),addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),X1)) = addition(antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero))))),X1),
inference(superposition,[],[f35,f82]) ).
fof(f157,plain,
! [X0,X1] : addition(antidomain(antidomain(multiplication(star(sK0),antidomain(one)))),addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),X1)) = addition(antidomain(antidomain(multiplication(star(sK0),antidomain(one)))),X1),
inference(forward_demodulation,[],[f143,f111]) ).
fof(f159,plain,
! [X0,X1] : addition(antidomain(antidomain(multiplication(star(sK0),zero))),addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),X1)) = addition(antidomain(antidomain(multiplication(star(sK0),zero))),X1),
inference(forward_demodulation,[],[f157,f88]) ).
fof(f161,plain,
! [X0,X1] : addition(antidomain(antidomain(zero)),addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),X1)) = addition(antidomain(antidomain(zero)),X1),
inference(forward_demodulation,[],[f159,f43]) ).
fof(f162,plain,
! [X0,X1] : addition(antidomain(one),addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),X1)) = addition(antidomain(one),X1),
inference(forward_demodulation,[],[f161,f111]) ).
fof(f163,plain,
! [X0,X1] : addition(zero,X1) = addition(zero,addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),X1)),
inference(forward_demodulation,[],[f162,f88]) ).
fof(f164,plain,
! [X0,X1] : addition(zero,X1) = addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),X1),
inference(forward_demodulation,[],[f163,f97]) ).
fof(f165,plain,
! [X0,X1] : addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))),X1) = X1,
inference(forward_demodulation,[],[f164,f97]) ).
fof(f177,plain,
antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(sK1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))))))))) != antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(sK1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))))))))),
inference(superposition,[],[f72,f165]) ).
fof(f183,plain,
$false,
inference(trivial_inequality_removal,[],[f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE133+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 13:12:16 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48 % (806678)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (806687)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2331223645:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (806687) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-806678-806687"...
% 0.18/0.48 % (806684)% WARNING: option uhcvi not known.
% 0.18/0.48 % (806687)...printing done.
% 0.18/0.48 % (806687)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (806687)------------------------------
% 0.18/0.49 % (806687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (806687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (806687)CaDiCaL version: 2.1.3
% 0.18/0.49 % (806687)Termination reason: Refutation
% 0.18/0.49 % (806687)Time elapsed: 0.008 s
% 0.18/0.49 % (806687)Peak memory usage: 12 MB
% 0.18/0.49 % (806687)Instructions burned: 12 (million)
% 0.18/0.49 % (806678)Success in time 0.041 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------