%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE082+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 : n001.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 11:40:17 AM UTC 2026
% Result : Theorem 10.18s 2.37s
% Output : Refutation 11.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of formulae : 132 ( 128 unt; 0 def)
% Number of atoms : 140 ( 139 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 5 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 225 ( 223 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f18,conjecture,
! [X0,X1] :
( ! [X2] :
( addition(domain(X2),antidomain(X2)) = one
& multiplication(domain(X2),antidomain(X2)) = zero )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( addition(domain(X2),antidomain(X2)) = one
& multiplication(domain(X2),antidomain(X2)) = zero )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( antidomain(multiplication(X0,domain(X1))) != addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1))))
& ! [X2] :
( addition(domain(X2),antidomain(X2)) = one
& multiplication(domain(X2),antidomain(X2)) = zero ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( antidomain(multiplication(sK0,domain(sK1))) != addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,domain(sK1))))
& ! [X2] :
( addition(domain(X2),antidomain(X2)) = one
& multiplication(domain(X2),antidomain(X2)) = zero ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f22,plain,
! [X2] : zero = multiplication(domain(X2),antidomain(X2)),
inference(cnf_transformation,[],[f21]) ).
fof(f23,plain,
! [X2] : one = addition(domain(X2),antidomain(X2)),
inference(cnf_transformation,[],[f21]) ).
fof(f24,plain,
antidomain(multiplication(sK0,domain(sK1))) != addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,domain(sK1)))),
inference(cnf_transformation,[],[f21]) ).
fof(f25,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f26,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
zero = domain(zero),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f31,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f36,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f37,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f42,plain,
! [X0,X1] : multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(superposition,[],[f33,f32]) ).
fof(f44,plain,
! [X0,X1] : one = addition(domain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(superposition,[],[f23,f32]) ).
fof(f48,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f34,f36]) ).
fof(f51,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),antidomain(X1)) = addition(multiplication(X0,antidomain(X1)),zero),
inference(superposition,[],[f34,f22]) ).
fof(f56,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),antidomain(X1)) = multiplication(X0,antidomain(X1)),
inference(forward_demodulation,[],[f51,f31]) ).
fof(f61,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = addition(multiplication(domain(X0),X1),zero),
inference(superposition,[],[f35,f22]) ).
fof(f70,plain,
! [X0,X1] : multiplication(domain(X0),X1) = multiplication(domain(X0),addition(X1,antidomain(X0))),
inference(forward_demodulation,[],[f61,f31]) ).
fof(f74,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f35,f37]) ).
fof(f87,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(superposition,[],[f56,f27]) ).
fof(f100,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = multiplication(zero,X1),
inference(superposition,[],[f38,f22]) ).
fof(f105,plain,
! [X2,X3,X0,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))),
inference(superposition,[],[f34,f38]) ).
fof(f111,plain,
! [X0,X1] : zero = multiplication(domain(X0),multiplication(antidomain(X0),X1)),
inference(forward_demodulation,[],[f100,f29]) ).
fof(f228,plain,
! [X0,X1] : addition(multiplication(domain(X0),X0),X1) = addition(X0,addition(multiplication(domain(X0),X0),X1)),
inference(superposition,[],[f26,f33]) ).
fof(f233,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f26,f35]) ).
fof(f267,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,addition(X3,X2)),multiplication(X1,X2)) = addition(multiplication(X0,X3),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f233,f34]) ).
fof(f330,plain,
! [X2,X0,X1] : addition(multiplication(X0,domain(X1)),multiplication(addition(X0,X2),antidomain(X1))) = addition(multiplication(X0,one),multiplication(X2,antidomain(X1))),
inference(superposition,[],[f267,f23]) ).
fof(f363,plain,
! [X2,X0,X1] : addition(multiplication(domain(X0),addition(X1,X2)),multiplication(antidomain(X0),X2)) = addition(multiplication(domain(X0),X1),multiplication(one,X2)),
inference(superposition,[],[f267,f23]) ).
fof(f393,plain,
! [X2,X0,X1] : addition(multiplication(domain(X0),X1),X2) = addition(multiplication(domain(X0),addition(X1,X2)),multiplication(antidomain(X0),X2)),
inference(forward_demodulation,[],[f363,f36]) ).
fof(f418,plain,
! [X2,X0,X1] : addition(multiplication(X0,domain(X1)),multiplication(addition(X0,X2),antidomain(X1))) = addition(X0,multiplication(X2,antidomain(X1))),
inference(forward_demodulation,[],[f330,f37]) ).
fof(f431,plain,
! [X2,X0,X1] : addition(multiplication(domain(X0),X1),X2) = addition(multiplication(antidomain(X0),X2),multiplication(domain(X0),addition(X1,X2))),
inference(forward_demodulation,[],[f393,f27]) ).
fof(f475,plain,
! [X0,X1] : addition(X0,multiplication(X0,antidomain(X1))) = addition(multiplication(X0,domain(X1)),multiplication(X0,antidomain(X1))),
inference(superposition,[],[f418,f25]) ).
fof(f519,plain,
! [X0,X1] : multiplication(X0,addition(domain(X1),antidomain(X1))) = addition(X0,multiplication(X0,antidomain(X1))),
inference(forward_demodulation,[],[f475,f35]) ).
fof(f533,plain,
! [X0,X1] : multiplication(X0,addition(domain(X1),antidomain(X1))) = multiplication(X0,addition(one,antidomain(X1))),
inference(forward_demodulation,[],[f519,f74]) ).
fof(f541,plain,
! [X0,X1] : multiplication(X0,one) = multiplication(X0,addition(one,antidomain(X1))),
inference(forward_demodulation,[],[f533,f23]) ).
fof(f547,plain,
! [X0,X1] : multiplication(X0,addition(one,antidomain(X1))) = X0,
inference(forward_demodulation,[],[f541,f37]) ).
fof(f556,plain,
! [X0,X1] : addition(multiplication(domain(X1),X0),X0) = addition(multiplication(antidomain(X1),X0),multiplication(domain(X1),X0)),
inference(superposition,[],[f431,f25]) ).
fof(f594,plain,
! [X0,X1] : addition(multiplication(domain(X1),X0),X0) = multiplication(addition(antidomain(X1),domain(X1)),X0),
inference(forward_demodulation,[],[f556,f34]) ).
fof(f605,plain,
! [X0,X1] : addition(multiplication(domain(X1),X0),X0) = multiplication(addition(domain(X1),antidomain(X1)),X0),
inference(forward_demodulation,[],[f594,f27]) ).
fof(f613,plain,
! [X0,X1] : multiplication(one,X0) = addition(multiplication(domain(X1),X0),X0),
inference(forward_demodulation,[],[f605,f23]) ).
fof(f618,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(domain(X1),X0)),
inference(forward_demodulation,[],[f613,f27]) ).
fof(f623,plain,
! [X0,X1] : multiplication(one,X0) = multiplication(addition(one,domain(X1)),X0),
inference(forward_demodulation,[],[f618,f48]) ).
fof(f627,plain,
! [X0,X1] : multiplication(addition(one,domain(X1)),X0) = X0,
inference(forward_demodulation,[],[f623,f36]) ).
fof(f634,plain,
! [X0] : one = addition(one,domain(X0)),
inference(superposition,[],[f27,f39]) ).
fof(f635,plain,
! [X2,X0,X1] : addition(multiplication(domain(X0),X1),multiplication(one,X2)) = addition(multiplication(domain(X0),addition(X1,X2)),multiplication(one,X2)),
inference(superposition,[],[f267,f39]) ).
fof(f637,plain,
! [X0,X1] : addition(multiplication(domain(X0),domain(X1)),multiplication(one,antidomain(X1))) = addition(domain(X0),multiplication(one,antidomain(X1))),
inference(superposition,[],[f418,f39]) ).
fof(f640,plain,
! [X0,X1] : addition(multiplication(domain(X0),domain(X1)),antidomain(X1)) = addition(domain(X0),antidomain(X1)),
inference(forward_demodulation,[],[f637,f36]) ).
fof(f642,plain,
! [X2,X0,X1] : addition(multiplication(domain(X0),X1),multiplication(one,X2)) = addition(multiplication(one,X2),multiplication(domain(X0),addition(X1,X2))),
inference(forward_demodulation,[],[f635,f27]) ).
fof(f645,plain,
! [X0,X1] : addition(antidomain(X1),multiplication(domain(X0),domain(X1))) = addition(domain(X0),antidomain(X1)),
inference(forward_demodulation,[],[f640,f27]) ).
fof(f647,plain,
! [X2,X0,X1] : addition(multiplication(domain(X0),X1),X2) = addition(X2,multiplication(domain(X0),addition(X1,X2))),
inference(forward_demodulation,[],[f642,f36]) ).
fof(f679,plain,
! [X2,X0,X1] : addition(multiplication(domain(X0),X1),zero) = multiplication(domain(X0),addition(X1,multiplication(antidomain(X0),X2))),
inference(superposition,[],[f35,f111]) ).
fof(f694,plain,
! [X2,X0,X1] : multiplication(domain(X0),X1) = multiplication(domain(X0),addition(X1,multiplication(antidomain(X0),X2))),
inference(forward_demodulation,[],[f679,f31]) ).
fof(f759,plain,
! [X2,X0,X1] : addition(multiplication(domain(X2),X1),X0) = addition(X0,multiplication(domain(X2),addition(X0,X1))),
inference(superposition,[],[f647,f27]) ).
fof(f773,plain,
! [X0,X1] : addition(multiplication(domain(X0),domain(X1)),antidomain(X1)) = addition(antidomain(X1),multiplication(domain(X0),one)),
inference(superposition,[],[f647,f23]) ).
fof(f802,plain,
! [X0,X1] : addition(multiplication(domain(X0),domain(X1)),antidomain(X1)) = addition(antidomain(X1),domain(X0)),
inference(forward_demodulation,[],[f773,f37]) ).
fof(f812,plain,
! [X0,X1] : addition(antidomain(X1),multiplication(domain(X0),domain(X1))) = addition(antidomain(X1),domain(X0)),
inference(forward_demodulation,[],[f802,f27]) ).
fof(f1091,plain,
! [X0,X1] : addition(one,X1) = addition(one,addition(domain(X0),X1)),
inference(superposition,[],[f26,f634]) ).
fof(f1156,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))) = multiplication(one,antidomain(multiplication(X0,X1))),
inference(superposition,[],[f87,f44]) ).
fof(f1192,plain,
! [X0,X1] : antidomain(multiplication(X0,X1)) = multiplication(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[],[f1156,f36]) ).
fof(f1222,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(multiplication(one,domain(X0))),antidomain(X0)),
inference(superposition,[],[f1192,f36]) ).
fof(f1255,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[],[f1222,f36]) ).
fof(f1312,plain,
! [X0] : multiplication(antidomain(domain(X0)),addition(one,antidomain(X0))) = addition(antidomain(domain(X0)),antidomain(X0)),
inference(superposition,[],[f74,f1255]) ).
fof(f1320,plain,
! [X0] : multiplication(antidomain(domain(X0)),addition(one,antidomain(X0))) = addition(antidomain(X0),antidomain(domain(X0))),
inference(forward_demodulation,[],[f1312,f27]) ).
fof(f1327,plain,
! [X0] : antidomain(domain(X0)) = addition(antidomain(X0),antidomain(domain(X0))),
inference(forward_demodulation,[],[f1320,f547]) ).
fof(f1334,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(X0,multiplication(addition(domain(X0),X1),X0)),
inference(superposition,[],[f228,f34]) ).
fof(f1335,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(X0,multiplication(domain(X0),addition(X0,X1))),
inference(superposition,[],[f228,f35]) ).
fof(f1372,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(multiplication(domain(X0),X1),X0),
inference(forward_demodulation,[],[f1335,f759]) ).
fof(f1373,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = multiplication(addition(one,addition(domain(X0),X1)),X0),
inference(forward_demodulation,[],[f1334,f48]) ).
fof(f1383,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(X0,multiplication(domain(X0),X1)),
inference(forward_demodulation,[],[f1372,f27]) ).
fof(f1384,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = multiplication(addition(domain(X0),X1),X0),
inference(forward_demodulation,[],[f1373,f1091]) ).
fof(f1401,plain,
! [X0,X1] : addition(X0,zero) = multiplication(domain(X0),addition(X0,multiplication(antidomain(X0),X1))),
inference(superposition,[],[f1383,f111]) ).
fof(f1430,plain,
! [X0] : addition(antidomain(X0),domain(antidomain(X0))) = multiplication(domain(antidomain(X0)),addition(antidomain(X0),domain(X0))),
inference(superposition,[],[f812,f1383]) ).
fof(f1434,plain,
! [X0] : addition(antidomain(X0),domain(antidomain(X0))) = multiplication(domain(antidomain(X0)),addition(domain(X0),antidomain(X0))),
inference(forward_demodulation,[],[f1430,f27]) ).
fof(f1454,plain,
! [X0] : addition(X0,zero) = multiplication(domain(X0),X0),
inference(forward_demodulation,[],[f1401,f694]) ).
fof(f1461,plain,
! [X0] : addition(antidomain(X0),domain(antidomain(X0))) = multiplication(domain(antidomain(X0)),one),
inference(forward_demodulation,[],[f1434,f23]) ).
fof(f1472,plain,
! [X0] : multiplication(domain(X0),X0) = X0,
inference(forward_demodulation,[],[f1454,f31]) ).
fof(f1476,plain,
! [X0] : domain(antidomain(X0)) = addition(antidomain(X0),domain(antidomain(X0))),
inference(forward_demodulation,[],[f1461,f37]) ).
fof(f1508,plain,
one = domain(one),
inference(superposition,[],[f37,f1472]) ).
fof(f1563,plain,
! [X0] : addition(one,antidomain(X0)) = addition(antidomain(X0),multiplication(one,domain(X0))),
inference(superposition,[],[f645,f1508]) ).
fof(f1575,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f1563,f36]) ).
fof(f1588,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f1575,f27]) ).
fof(f1594,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f1588,f23]) ).
fof(f1920,plain,
! [X0] : multiplication(domain(zero),multiplication(domain(X0),domain(antidomain(X0)))) = addition(multiplication(domain(X0),domain(antidomain(X0))),multiplication(domain(zero),multiplication(domain(X0),domain(antidomain(X0))))),
inference(superposition,[],[f42,f22]) ).
fof(f1974,plain,
! [X0] : multiplication(domain(zero),multiplication(domain(X0),domain(antidomain(X0)))) = multiplication(addition(domain(X0),multiplication(domain(zero),domain(X0))),domain(antidomain(X0))),
inference(forward_demodulation,[],[f1920,f105]) ).
fof(f2008,plain,
! [X0] : multiplication(domain(zero),multiplication(domain(X0),domain(antidomain(X0)))) = multiplication(multiplication(addition(one,domain(zero)),domain(X0)),domain(antidomain(X0))),
inference(forward_demodulation,[],[f1974,f48]) ).
fof(f2039,plain,
! [X0] : multiplication(domain(zero),multiplication(domain(X0),domain(antidomain(X0)))) = multiplication(addition(one,domain(zero)),multiplication(domain(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[],[f2008,f38]) ).
fof(f2068,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = multiplication(domain(zero),multiplication(domain(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[],[f2039,f627]) ).
fof(f2089,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = multiplication(zero,multiplication(domain(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[],[f2068,f28]) ).
fof(f2103,plain,
! [X0] : zero = multiplication(domain(X0),domain(antidomain(X0))),
inference(forward_demodulation,[],[f2089,f29]) ).
fof(f2227,plain,
! [X0] : addition(antidomain(antidomain(X0)),zero) = addition(domain(X0),antidomain(antidomain(X0))),
inference(superposition,[],[f645,f2103]) ).
fof(f2270,plain,
! [X0] : antidomain(antidomain(X0)) = addition(domain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f2227,f31]) ).
fof(f2299,plain,
! [X0] : multiplication(addition(one,antidomain(antidomain(X0))),X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(superposition,[],[f1384,f2270]) ).
fof(f2300,plain,
! [X0] : multiplication(domain(antidomain(X0)),domain(X0)) = multiplication(domain(antidomain(X0)),antidomain(antidomain(X0))),
inference(superposition,[],[f70,f2270]) ).
fof(f2313,plain,
! [X0] : zero = multiplication(domain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[],[f2300,f22]) ).
fof(f2314,plain,
! [X0] : multiplication(one,X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(forward_demodulation,[],[f2299,f1594]) ).
fof(f2320,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f2314,f36]) ).
fof(f2331,plain,
! [X0] : zero = multiplication(domain(antidomain(X0)),X0),
inference(superposition,[],[f111,f2320]) ).
fof(f2384,plain,
! [X0] : addition(antidomain(X0),zero) = addition(antidomain(X0),domain(antidomain(X0))),
inference(superposition,[],[f812,f2313]) ).
fof(f2429,plain,
! [X0] : addition(antidomain(X0),zero) = domain(antidomain(X0)),
inference(forward_demodulation,[],[f2384,f1476]) ).
fof(f2443,plain,
! [X0] : antidomain(X0) = domain(antidomain(X0)),
inference(forward_demodulation,[],[f2429,f31]) ).
fof(f2625,plain,
! [X0] : addition(antidomain(X0),zero) = addition(antidomain(X0),domain(antidomain(domain(X0)))),
inference(superposition,[],[f812,f2331]) ).
fof(f2671,plain,
! [X0] : addition(antidomain(X0),zero) = addition(antidomain(X0),antidomain(domain(X0))),
inference(forward_demodulation,[],[f2625,f2443]) ).
fof(f2695,plain,
! [X0] : addition(antidomain(X0),zero) = antidomain(domain(X0)),
inference(forward_demodulation,[],[f2671,f1327]) ).
fof(f2705,plain,
! [X0] : antidomain(X0) = antidomain(domain(X0)),
inference(forward_demodulation,[],[f2695,f31]) ).
fof(f2714,plain,
! [X0,X1] : antidomain(multiplication(X0,domain(X1))) = antidomain(domain(multiplication(X0,X1))),
inference(superposition,[],[f2705,f32]) ).
fof(f2758,plain,
! [X0,X1] : antidomain(multiplication(X0,X1)) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[],[f2714,f2705]) ).
fof(f2773,plain,
antidomain(multiplication(sK0,sK1)) != addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,sK1))),
inference(superposition,[],[f24,f2758]) ).
fof(f2822,plain,
$false,
inference(forward_subsumption_resolution,[],[f2773,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE082+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 13:15:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 10.18/2.37 % (3559420)Detected formulas, will run a generic FOF schedule.
% 10.18/2.37 % (3559446)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2662290082:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.18/2.37 % (3559443)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=3153670737:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.18/2.37 % (3559444)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1369958662:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.18/2.37 % (3559441)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=3355220266:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.18/2.37 % (3559442)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=1922057265:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.18/2.37 % (3559446)Instruction limit reached!
% 10.18/2.37 % (3559446)------------------------------
% 10.18/2.37 % (3559446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559446)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559446)Termination reason: Instruction limit
% 10.18/2.37 % (3559446)Termination phase: Saturation
% 10.18/2.37 % (3559446)Time elapsed: 0.043 s
% 10.18/2.37 % (3559446)Peak memory usage: 89 MB
% 10.18/2.37 % (3559446)Instructions burned: 141 (million)
% 10.18/2.37 % (3559447)dis-21_1_sil=8000:lcm=predicate:random_seed=2292775420: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)
% 10.18/2.37 % (3559447)Refutation not found, incomplete strategy
% 10.18/2.37 % (3559447)------------------------------
% 10.18/2.37 % (3559447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559447)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559447)Termination reason: Refutation not found, incomplete strategy
% 10.18/2.37 % (3559447)Time elapsed: 0.002 s
% 10.18/2.37 % (3559447)Peak memory usage: 88 MB
% 10.18/2.37 % (3559447)Instructions burned: 1 (million)
% 10.18/2.37 % (3559445)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1410990744:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.18/2.37 % (3559444)Instruction limit reached!
% 10.18/2.37 % (3559444)------------------------------
% 10.18/2.37 % (3559444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559444)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559444)Termination reason: Instruction limit
% 10.18/2.37 % (3559444)Termination phase: Saturation
% 10.18/2.37 % (3559444)Time elapsed: 0.066 s
% 10.18/2.37 % (3559444)Peak memory usage: 89 MB
% 10.18/2.37 % (3559444)Instructions burned: 109 (million)
% 10.18/2.37 % (3559445)Instruction limit reached!
% 10.18/2.37 % (3559445)------------------------------
% 10.18/2.37 % (3559445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559445)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559445)Termination reason: Instruction limit
% 10.18/2.37 % (3559445)Termination phase: Saturation
% 10.18/2.37 % (3559445)Time elapsed: 0.071 s
% 10.18/2.37 % (3559445)Peak memory usage: 89 MB
% 10.18/2.37 % (3559445)Instructions burned: 119 (million)
% 10.18/2.37 % (3559454)lrs+10_1_sil=8000:sp=occurrence:random_seed=983523391:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.18/2.37 % (3559454)Instruction limit reached!
% 10.18/2.37 % (3559454)------------------------------
% 10.18/2.37 % (3559454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559454)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559454)Termination reason: Instruction limit
% 10.18/2.37 % (3559454)Termination phase: Saturation
% 10.18/2.37 % (3559454)Time elapsed: 0.135 s
% 10.18/2.37 % (3559454)Peak memory usage: 91 MB
% 10.18/2.37 % (3559454)Instructions burned: 285 (million)
% 10.18/2.37 % (3559456)lrs+10_1_sil=32000:urr=on:br=off:random_seed=14103206:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.18/2.37 % (3559447)------------------------------
% 10.18/2.37 % (3559447)------------------------------
% 10.18/2.37 % (3559457)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3196078858:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.18/2.37 % (3559456)Instruction limit reached!
% 10.18/2.37 % (3559456)------------------------------
% 10.18/2.37 % (3559456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559456)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559456)Termination reason: Instruction limit
% 10.18/2.37 % (3559456)Termination phase: Saturation
% 10.18/2.37 % (3559456)Time elapsed: 0.158 s
% 10.18/2.37 % (3559456)Peak memory usage: 90 MB
% 10.18/2.37 % (3559456)Instructions burned: 157 (million)
% 10.18/2.37 % (3559469)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=2845075166:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 10.18/2.37 % (3559475)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2118835154:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 10.18/2.37 % (3559469)Instruction limit reached!
% 10.18/2.37 % (3559469)------------------------------
% 10.18/2.37 % (3559469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559469)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559469)Termination reason: Instruction limit
% 10.18/2.37 % (3559469)Termination phase: Saturation
% 10.18/2.37 % (3559469)Time elapsed: 0.118 s
% 10.18/2.37 % (3559469)Peak memory usage: 92 MB
% 10.18/2.37 % (3559469)Instructions burned: 248 (million)
% 10.18/2.37 % (3559457)Instruction limit reached!
% 10.18/2.37 % (3559457)------------------------------
% 10.18/2.37 % (3559457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559457)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559457)Termination reason: Instruction limit
% 10.18/2.37 % (3559457)Termination phase: Saturation
% 10.18/2.37 % (3559457)Time elapsed: 0.330 s
% 10.18/2.37 % (3559457)Peak memory usage: 92 MB
% 10.18/2.37 % (3559457)Instructions burned: 326 (million)
% 10.18/2.37 % (3559478)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=858826022:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 10.18/2.37 % (3559475)Instruction limit reached!
% 10.18/2.37 % (3559475)------------------------------
% 10.18/2.37 % (3559475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559475)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559475)Termination reason: Instruction limit
% 10.18/2.37 % (3559475)Termination phase: Saturation
% 10.18/2.37 % (3559475)Time elapsed: 0.228 s
% 10.18/2.37 % (3559475)Peak memory usage: 91 MB
% 10.18/2.37 % (3559475)Instructions burned: 294 (million)
% 10.18/2.37 % (3559482)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=324029885:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 10.18/2.37 % (3559486)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2024104283:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 10.18/2.37 % (3559486)Refutation not found, incomplete strategy
% 10.18/2.37 % (3559486)------------------------------
% 10.18/2.37 % (3559486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559486)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559486)Termination reason: Refutation not found, incomplete strategy
% 10.18/2.37 % (3559486)Time elapsed: 0.001 s
% 10.18/2.37 % (3559486)Peak memory usage: 87 MB
% 10.18/2.37 % (3559482)Instruction limit reached!
% 10.18/2.37 % (3559482)------------------------------
% 10.18/2.37 % (3559482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559482)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559482)Termination reason: Instruction limit
% 10.18/2.37 % (3559482)Termination phase: Saturation
% 10.18/2.37 % (3559482)Time elapsed: 0.072 s
% 10.18/2.37 % (3559482)Peak memory usage: 90 MB
% 10.18/2.37 % (3559482)Instructions burned: 114 (million)
% 10.18/2.37 % (3559488)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1864091763:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 10.18/2.37 % (3559488)Instruction limit reached!
% 10.18/2.37 % (3559488)------------------------------
% 10.18/2.37 % (3559488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.18/2.37 % (3559488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.18/2.37 % (3559488)CaDiCaL version: 2.1.3
% 10.18/2.37 % (3559488)Termination reason: Instruction limit
% 10.18/2.37 % (3559488)Termination phase: Saturation
% 10.18/2.37 % (3559488)Time elapsed: 0.066 s
% 10.18/2.37 % (3559488)Peak memory usage: 89 MB
% 10.18/2.37 % (3559488)Instructions burned: 115 (million)
% 10.18/2.37 % (3559491)lrs+10_1_sil=8000:sp=occurrence:random_seed=4086947245:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2989 on theBenchmark for (2989ds/907Mi)
% 10.18/2.37 % (3559442)First to succeed.
% 10.18/2.37 % (3559442)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3559420"
% 10.18/2.37 % (3559486)------------------------------
% 10.18/2.37 % (3559486)------------------------------
% 10.18/2.37 % (3559478)Also succeeded, but the first one will report.
% 10.18/2.37 % (3559495)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4185048643:i=437:sd=1:aac=none:ss=included_2987 on theBenchmark for (2987ds/437Mi)
% 10.18/2.37 % (3559496)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1873828206:i=5202:ss=axioms:sgt=16_2987 on theBenchmark for (2987ds/5202Mi)
% 10.18/2.37 % (3559442)Refutation found. Thanks to Tanya!
% 10.18/2.37 % SZS status Theorem for theBenchmark
% 10.18/2.37 % SZS output start Proof for theBenchmark
% See solution above
% 11.26/2.57 % (3559442)------------------------------
% 11.26/2.57 % (3559442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.26/2.57 % (3559442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.26/2.57 % (3559442)CaDiCaL version: 2.1.3
% 11.26/2.57 % (3559442)Termination reason: Refutation
% 11.26/2.57 % (3559442)Time elapsed: 1.089 s
% 11.26/2.57 % (3559442)Peak memory usage: 132 MB
% 11.26/2.57 % (3559442)Instructions burned: 1320 (million)
% 11.26/2.57 % (3559442)------------------------------
% 11.26/2.57 % (3559442)------------------------------
% 11.26/2.57 % (3559420)Success in time 1.514 s
% 11.26/2.57 % Vampire exiting
%------------------------------------------------------------------------------